libMesh::FELagrangeVec< Dim > Class Template Reference

FELagrangeVec objects are used for working with vector-valued finite elements. More...

#include <fe.h>

Inheritance diagram for libMesh::FELagrangeVec< Dim >:

Public Types
typedef FEGenericBase< typenameFEOutputType< T >::type >::OutputShape	OutputShape
typedef TensorTools::IncrementRank< OutputShape >::type	OutputGradient
typedef TensorTools::IncrementRank< OutputGradient >::type	OutputTensor
typedef TensorTools::DecrementRank< OutputShape >::type	OutputDivergence
typedef TensorTools::MakeNumber< OutputShape >::type	OutputNumber
typedef TensorTools::IncrementRank< OutputNumber >::type	OutputNumberGradient
typedef TensorTools::IncrementRank< OutputNumberGradient >::type	OutputNumberTensor
typedef TensorTools::DecrementRank< OutputNumber >::type	OutputNumberDivergence

Public Member Functions
	FELagrangeVec (const FEType &fet)
	Constructor.
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
	Subdivision finite elements.
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *libmesh_dbg_var(elem), const Order, const unsigned int, const Point &, const bool)
Real	shape (const FEType, const Elem *libmesh_dbg_var(elem), const unsigned int, const Point &, const bool)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const Point &p, const bool libmesh_dbg_var(add_p_level))
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int, const Point &, const bool)
Real	shape (const ElemType elem_type, const Order order, const unsigned int i, const Point &p)
Real	shape (const ElemType, const Order, const unsigned int i, const Point &p)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *, const Order, const unsigned int i, const Point &p, const bool)
Real	shape (const FEType, const Elem *, const unsigned int i, const Point &p, const bool)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const ElemType, const Order order, const unsigned int i, const Point &p)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
Real	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
RealVectorValue	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealVectorValue	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealVectorValue	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
RealVectorValue	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealVectorValue	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealVectorValue	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealVectorValue	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
RealGradient	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
RealGradient	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int, const Point &, const bool)
Real	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int, const Point &, const bool)
Real	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int, const Point &, const bool)
Real	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int, const Point &, const bool)
Real	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const Elem *, const Order, const unsigned int, const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int, const Point &, const bool)
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const FEType, const Elem *, const unsigned int libmesh_dbg_var(i), const Point &, const bool)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
Real	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level)
void	shapes (const Elem *elem, const Order o, const unsigned int i, const std::vector< Point > &p, std::vector< OutputShape > &v, const bool add_p_level)
void	shapes (const Elem *elem, const Order o, const unsigned int i, const std::vector< Point > &p, std::vector< OutputShape > &vi, const bool add_p_level)
void	shapes (const Elem *elem, const Order o, const unsigned int i, const std::vector< Point > &p, std::vector< OutputShape > &vi, const bool add_p_level)
void	shapes (const Elem *elem, const Order o, const unsigned int i, const std::vector< Point > &p, std::vector< OutputShape > &vi, const bool add_p_level)
void	all_shapes (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< OutputShape > > &v, const bool add_p_level)
void	all_shapes (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< OutputShape > > &v, const bool add_p_level)
void	all_shapes (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< OutputShape > > &v, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *libmesh_dbg_var(elem), const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *libmesh_dbg_var(elem), const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int, const Point &p, const bool libmesh_dbg_var(add_p_level))
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType elem_type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const ElemType elem_type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealVectorValue	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealVectorValue	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealVectorValue	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealVectorValue	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealVectorValue	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealVectorValue	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealVectorValue	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealVectorValue	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &, const bool add_p_level)
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &point_in, const bool libmesh_dbg_var(add_p_level))
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &point_in, const bool libmesh_dbg_var(add_p_level))
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &point_in, const bool libmesh_dbg_var(add_p_level))
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
void	shape_derivs (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const std::vector< Point > &p, std::vector< OutputShape > &v, const bool add_p_level)
void	shape_derivs (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const std::vector< Point > &p, std::vector< OutputShape > &v, const bool add_p_level)
void	shape_derivs (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const std::vector< Point > &p, std::vector< OutputShape > &v, const bool add_p_level)
void	shape_derivs (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const std::vector< Point > &p, std::vector< OutputShape > &v, const bool add_p_level)
void	all_shape_derivs (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< OutputShape > > *comps[3], const bool add_p_level)
void	all_shape_derivs (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< Real > > *comps[3], const bool add_p_level)
void	all_shape_derivs (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< Real > > *comps[3], const bool add_p_level)
void	all_shape_derivs (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< Real > > *comps[3], const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *libmesh_dbg_var(elem), const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *libmesh_dbg_var(elem), const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int, const Point &p, const bool libmesh_dbg_var(add_p_level))
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType elem_type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const ElemType elem_type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealVectorValue	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealVectorValue	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealVectorValue	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealVectorValue	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
RealVectorValue	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealVectorValue	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealVectorValue	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealVectorValue	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &, const bool add_p_level)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int libmesh_dbg_var(i), const unsigned int libmesh_dbg_var(j), const Point &, const bool add_p_level)
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
RealGradient	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
RealGradient	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const FEType, const Elem *, const unsigned int, const unsigned int, const Point &, const bool)
Real	shape_second_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &point_in, const bool libmesh_dbg_var(add_p_level))
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &point_in, const bool libmesh_dbg_var(add_p_level))
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
Real	shape_second_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &point_in, const bool libmesh_dbg_var(add_p_level))
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
Real	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level)
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool add_p_level, const unsigned)
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool add_p_level, const unsigned)
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool add_p_level, const unsigned)
void	nodal_soln (const Elem *, const Order, const std::vector< Number > &, std::vector< Number > &, bool, const unsigned)
void	nodal_soln (const Elem *, const Order, const std::vector< Number > &, std::vector< Number > &, bool, const unsigned)
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool add_p_level, const unsigned vdim)
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool add_p_level, const unsigned)
void	nodal_soln (const Elem *, const Order, const std::vector< Number > &, std::vector< Number > &, bool, const unsigned)
void	nodal_soln (const Elem *, const Order, const std::vector< Number > &, std::vector< Number > &, bool, const unsigned)
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool add_p_level, const unsigned vdim)
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool add_p_level, const unsigned)
void	nodal_soln (const Elem *, const Order, const std::vector< Number > &, std::vector< Number > &, bool, const unsigned)
void	nodal_soln (const Elem *, const Order, const std::vector< Number > &, std::vector< Number > &, bool, const unsigned)
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool add_p_level, const unsigned vdim)
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool add_p_level, const unsigned)
void	nodal_soln (const Elem *elem, const Order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, const bool, const unsigned)
void	side_nodal_soln (const Elem *, const Order, const unsigned int side, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln_on_side, const bool, const unsigned)
void	side_nodal_soln (const Elem *elem, const Order o, const unsigned int side, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln_on_side, const bool add_p_level, const unsigned)
void	side_nodal_soln (const Elem *elem, const Order o, const unsigned int side, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln_on_side, const bool add_p_level, const unsigned)
virtual unsigned int	n_shape_functions () const override
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType, const Order)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *, const Order)
unsigned int	n_dofs (const Elem *, const Order)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType, const Order)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *, const Order)
unsigned int	n_dofs (const Elem *, const Order)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType, const Order)
unsigned int	n_dofs (const ElemType, const Order)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *, const Order)
unsigned int	n_dofs (const Elem *, const Order)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType, const Order o)
unsigned int	n_dofs (const ElemType, const Order o)
unsigned int	n_dofs (const ElemType, const Order o)
unsigned int	n_dofs (const Elem *, const Order o)
unsigned int	n_dofs (const Elem *, const Order o)
unsigned int	n_dofs (const Elem *, const Order o)
unsigned int	n_dofs (const Elem *, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType, const Order)
unsigned int	n_dofs (const Elem *, const Order)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const ElemType t, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs (const Elem *e, const Order o)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_at_node (const Elem &, const Order, const unsigned int)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const ElemType, const Order)
unsigned int	n_dofs_per_elem (const Elem &, const Order)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
virtual FEContinuity	get_continuity () const override
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
FEContinuity	get_continuity () const
virtual bool	is_hierarchic () const override
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
bool	is_hierarchic () const
void	dofs_on_side (const Elem *const, const Order, unsigned int, std::vector< unsigned int > &di, bool)
void	dofs_on_edge (const Elem *const, const Order, unsigned int, std::vector< unsigned int > &di, bool)
Point	inverse_map (const Elem *, const Point &, const Real, const bool)
void	inverse_map (const Elem *, const std::vector< Point > &, std::vector< Point > &, Real, bool)
virtual void	reinit (const Elem *elem, const std::vector< Point > *const pts=nullptr, const std::vector< Real > *const weights=nullptr) override
	This is at the core of this class.
virtual void	reinit (const Elem *elem, const unsigned int side, const Real tolerance=TOLERANCE, const std::vector< Point > *const pts=nullptr, const std::vector< Real > *const weights=nullptr) override
	Reinitializes all the physical element-dependent data based on the side of face.
virtual void	reinit_dual_shape_coeffs (const Elem *elem, const std::vector< Point > &pts, const std::vector< Real > &JxW) override
	This re-computes the dual shape function coefficients.
virtual void	reinit_default_dual_shape_coeffs (const Elem *elem) override
	This computes the default dual shape function coefficients.
virtual void	edge_reinit (const Elem *elem, const unsigned int edge, const Real tolerance=TOLERANCE, const std::vector< Point > *const pts=nullptr, const std::vector< Real > *const weights=nullptr) override
	Reinitializes all the physical element-dependent data based on the edge.
void	edge_reinit (Elem const *, unsigned int, Real, const std::vector< Point > *const, const std::vector< Real > *const)
	Reinitializes all the physical element-dependent data based on the edge of the element elem.
virtual void	side_map (const Elem *elem, const Elem *side, const unsigned int s, const std::vector< Point > &reference_side_points, std::vector< Point > &reference_points) override
	Computes the reference space quadrature points on the side of an element based on the side quadrature points.
void	side_map (const Elem *, const Elem *, const unsigned int, const std::vector< Point > &, std::vector< Point > &)
	Computes the reference space quadrature points on the side of an element based on the side quadrature points.
virtual void	edge_map (const Elem *elem, const Elem *edge, const unsigned int e, const std::vector< Point > &reference_edge_points, std::vector< Point > &reference_points)
	Computes the reference space quadrature points on the side of an element based on the edge quadrature points.
virtual void	attach_quadrature_rule (QBase *q) override
	Provides the class with the quadrature rule, which provides the locations (on a reference element) where the shape functions are to be calculated.
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
virtual bool	shapes_need_reinit () const override
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
bool	shapes_need_reinit () const
std::unique_ptr< FEGenericBase< Real > >	build (const unsigned int dim, const FEType &fet)
std::unique_ptr< FEGenericBase< RealGradient > >	build (const unsigned int dim, const FEType &fet)
std::unique_ptr< FEGenericBase< Real > >	build_InfFE (const unsigned int dim, const FEType &fet)
std::unique_ptr< FEGenericBase< RealGradient > >	build_InfFE (const unsigned int, const FEType &)
const std::vector< std::vector< OutputShape > > &	get_phi () const
const std::vector< std::vector< OutputShape > > &	get_dual_phi () const
virtual void	request_phi () const override
	request phi calculations
virtual void	request_dual_phi () const override
const std::vector< std::vector< OutputGradient > > &	get_dphi () const
const std::vector< std::vector< OutputGradient > > &	get_dual_dphi () const
virtual void	request_dphi () const override
	request dphi calculations
virtual void	request_dual_dphi () const override
const DenseMatrix< Real > &	get_dual_coeff () const
virtual_for_inffe const std::vector< std::vector< OutputShape > > &	get_curl_phi () const
virtual_for_inffe const std::vector< std::vector< OutputDivergence > > &	get_div_phi () const
const std::vector< std::vector< OutputShape > > &	get_dphidx () const
const std::vector< std::vector< OutputShape > > &	get_dphidy () const
const std::vector< std::vector< OutputShape > > &	get_dphidz () const
const std::vector< std::vector< OutputShape > > &	get_dphidxi () const
const std::vector< std::vector< OutputShape > > &	get_dphideta () const
const std::vector< std::vector< OutputShape > > &	get_dphidzeta () const
const std::vector< std::vector< OutputTensor > > &	get_d2phi () const
const std::vector< std::vector< OutputTensor > > &	get_dual_d2phi () const
const std::vector< std::vector< OutputShape > > &	get_d2phidx2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxdy () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxdz () const
const std::vector< std::vector< OutputShape > > &	get_d2phidy2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidydz () const
const std::vector< std::vector< OutputShape > > &	get_d2phidz2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxi2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxideta () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxidzeta () const
const std::vector< std::vector< OutputShape > > &	get_d2phideta2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidetadzeta () const
const std::vector< std::vector< OutputShape > > &	get_d2phidzeta2 () const
const std::vector< OutputGradient > &	get_dphase () const
virtual const std::vector< Real > &	get_Sobolev_weight () const
virtual const std::vector< RealGradient > &	get_Sobolev_dweight () const
virtual const std::vector< Real > &	get_Sobolev_weightxR_sq () const
virtual const std::vector< RealGradient > &	get_Sobolev_dweightxR_sq () const
virtual const std::vector< std::vector< OutputShape > > &	get_phi_over_decayxR () const
virtual const std::vector< std::vector< OutputGradient > > &	get_dphi_over_decayxR () const
virtual const std::vector< std::vector< OutputGradient > > &	get_dphi_over_decay () const
virtual void	print_phi (std::ostream &os) const override
	Prints the value of each shape function at each quadrature point.
virtual void	print_dual_phi (std::ostream &os) const override
virtual void	print_dphi (std::ostream &os) const override
	Prints the value of each shape function's derivative at each quadrature point.
virtual void	print_dual_dphi (std::ostream &os) const override
virtual void	print_d2phi (std::ostream &os) const override
	Prints the value of each shape function's second derivatives at each quadrature point.
virtual void	print_dual_d2phi (std::ostream &os) const override
unsigned int	get_dim () const
void	get_nothing () const
virtual_for_inffe const std::vector< Point > &	get_xyz () const
virtual const std::vector< Real > &	get_JxWxdecay_sq () const
	This function is the variant of get_JxW() for InfFE.
virtual_for_inffe const std::vector< Real > &	get_JxW () const
virtual_for_inffe const std::vector< RealGradient > &	get_dxyzdxi () const
virtual_for_inffe const std::vector< RealGradient > &	get_dxyzdeta () const
virtual_for_inffe const std::vector< RealGradient > &	get_dxyzdzeta () const
virtual_for_inffe const std::vector< RealGradient > &	get_d2xyzdxi2 () const
virtual_for_inffe const std::vector< RealGradient > &	get_d2xyzdeta2 () const
virtual_for_inffe const std::vector< RealGradient > &	get_d2xyzdzeta2 () const
virtual_for_inffe const std::vector< RealGradient > &	get_d2xyzdxideta () const
virtual_for_inffe const std::vector< RealGradient > &	get_d2xyzdxidzeta () const
virtual_for_inffe const std::vector< RealGradient > &	get_d2xyzdetadzeta () const
virtual_for_inffe const std::vector< Real > &	get_dxidx () const
virtual_for_inffe const std::vector< Real > &	get_dxidy () const
virtual_for_inffe const std::vector< Real > &	get_dxidz () const
virtual_for_inffe const std::vector< Real > &	get_detadx () const
virtual_for_inffe const std::vector< Real > &	get_detady () const
virtual_for_inffe const std::vector< Real > &	get_detadz () const
virtual_for_inffe const std::vector< Real > &	get_dzetadx () const
virtual_for_inffe const std::vector< Real > &	get_dzetady () const
virtual_for_inffe const std::vector< Real > &	get_dzetadz () const
virtual_for_inffe const std::vector< std::vector< Point > > &	get_tangents () const
virtual_for_inffe const std::vector< Point > &	get_normals () const
virtual_for_inffe const std::vector< Real > &	get_curvatures () const
virtual unsigned int	n_quadrature_points () const
const Elem *	get_elem () const
ElemType	get_type () const
unsigned int	get_p_level () const
FEType	get_fe_type () const
Order	get_order () const
void	set_fe_order (int new_order)
	Sets the base FE order of the finite element.
FEFamily	get_family () const
const FEMap &	get_fe_map () const
FEMap &	get_fe_map ()
void	print_JxW (std::ostream &os) const
	Prints the Jacobian times the weight for each quadrature point.
void	print_xyz (std::ostream &os) const
	Prints the spatial location of each quadrature point (on the physical element).
void	print_info (std::ostream &os) const
	Prints all the relevant information about the current element.
void	set_calculate_dual (const bool val)
	set calculate_dual as needed
void	set_calculate_default_dual_coeff (const bool val)
	set calculate_default_dual_coeff as needed
void	add_p_level_in_reinit (bool value)
	Indicate whether to add p-refinement levels in init/reinit methods.
bool	add_p_level_in_reinit () const
	Whether to add p-refinement levels in init/reinit methods.

Static Public Member Functions
static OutputShape	shape (const ElemType t, const Order o, const unsigned int i, const Point &p)
static OutputShape	shape (const Elem *elem, const Order o, const unsigned int i, const Point &p, const bool add_p_level=true)
static OutputShape	shape (const FEType fet, const Elem *elem, const unsigned int i, const Point &p, const bool add_p_level=true)
static void	shapes (const Elem *elem, const Order o, const unsigned int i, const std::vector< Point > &p, std::vector< OutputShape > &v, const bool add_p_level=true)
	Fills v with the values of the \( i^{th} \) shape function, evaluated at all points p.
static void	all_shapes (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< OutputShape > > &v, const bool add_p_level=true)
	Fills v[i][qp] with the values of the \( i^{th} \) shape functions, evaluated at all points in p.
static OutputShape	shape_deriv (const ElemType t, const Order o, const unsigned int i, const unsigned int j, const Point &p)
static OutputShape	shape_deriv (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level=true)
static OutputShape	shape_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level=true)
static void	shape_derivs (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const std::vector< Point > &p, std::vector< OutputShape > &v, const bool add_p_level=true)
	Fills v with the \( j^{th} \) derivative of the \( i^{th} \) shape function, evaluated at all points p.
static void	all_shape_derivs (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< OutputShape > > *comps[3], const bool add_p_level=true)
	Fills comps with dphidxi (and in higher dimensions, eta/zeta) derivative component values for all shape functions, evaluated at all points in p.
static OutputShape	shape_second_deriv (const ElemType t, const Order o, const unsigned int i, const unsigned int j, const Point &p)
static OutputShape	shape_second_deriv (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level=true)
static OutputShape	shape_second_deriv (const FEType fet, const Elem *elem, const unsigned int i, const unsigned int j, const Point &p, const bool add_p_level=true)
static void	nodal_soln (const Elem *elem, const Order o, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln, bool add_p_level=true, const unsigned vdim=1)
	Build the nodal soln from the element soln.
static void	side_nodal_soln (const Elem *elem, const Order o, const unsigned int side, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln_on_side, bool add_p_level=true, const unsigned vdim=1)
	Build the nodal soln on one side from the (full) element soln.
static unsigned int	n_shape_functions (const ElemType t, const Order o)
static unsigned int	n_dofs (const ElemType t, const Order o)
static unsigned int	n_dofs (const Elem *e, const Order o)
static unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
static unsigned int	n_dofs_at_node (const Elem &e, const Order o, const unsigned int n)
static unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
static unsigned int	n_dofs_per_elem (const Elem &e, const Order o)
static void	dofs_on_side (const Elem *const elem, const Order o, unsigned int s, std::vector< unsigned int > &di, bool add_p_level=true)
	Fills the vector di with the local degree of freedom indices associated with side s of element elem.
static void	dofs_on_edge (const Elem *const elem, const Order o, unsigned int e, std::vector< unsigned int > &di, bool add_p_level=true)
	Fills the vector di with the local degree of freedom indices associated with edge e of element elem.
static Point	inverse_map (const Elem *elem, const Point &p, const Real tolerance=TOLERANCE, const bool secure=true)
static void	inverse_map (const Elem *elem, const std::vector< Point > &physical_points, std::vector< Point > &reference_points, const Real tolerance=TOLERANCE, const bool secure=true)
static void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
	Computes the constraint matrix contributions (for non-conforming adapted meshes) corresponding to variable number var_number, using element-specific optimizations if possible.
static Point	map (const Elem *elem, const Point &reference_point)
static Point	map_xi (const Elem *elem, const Point &reference_point)
static Point	map_eta (const Elem *elem, const Point &reference_point)
static Point	map_zeta (const Elem *elem, const Point &reference_point)
static std::unique_ptr< FEGenericBase >	build (const unsigned int dim, const FEType &type)
	Builds a specific finite element type.
static std::unique_ptr< FEGenericBase >	build_InfFE (const unsigned int dim, const FEType &type)
	Builds a specific infinite element type.
static void	compute_proj_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
	Computes the constraint matrix contributions (for non-conforming adapted meshes) corresponding to variable number var_number, using generic projections.
static void	coarsened_dof_values (const NumericVector< Number > &global_vector, const DofMap &dof_map, const Elem *coarse_elem, DenseVector< Number > &coarse_dofs, const unsigned int var, const bool use_old_dof_indices=false)
	Creates a local projection on coarse_elem, based on the DoF values in global_vector for it's children.
static void	coarsened_dof_values (const NumericVector< Number > &global_vector, const DofMap &dof_map, const Elem *coarse_elem, DenseVector< Number > &coarse_dofs, const bool use_old_dof_indices=false)
	Creates a local projection on coarse_elem, based on the DoF values in global_vector for it's children.
static void	compute_periodic_constraints (DofConstraints &constraints, DofMap &dof_map, const PeriodicBoundaries &boundaries, const MeshBase &mesh, const PointLocatorBase *point_locator, const unsigned int variable_number, const Elem *elem)
	Computes the constraint matrix contributions (for meshes with periodic boundary conditions) corresponding to variable number var_number, using generic projections.
static bool	on_reference_element (const Point &p, const ElemType t, const Real eps=TOLERANCE)
static void	get_refspace_nodes (const ElemType t, std::vector< Point > &nodes)
static void	compute_node_constraints (NodeConstraints &constraints, const Elem *elem)
	Computes the nodal constraint contributions (for non-conforming adapted meshes), using Lagrange geometry.
static void	compute_periodic_node_constraints (NodeConstraints &constraints, const PeriodicBoundaries &boundaries, const MeshBase &mesh, const PointLocatorBase *point_locator, const Elem *elem)
	Computes the node position constraint equation contributions (for meshes with periodic boundary conditions)
static void	print_info (std::ostream &out_stream=libMesh::out)
	Prints the reference information, by default to libMesh::out.
static std::string	get_info ()
	Gets a string containing the reference information.
static unsigned int	n_objects ()
	Prints the number of outstanding (created, but not yet destroyed) objects.
static void	enable_print_counter_info ()
	Methods to enable/disable the reference counter output from print_info().
static void	disable_print_counter_info ()

Protected Types
typedef std::map< std::string, std::pair< unsigned int, unsigned int > >	Counts
	Data structure to log the information.

Protected Member Functions
virtual void	init_shape_functions (const std::vector< Point > &qp, const Elem *e)
	Update the various member data fields phi, dphidxi, dphideta, dphidzeta, etc.
void	init_dual_shape_functions (unsigned int n_shapes, unsigned int n_qp)
	Init dual_phi and potentially dual_dphi, dual_d2phi.
virtual void	init_base_shape_functions (const std::vector< Point > &qp, const Elem *e) override
	Initialize the data fields for the base of an an infinite element.
void	cache (const Elem *elem)
	Repopulate the element cache with the node locations, edge and face orientations of the element elem.
bool	matches_cache (const Elem *elem)
	Check if the node locations, edge and face orientations held in the element cache match those of element elem.
virtual_for_inffe void	determine_calculations ()
	Determine which values are to be calculated, for both the FE itself and for the FEMap.
bool	calculating_nothing () const
virtual void	compute_shape_functions (const Elem *elem, const std::vector< Point > &qp) override
	After having updated the jacobian and the transformation from local to global coordinates in FEMap::compute_map(), the first derivatives of the shape functions are transformed to global coordinates, giving dphi, dphidx, dphidy, and dphidz.
void	compute_dual_shape_coeffs (const std::vector< Real > &JxW, const std::vector< std::vector< OutputShape > > &phi)
	Compute the dual basis coefficients dual_coeff we rely on the JxW (or weights) and the phi values, which can come from default or customized qrule.
void	compute_dual_shape_coeffs (const std::vector< Real > &, const std::vector< std::vector< OutputShape > > &)
void	compute_dual_shape_coeffs (const std::vector< Real > &JxW, const std::vector< std::vector< OutputShape > > &phi_vals)
void	compute_dual_shape_functions ()
	Compute dual_phi, dual_dphi, dual_d2phi It is only valid for this to be called after reinit has occurred with a quadrature rule.
void	compute_dual_shape_functions ()
void	compute_dual_shape_functions ()
void	increment_constructor_count (const std::string &name) noexcept
	Increments the construction counter.
void	increment_destructor_count (const std::string &name) noexcept
	Increments the destruction counter.

Static Protected Member Functions
static void	default_all_shape_derivs (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< OutputShape > > *comps[3], const bool add_p_level=true)
	A default implementation for all_shape_derivs.
static void	default_shapes (const Elem *elem, const Order o, const unsigned int i, const std::vector< Point > &p, std::vector< OutputShape > &v, const bool add_p_level=true)
	A default implementation for shapes.
static void	default_all_shapes (const Elem *elem, const Order o, const std::vector< Point > &p, std::vector< std::vector< OutputShape > > &v, const bool add_p_level=true)
	A default implementation for all_shapes.
static void	default_shape_derivs (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const std::vector< Point > &p, std::vector< OutputShape > &v, const bool add_p_level=true)
	A default implementation for shape_derivs.
static void	default_side_nodal_soln (const Elem *elem, const Order o, const unsigned int side, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln_on_side, bool add_p_level=true, const unsigned vdim=1)
	A default implementation for side_nodal_soln.

Protected Attributes
std::vector< Point >	cached_nodes
	Vectors holding the node locations, edge and face orientations of the last element we cached.
std::vector< bool >	cached_edges
std::vector< bool >	cached_faces
ElemType	last_side
	The last side and last edge we did a reinit on.
ElemType	last_edge
std::unique_ptr< FETransformationBase< FEOutputType< T >::type > >	_fe_trans
	Object that handles computing shape function values, gradients, etc in the physical domain.
std::vector< std::vector< OutputShape > >	phi
	Shape function values.
std::vector< std::vector< OutputShape > >	dual_phi
std::vector< std::vector< OutputGradient > >	dphi
	Shape function derivative values.
std::vector< std::vector< OutputGradient > >	dual_dphi
DenseMatrix< Real >	dual_coeff
	Coefficient matrix for the dual basis.
std::vector< std::vector< OutputShape > >	curl_phi
	Shape function curl values.
std::vector< std::vector< OutputDivergence > >	div_phi
	Shape function divergence values.
std::vector< std::vector< OutputShape > >	dphidxi
	Shape function derivatives in the xi direction.
std::vector< std::vector< OutputShape > >	dphideta
	Shape function derivatives in the eta direction.
std::vector< std::vector< OutputShape > >	dphidzeta
	Shape function derivatives in the zeta direction.
std::vector< std::vector< OutputShape > >	dphidx
	Shape function derivatives in the x direction.
std::vector< std::vector< OutputShape > >	dphidy
	Shape function derivatives in the y direction.
std::vector< std::vector< OutputShape > >	dphidz
	Shape function derivatives in the z direction.
std::vector< std::vector< OutputTensor > >	d2phi
	Shape function second derivative values.
std::vector< std::vector< OutputTensor > >	dual_d2phi
std::vector< std::vector< OutputShape > >	d2phidxi2
	Shape function second derivatives in the xi direction.
std::vector< std::vector< OutputShape > >	d2phidxideta
	Shape function second derivatives in the xi-eta direction.
std::vector< std::vector< OutputShape > >	d2phidxidzeta
	Shape function second derivatives in the xi-zeta direction.
std::vector< std::vector< OutputShape > >	d2phideta2
	Shape function second derivatives in the eta direction.
std::vector< std::vector< OutputShape > >	d2phidetadzeta
	Shape function second derivatives in the eta-zeta direction.
std::vector< std::vector< OutputShape > >	d2phidzeta2
	Shape function second derivatives in the zeta direction.
std::vector< std::vector< OutputShape > >	d2phidx2
	Shape function second derivatives in the x direction.
std::vector< std::vector< OutputShape > >	d2phidxdy
	Shape function second derivatives in the x-y direction.
std::vector< std::vector< OutputShape > >	d2phidxdz
	Shape function second derivatives in the x-z direction.
std::vector< std::vector< OutputShape > >	d2phidy2
	Shape function second derivatives in the y direction.
std::vector< std::vector< OutputShape > >	d2phidydz
	Shape function second derivatives in the y-z direction.
std::vector< std::vector< OutputShape > >	d2phidz2
	Shape function second derivatives in the z direction.
std::vector< OutputGradient >	dphase
	Used for certain infinite element families: the first derivatives of the phase term in global coordinates, over all quadrature points.
std::vector< RealGradient >	dweight
	Used for certain infinite element families: the global derivative of the additional radial weight \( 1/{r^2} \), over all quadrature points.
std::vector< Real >	weight
	Used for certain infinite element families: the additional radial weight \( 1/{r^2} \) in local coordinates, over all quadrature points.
std::unique_ptr< FEMap >	_fe_map
const unsigned int	dim
	The dimensionality of the object.
bool	calculations_started
	Have calculations with this object already been started? Then all get_* functions should already have been called.
bool	calculate_dual
	Are we calculating dual basis?
bool	calculate_default_dual_coeff
	Are we calculating the coefficient for the dual basis using the default qrule?
bool	calculate_nothing
	Are we potentially deliberately calculating nothing?
bool	calculate_map
	Are we calculating mapping functions?
bool	calculate_phi
	Should we calculate shape functions?
bool	calculate_dphi
	Should we calculate shape function gradients?
bool	calculate_d2phi
	Should we calculate shape function hessians?
const bool	calculate_d2phi =false
bool	calculate_curl_phi
	Should we calculate shape function curls?
bool	calculate_div_phi
	Should we calculate shape function divergences?
bool	calculate_dphiref
	Should we calculate reference shape function gradients?
FEType	fe_type
	The finite element type for this object.
ElemType	_elem_type
	The element type the current data structures were set up for.
const Elem *	_elem
	The element the current data structures were set up for.
unsigned int	_elem_p_level
	The element p-refinement level the current data structures are set up for.
unsigned int	_p_level
	The p refinement level the current data structures are set up for.
QBase *	qrule
	A pointer to the quadrature rule employed.
bool	shapes_on_quadrature
	A flag indicating if current data structures correspond to quadrature rule points.
unsigned int	_n_total_qp
	The total number of quadrature points for the current configuration.
bool	_add_p_level_in_reinit
	Whether to add p-refinement levels in init/reinit methods.

Static Protected Attributes
static Counts	_counts
	Actually holds the data.
static Threads::atomic< unsigned int >	_n_objects
	The number of objects.
static Threads::spin_mutex	_mutex
	Mutual exclusion object to enable thread-safe reference counting.
static bool	_enable_print_counter = true
	Flag to control whether reference count information is printed when print_info is called.

Detailed Description

template<unsigned int Dim>
class libMesh::FELagrangeVec< Dim >

FELagrangeVec objects are used for working with vector-valued finite elements.

Author

Paul T. Bauman

Date

2013

Definition at line 1243 of file fe.h.

Member Typedef Documentation

Counts

typedef std::map<std::string, std::pair<unsigned int, unsigned int> > libMesh::ReferenceCounter::Counts

protectedinherited

Data structure to log the information.

The log is identified by the class name.

Definition at line 119 of file reference_counter.h.

OutputDivergence

typedef TensorTools::DecrementRank<OutputShape>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputDivergence

inherited

Definition at line 122 of file fe_base.h.

OutputGradient

typedef TensorTools::IncrementRank<OutputShape>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputGradient

inherited

Definition at line 120 of file fe_base.h.

OutputNumber

typedef TensorTools::MakeNumber<OutputShape>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputNumber

inherited

Definition at line 123 of file fe_base.h.

OutputNumberDivergence

typedef TensorTools::DecrementRank<OutputNumber>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputNumberDivergence

inherited

Definition at line 126 of file fe_base.h.

OutputNumberGradient

typedef TensorTools::IncrementRank<OutputNumber>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputNumberGradient

inherited

Definition at line 124 of file fe_base.h.

OutputNumberTensor

typedef TensorTools::IncrementRank<OutputNumberGradient>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputNumberTensor

inherited

Definition at line 125 of file fe_base.h.

OutputShape

typedef FEGenericBase<typenameFEOutputType<T>::type>::OutputShape libMesh::FE< Dim, T >::OutputShape

inherited

Definition at line 139 of file fe.h.

OutputTensor

typedef TensorTools::IncrementRank<OutputGradient>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputTensor

inherited

Definition at line 121 of file fe_base.h.

Constructor & Destructor Documentation

FELagrangeVec()

template<unsigned int Dim>

libMesh::FELagrangeVec< Dim >::FELagrangeVec ( const FEType &  fet )

inlineexplicit

Constructor.

Creates a vector Lagrange finite element to be used in dimension Dim.

Definition at line 1252 of file fe.h.

                                    :
    FE<Dim,LAGRANGE_VEC> (fet)
  {}

Member Function Documentation

add_p_level_in_reinit() [1/2]

bool libMesh::FEAbstract::add_p_level_in_reinit ( ) const

inlineinherited

Whether to add p-refinement levels in init/reinit methods.

Definition at line 636 of file fe_abstract.h.

{ return _add_p_level_in_reinit; }

References libMesh::FEAbstract::_add_p_level_in_reinit.

add_p_level_in_reinit() [2/2]

void libMesh::FEAbstract::add_p_level_in_reinit ( bool  value )

inlineinherited

Indicate whether to add p-refinement levels in init/reinit methods.

Definition at line 631 of file fe_abstract.h.

{ _add_p_level_in_reinit = value; }

References libMesh::FEAbstract::_add_p_level_in_reinit, and value.

Referenced by libMesh::FEMContext::build_new_fe().

all_shape_derivs() [1/5]

void libMesh::FE< 3, LAGRANGE >::all_shape_derivs ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< OutputShape > > *  comps[3], const bool  add_p_level  )

inherited

Definition at line 238 of file fe_lagrange_shape_3D.C.

{
  const ElemType type = elem->type();
 
  // Just loop on the harder-to-optimize cases
  if (type != HEX8 && type != HEX27)
    {
      FE<3,LAGRANGE>::default_all_shape_derivs
        (elem,o,p,comps,add_p_level);
      return;
    }
 
#if LIBMESH_DIM == 3
 
  libmesh_assert(comps[0]);
  libmesh_assert(comps[1]);
  libmesh_assert(comps[2]);
  const unsigned int n_sf = comps[0]->size();
 
  switch (o)
    {
      // linear Lagrange shape functions
    case FIRST:
      {
        switch (type)
          {
            // trilinear hexahedral shape functions
          case HEX8:
          case HEX20:
          case HEX27:
            {
              libmesh_assert_equal_to (n_sf, 8);
 
              //                                0  1  2  3  4  5  6  7
              static const unsigned int i0[] = {0, 1, 1, 0, 0, 1, 1, 0};
              static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 1, 1};
              static const unsigned int i2[] = {0, 0, 0, 0, 1, 1, 1, 1};
 
              for (auto qp : index_range(p))
                {
                  const Point & q_point = p[qp];
                  // Compute hex shape functions as a tensor-product
                  const Real xi   = q_point(0);
                  const Real eta  = q_point(1);
                  const Real zeta = q_point(2);
 
                  // one_d_shapes[dim][i] = phi_i(p(dim))
                  Real one_d_shapes[3][2] = {
                    {fe_lagrange_1D_linear_shape(0, xi),
                     fe_lagrange_1D_linear_shape(1, xi)},
                    {fe_lagrange_1D_linear_shape(0, eta),
                     fe_lagrange_1D_linear_shape(1, eta)},
                    {fe_lagrange_1D_linear_shape(0, zeta),
                     fe_lagrange_1D_linear_shape(1, zeta)}};
 
                  // one_d_derivs[dim][i] = dphi_i/dxi(p(dim))
                  Real one_d_derivs[3][2] = {
                    {fe_lagrange_1D_linear_shape_deriv(0, 0, xi),
                     fe_lagrange_1D_linear_shape_deriv(1, 0, xi)},
                    {fe_lagrange_1D_linear_shape_deriv(0, 0, eta),
                     fe_lagrange_1D_linear_shape_deriv(1, 0, eta)},
                    {fe_lagrange_1D_linear_shape_deriv(0, 0, zeta),
                     fe_lagrange_1D_linear_shape_deriv(1, 0, zeta)}};
 
                    for (unsigned int i : make_range(n_sf))
                      {
                        (*comps[0])[i][qp] = one_d_derivs[0][i0[i]] *
                                             one_d_shapes[1][i1[i]] *
                                             one_d_shapes[2][i2[i]];
                        (*comps[1])[i][qp] = one_d_shapes[0][i0[i]] *
                                             one_d_derivs[1][i1[i]] *
                                             one_d_shapes[2][i2[i]];
                        (*comps[2])[i][qp] = one_d_shapes[0][i0[i]] *
                                             one_d_shapes[1][i1[i]] *
                                             one_d_derivs[2][i2[i]];
                      }
                }
              return;
            }
 
          default:
            libmesh_error(); // How did we get here?
          }
      }
 
 
      // quadratic Lagrange shape functions
    case SECOND:
      {
        switch (type)
          {
            // triquadratic hexahedral shape functions
          case HEX8:
// TODO: refactor to optimize this
//            libmesh_assert_msg(T == L2_LAGRANGE,
//                               "High order on first order elements only supported for L2 families");
            libmesh_fallthrough();
          case HEX27:
            {
              libmesh_assert_less_equal (n_sf, 27);
 
              // The only way to make any sense of this
              // is to look at the mgflo/mg2/mgf documentation
              // and make the cut-out cube!
              //                                0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
              static const unsigned int i0[] = {0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 2, 0, 0, 1, 1, 0, 2, 1, 2, 0, 2, 2, 1, 2, 0, 2, 2};
              static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 2, 0, 0, 1, 1, 0, 2, 1, 2, 2, 0, 2, 1, 2, 2, 2};
              static const unsigned int i2[] = {0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, 0, 2, 2, 2, 2, 1, 2};
 
              for (auto qp : index_range(p))
                {
                  const Point & q_point = p[qp];
                  // Compute hex shape functions as a tensor-product
                  const Real xi   = q_point(0);
                  const Real eta  = q_point(1);
                  const Real zeta = q_point(2);
 
                  // one_d_shapes[dim][i] = phi_i(p(dim))
                  Real one_d_shapes[3][3] = {
                    {fe_lagrange_1D_quadratic_shape(0, xi),
                     fe_lagrange_1D_quadratic_shape(1, xi),
                     fe_lagrange_1D_quadratic_shape(2, xi)},
                    {fe_lagrange_1D_quadratic_shape(0, eta),
                     fe_lagrange_1D_quadratic_shape(1, eta),
                     fe_lagrange_1D_quadratic_shape(2, eta)},
                    {fe_lagrange_1D_quadratic_shape(0, zeta),
                     fe_lagrange_1D_quadratic_shape(1, zeta),
                     fe_lagrange_1D_quadratic_shape(2, zeta)}};
 
                  // one_d_derivs[dim][i] = dphi_i/dxi(p(dim))
                  Real one_d_derivs[3][3] = {
                    {fe_lagrange_1D_quadratic_shape_deriv(0, 0, xi),
                     fe_lagrange_1D_quadratic_shape_deriv(1, 0, xi),
                     fe_lagrange_1D_quadratic_shape_deriv(2, 0, xi)},
                    {fe_lagrange_1D_quadratic_shape_deriv(0, 0, eta),
                     fe_lagrange_1D_quadratic_shape_deriv(1, 0, eta),
                     fe_lagrange_1D_quadratic_shape_deriv(2, 0, eta)},
                    {fe_lagrange_1D_quadratic_shape_deriv(0, 0, zeta),
                     fe_lagrange_1D_quadratic_shape_deriv(1, 0, zeta),
                     fe_lagrange_1D_quadratic_shape_deriv(2, 0, zeta)}};
 
                    for (unsigned int i : make_range(n_sf))
                      {
                        (*comps[0])[i][qp] = one_d_derivs[0][i0[i]] *
                                             one_d_shapes[1][i1[i]] *
                                             one_d_shapes[2][i2[i]];
                        (*comps[1])[i][qp] = one_d_shapes[0][i0[i]] *
                                             one_d_derivs[1][i1[i]] *
                                             one_d_shapes[2][i2[i]];
                        (*comps[2])[i][qp] = one_d_shapes[0][i0[i]] *
                                             one_d_shapes[1][i1[i]] *
                                             one_d_derivs[2][i2[i]];
                      }
                }
              return;
            }
 
          default:
            libmesh_error(); // How did we get here?
          }
      }
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order on HEX!: " << o);
    }
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, o, p, v, add_p_level);
  libmesh_not_implemented();
#endif // LIBMESH_DIM == 3
}

all_shape_derivs() [2/5]

static void libMesh::FE< Dim, T >::all_shape_derivs ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< OutputShape > > *  comps[3], const bool  add_p_level = true  )

staticinherited

Fills comps with dphidxi (and in higher dimensions, eta/zeta) derivative component values for all shape functions, evaluated at all points in p.

You must specify element order directly. Output component arrays in comps should already be the appropriate size.

On a p-refined element, o should be the base order of the element if add_p_level is left true, or can be the base order of the element if add_p_level is set to false.

all_shape_derivs() [3/5]

void libMesh::FE< 1, RATIONAL_BERNSTEIN >::all_shape_derivs ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< Real > > *  comps[3], const bool  add_p_level  )

inherited

Definition at line 224 of file fe_rational_shape_1D.C.

{
  FEType underlying_fe_type(o, _underlying_fe_family);
 
  rational_all_shape_derivs (*elem, underlying_fe_type, p,
                             comps, add_p_level);
}

all_shape_derivs() [4/5]

void libMesh::FE< 2, RATIONAL_BERNSTEIN >::all_shape_derivs ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< Real > > *  comps[3], const bool  add_p_level  )

inherited

Definition at line 222 of file fe_rational_shape_2D.C.

{
  FEType underlying_fe_type(o, _underlying_fe_family);
 
  rational_all_shape_derivs (*elem, underlying_fe_type, p,
                             comps, add_p_level);
}

all_shape_derivs() [5/5]

void libMesh::FE< 3, RATIONAL_BERNSTEIN >::all_shape_derivs ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< Real > > *  comps[3], const bool  add_p_level  )

inherited

Definition at line 218 of file fe_rational_shape_3D.C.

{
  FEType underlying_fe_type(o, _underlying_fe_family);
 
  rational_all_shape_derivs (*elem, underlying_fe_type, p,
                             comps, add_p_level);
}

all_shapes() [1/4]

void libMesh::FE< 1, RATIONAL_BERNSTEIN >::all_shapes ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< OutputShape > > &  v, const bool  add_p_level  )

inherited

Definition at line 193 of file fe_rational_shape_1D.C.

{
  FEType underlying_fe_type(o, _underlying_fe_family);
 
  rational_all_shapes(*elem, underlying_fe_type, p, v, add_p_level);
}

all_shapes() [2/4]

void libMesh::FE< 2, RATIONAL_BERNSTEIN >::all_shapes ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< OutputShape > > &  v, const bool  add_p_level  )

inherited

Definition at line 191 of file fe_rational_shape_2D.C.

{
  FEType underlying_fe_type(o, _underlying_fe_family);
 
  rational_all_shapes(*elem, underlying_fe_type, p, v, add_p_level);
}

all_shapes() [3/4]

void libMesh::FE< 3, RATIONAL_BERNSTEIN >::all_shapes ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< OutputShape > > &  v, const bool  add_p_level  )

inherited

Definition at line 187 of file fe_rational_shape_3D.C.

{
  FEType underlying_fe_type(o, _underlying_fe_family);
 
  rational_all_shapes(*elem, underlying_fe_type, p, v, add_p_level);
}

all_shapes() [4/4]

static void libMesh::FE< Dim, T >::all_shapes ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< OutputShape > > &  v, const bool  add_p_level = true  )

staticinherited

Fills v[i][qp] with the values of the \( i^{th} \) shape functions, evaluated at all points in p.

You must specify element order directly. v should already be the appropriate size.

On a p-refined element, o should be the base order of the element if add_p_level is left true, or can be the base order of the element if add_p_level is set to false.

attach_quadrature_rule()

void libMesh::FE< Dim, T >::attach_quadrature_rule ( QBase *  q )

overridevirtualinherited

Provides the class with the quadrature rule, which provides the locations (on a reference element) where the shape functions are to be calculated.

Implements libMesh::FEAbstract.

Definition at line 637 of file fe.C.

{
  libmesh_assert(q);
  this->qrule = q;
  // make sure we don't cache results from a previous quadrature rule
  this->_elem = nullptr;
  this->_elem_type = INVALID_ELEM;
  return;
}

build() [1/3]

std::unique_ptr< FEGenericBase< Real > > libMesh::FEGenericBase< Real >::build ( const unsigned int  dim, const FEType &  fet  )

inherited

Definition at line 191 of file fe_base.C.

{
  switch (dim)
    {
      // 0D
    case 0:
      {
        switch (fet.family)
          {
          case CLOUGH:
            return std::make_unique<FE<0,CLOUGH>>(fet);
 
          case HERMITE:
            return std::make_unique<FE<0,HERMITE>>(fet);
 
          case LAGRANGE:
            return std::make_unique<FE<0,LAGRANGE>>(fet);
 
          case L2_LAGRANGE:
            return std::make_unique<FE<0,L2_LAGRANGE>>(fet);
 
          case HIERARCHIC:
            return std::make_unique<FE<0,HIERARCHIC>>(fet);
 
          case L2_HIERARCHIC:
            return std::make_unique<FE<0,L2_HIERARCHIC>>(fet);
 
          case SIDE_HIERARCHIC:
            return std::make_unique<FE<0,SIDE_HIERARCHIC>>(fet);
 
          case MONOMIAL:
            return std::make_unique<FE<0,MONOMIAL>>(fet);
 
#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
          case SZABAB:
            return std::make_unique<FE<0,SZABAB>>(fet);
 
          case BERNSTEIN:
            return std::make_unique<FE<0,BERNSTEIN>>(fet);
 
          case RATIONAL_BERNSTEIN:
            return std::make_unique<FE<0,RATIONAL_BERNSTEIN>>(fet);
#endif
 
          case XYZ:
            return std::make_unique<FEXYZ<0>>(fet);
 
          case SCALAR:
            return std::make_unique<FEScalar<0>>(fet);
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
          }
      }
      // 1D
    case 1:
      {
        switch (fet.family)
          {
          case CLOUGH:
            return std::make_unique<FE<1,CLOUGH>>(fet);
 
          case HERMITE:
            return std::make_unique<FE<1,HERMITE>>(fet);
 
          case LAGRANGE:
            return std::make_unique<FE<1,LAGRANGE>>(fet);
 
          case L2_LAGRANGE:
            return std::make_unique<FE<1,L2_LAGRANGE>>(fet);
 
          case HIERARCHIC:
            return std::make_unique<FE<1,HIERARCHIC>>(fet);
 
          case L2_HIERARCHIC:
            return std::make_unique<FE<1,L2_HIERARCHIC>>(fet);
 
          case SIDE_HIERARCHIC:
            return std::make_unique<FE<1,SIDE_HIERARCHIC>>(fet);
 
          case MONOMIAL:
            return std::make_unique<FE<1,MONOMIAL>>(fet);
 
#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
          case SZABAB:
            return std::make_unique<FE<1,SZABAB>>(fet);
 
          case BERNSTEIN:
            return std::make_unique<FE<1,BERNSTEIN>>(fet);
 
          case RATIONAL_BERNSTEIN:
            return std::make_unique<FE<1,RATIONAL_BERNSTEIN>>(fet);
#endif
 
          case XYZ:
            return std::make_unique<FEXYZ<1>>(fet);
 
          case SCALAR:
            return std::make_unique<FEScalar<1>>(fet);
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
          }
      }
 
 
      // 2D
    case 2:
      {
        switch (fet.family)
          {
          case CLOUGH:
            return std::make_unique<FE<2,CLOUGH>>(fet);
 
          case HERMITE:
            return std::make_unique<FE<2,HERMITE>>(fet);
 
          case LAGRANGE:
            return std::make_unique<FE<2,LAGRANGE>>(fet);
 
          case L2_LAGRANGE:
            return std::make_unique<FE<2,L2_LAGRANGE>>(fet);
 
          case HIERARCHIC:
            return std::make_unique<FE<2,HIERARCHIC>>(fet);
 
          case L2_HIERARCHIC:
            return std::make_unique<FE<2,L2_HIERARCHIC>>(fet);
 
          case SIDE_HIERARCHIC:
            return std::make_unique<FE<2,SIDE_HIERARCHIC>>(fet);
 
          case MONOMIAL:
            return std::make_unique<FE<2,MONOMIAL>>(fet);
 
#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
          case SZABAB:
            return std::make_unique<FE<2,SZABAB>>(fet);
 
          case BERNSTEIN:
            return std::make_unique<FE<2,BERNSTEIN>>(fet);
 
          case RATIONAL_BERNSTEIN:
            return std::make_unique<FE<2,RATIONAL_BERNSTEIN>>(fet);
#endif
 
          case XYZ:
            return std::make_unique<FEXYZ<2>>(fet);
 
          case SCALAR:
            return std::make_unique<FEScalar<2>>(fet);
 
          case SUBDIVISION:
            return std::make_unique<FESubdivision>(fet);
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
          }
      }
 
 
      // 3D
    case 3:
      {
        switch (fet.family)
          {
          case CLOUGH:
            libmesh_error_msg("ERROR: Clough-Tocher elements currently only support 1D and 2D");
 
          case HERMITE:
            return std::make_unique<FE<3,HERMITE>>(fet);
 
          case LAGRANGE:
            return std::make_unique<FE<3,LAGRANGE>>(fet);
 
          case L2_LAGRANGE:
            return std::make_unique<FE<3,L2_LAGRANGE>>(fet);
 
          case HIERARCHIC:
            return std::make_unique<FE<3,HIERARCHIC>>(fet);
 
          case L2_HIERARCHIC:
            return std::make_unique<FE<3,L2_HIERARCHIC>>(fet);
 
          case SIDE_HIERARCHIC:
            return std::make_unique<FE<3,SIDE_HIERARCHIC>>(fet);
 
          case MONOMIAL:
            return std::make_unique<FE<3,MONOMIAL>>(fet);
 
#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
          case SZABAB:
            return std::make_unique<FE<3,SZABAB>>(fet);
 
          case BERNSTEIN:
            return std::make_unique<FE<3,BERNSTEIN>>(fet);
 
          case RATIONAL_BERNSTEIN:
            return std::make_unique<FE<3,RATIONAL_BERNSTEIN>>(fet);
#endif
 
          case XYZ:
            return std::make_unique<FEXYZ<3>>(fet);
 
          case SCALAR:
            return std::make_unique<FEScalar<3>>(fet);
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
          }
      }
 
    default:
      libmesh_error_msg("Invalid dimension dim = " << dim);
    }
}

build() [2/3]

std::unique_ptr< FEGenericBase< RealGradient > > libMesh::FEGenericBase< RealGradient >::build ( const unsigned int  dim, const FEType &  fet  )

inherited

Definition at line 413 of file fe_base.C.

{
  switch (dim)
    {
      // 0D
    case 0:
      {
        switch (fet.family)
          {
          case HIERARCHIC_VEC:
            return std::make_unique<FEHierarchicVec<0>>(fet);
 
          case L2_HIERARCHIC_VEC:
            return std::make_unique<FEL2HierarchicVec<0>>(fet);
 
          case LAGRANGE_VEC:
            return std::make_unique<FELagrangeVec<0>>(fet);
 
          case L2_LAGRANGE_VEC:
            return std::make_unique<FEL2LagrangeVec<0>>(fet);
 
          case MONOMIAL_VEC:
            return std::make_unique<FEMonomialVec<0>>(fet);
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
          }
      }
    case 1:
      {
        switch (fet.family)
          {
          case HIERARCHIC_VEC:
            return std::make_unique<FEHierarchicVec<1>>(fet);
 
          case L2_HIERARCHIC_VEC:
            return std::make_unique<FEL2HierarchicVec<1>>(fet);
 
          case LAGRANGE_VEC:
            return std::make_unique<FELagrangeVec<1>>(fet);
 
          case L2_LAGRANGE_VEC:
            return std::make_unique<FEL2LagrangeVec<1>>(fet);
 
          case MONOMIAL_VEC:
            return std::make_unique<FEMonomialVec<1>>(fet);
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
          }
      }
    case 2:
      {
        switch (fet.family)
          {
          case HIERARCHIC_VEC:
            return std::make_unique<FEHierarchicVec<2>>(fet);
 
          case L2_HIERARCHIC_VEC:
            return std::make_unique<FEL2HierarchicVec<2>>(fet);
 
          case LAGRANGE_VEC:
            return std::make_unique<FELagrangeVec<2>>(fet);
 
          case L2_LAGRANGE_VEC:
            return std::make_unique<FEL2LagrangeVec<2>>(fet);
 
          case MONOMIAL_VEC:
            return std::make_unique<FEMonomialVec<2>>(fet);
 
          case NEDELEC_ONE:
            return std::make_unique<FENedelecOne<2>>(fet);
 
          case RAVIART_THOMAS:
            return std::make_unique<FERaviartThomas<2>>(fet);
 
          case L2_RAVIART_THOMAS:
            return std::make_unique<FEL2RaviartThomas<2>>(fet);
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
          }
      }
    case 3:
      {
        switch (fet.family)
          {
          case HIERARCHIC_VEC:
            return std::make_unique<FEHierarchicVec<3>>(fet);
 
          case L2_HIERARCHIC_VEC:
            return std::make_unique<FEL2HierarchicVec<3>>(fet);
 
          case LAGRANGE_VEC:
            return std::make_unique<FELagrangeVec<3>>(fet);
 
          case L2_LAGRANGE_VEC:
            return std::make_unique<FEL2LagrangeVec<3>>(fet);
 
          case MONOMIAL_VEC:
            return std::make_unique<FEMonomialVec<3>>(fet);
 
          case NEDELEC_ONE:
            return std::make_unique<FENedelecOne<3>>(fet);
 
          case RAVIART_THOMAS:
            return std::make_unique<FERaviartThomas<3>>(fet);
 
          case L2_RAVIART_THOMAS:
            return std::make_unique<FEL2RaviartThomas<3>>(fet);
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.family == " << Utility::enum_to_string(fet.family));
          }
      }
 
    default:
      libmesh_error_msg("Invalid dimension dim = " << dim);
    } // switch(dim)
}

build() [3/3]

static std::unique_ptr< FEGenericBase > libMesh::FEGenericBase< FEOutputType< T >::type >::build ( const unsigned int  dim, const FEType &  type  )

staticinherited

Builds a specific finite element type.

A std::unique_ptr<FEGenericBase> is returned to prevent a memory leak. This way the user need not remember to delete the object.

The build call will fail if the OutputType of this class is not compatible with the output required for the requested type

build_InfFE() [1/3]

std::unique_ptr< FEGenericBase< Real > > libMesh::FEGenericBase< Real >::build_InfFE ( const unsigned int  dim, const FEType &  fet  )

inherited

Definition at line 546 of file fe_base.C.

{
  switch (dim)
    {
 
      // 1D
    case 1:
      {
        switch (fet.radial_family)
          {
          case INFINITE_MAP:
            libmesh_error_msg("ERROR: Can't build an infinite element with FEFamily = " << Utility::enum_to_string(fet.radial_family));
 
          case JACOBI_20_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<1,JACOBI_20_00,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          case JACOBI_30_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<1,JACOBI_30_00,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          case LEGENDRE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<1,LEGENDRE,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          case LAGRANGE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<1,LAGRANGE,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.radial_family= " << Utility::enum_to_string(fet.radial_family));
          }
      }
 
 
 
 
      // 2D
    case 2:
      {
        switch (fet.radial_family)
          {
          case INFINITE_MAP:
            libmesh_error_msg("ERROR: Can't build an infinite element with FEFamily = " << Utility::enum_to_string(fet.radial_family));
 
          case JACOBI_20_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<2,JACOBI_20_00,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          case JACOBI_30_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<2,JACOBI_30_00,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          case LEGENDRE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<2,LEGENDRE,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          case LAGRANGE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<2,LAGRANGE,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.radial_family= " << Utility::enum_to_string(fet.radial_family));
          }
      }
 
 
 
 
      // 3D
    case 3:
      {
        switch (fet.radial_family)
          {
          case INFINITE_MAP:
            libmesh_error_msg("ERROR: Don't build an infinite element with FEFamily = " << Utility::enum_to_string(fet.radial_family));
 
          case JACOBI_20_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<3,JACOBI_20_00,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          case JACOBI_30_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<3,JACOBI_30_00,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          case LEGENDRE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<3,LEGENDRE,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          case LAGRANGE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return std::make_unique<InfFE<3,LAGRANGE,CARTESIAN>>(fet);
 
                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << Utility::enum_to_string(fet.inf_map));
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Bad FEType.radial_family= " << Utility::enum_to_string(fet.radial_family));
          }
      }
 
    default:
      libmesh_error_msg("Invalid dimension dim = " << dim);
    }
}

build_InfFE() [2/3]

static std::unique_ptr< FEGenericBase > libMesh::FEGenericBase< FEOutputType< T >::type >::build_InfFE ( const unsigned int  dim, const FEType &  type  )

staticinherited

Builds a specific infinite element type.

A std::unique_ptr<FEGenericBase> is returned to prevent a memory leak. This way the user need not remember to delete the object.

The build call will fail if the OutputShape of this class is not compatible with the output required for the requested type

build_InfFE() [3/3]

std::unique_ptr< FEGenericBase< RealGradient > > libMesh::FEGenericBase< RealGradient >::build_InfFE ( const unsigned int  , const FEType &    )

inherited

Definition at line 750 of file fe_base.C.

{
  // No vector types defined... YET.
  libmesh_not_implemented();
  return std::unique_ptr<FEVectorBase>();
}

cache()

void libMesh::FE< Dim, T >::cache ( const Elem *  elem )

protectedinherited

Repopulate the element cache with the node locations, edge and face orientations of the element elem.

Definition at line 803 of file fe.C.

{
  cached_nodes.resize(elem->n_nodes());
  for (auto n : elem->node_index_range())
    cached_nodes[n] = elem->point(n);
 
  if (FEInterface::orientation_dependent(T))
    {
      cached_edges.resize(elem->n_edges());
      for (auto n : elem->edge_index_range())
        cached_edges[n] = elem->positive_edge_orientation(n);
 
      cached_faces.resize(elem->n_faces());
      for (auto n : elem->face_index_range())
        cached_faces[n] = elem->positive_face_orientation(n);
    }
}

calculating_nothing()

bool libMesh::FEGenericBase< FEOutputType< T >::type >::calculating_nothing ( ) const

inlineprotectedinherited

Returns

true iff no calculations have been requested of this FE object or of its associated FEMap

Definition at line 568 of file fe_base.h.

  {
    return calculate_nothing &&
      !this->calculate_phi && !this->calculate_dphi &&
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
      !this->calculate_d2phi &&
#endif
      !this->calculate_curl_phi && !this->calculate_div_phi &&
      !this->calculate_map;
  }

coarsened_dof_values() [1/2]

void libMesh::FEGenericBase< FEOutputType< T >::type >::coarsened_dof_values ( const NumericVector< Number > &  global_vector, const DofMap &  dof_map, const Elem *  coarse_elem, DenseVector< Number > &  coarse_dofs, const bool  use_old_dof_indices = false  )

staticinherited

Creates a local projection on coarse_elem, based on the DoF values in global_vector for it's children.

Computes a vector of coefficients corresponding to all dof_indices.

Definition at line 178 of file fe_base.C.

{
  Ue.resize(0);
 
  for (auto v : make_range(dof_map.n_variables()))
    {
      DenseVector<Number> Usub;
 
      coarsened_dof_values(old_vector, dof_map, elem, Usub,
                           v, use_old_dof_indices);
 
      Ue.append (Usub);
    }
}

coarsened_dof_values() [2/2]

void libMesh::FEGenericBase< FEOutputType< T >::type >::coarsened_dof_values ( const NumericVector< Number > &  global_vector, const DofMap &  dof_map, const Elem *  coarse_elem, DenseVector< Number > &  coarse_dofs, const unsigned int  var, const bool  use_old_dof_indices = false  )

staticinherited

Creates a local projection on coarse_elem, based on the DoF values in global_vector for it's children.

Computes a vector of coefficients corresponding to dof_indices for only the single given var

Definition at line 165 of file fe_base.C.

{
  // Side/edge local DOF indices
  std::vector<unsigned int> new_side_dofs, old_side_dofs;
 
  // FIXME: what about 2D shells in 3D space?
  unsigned int dim = elem->dim();
 
  // Cache n_children(); it's a virtual call but it's const.
  const unsigned int n_children = elem->n_children();
 
  // We use local FE objects for now
  // FIXME: we should use more, external objects instead for efficiency
  const FEType & base_fe_type = dof_map.variable_type(var);
  std::unique_ptr<FEGenericBase<OutputShape>> fe
    (FEGenericBase<OutputShape>::build(dim, base_fe_type));
  std::unique_ptr<FEGenericBase<OutputShape>> fe_coarse
    (FEGenericBase<OutputShape>::build(dim, base_fe_type));
 
  std::unique_ptr<QBase> qrule     (base_fe_type.default_quadrature_rule(dim));
  std::unique_ptr<QBase> qedgerule (base_fe_type.default_quadrature_rule(1));
  std::unique_ptr<QBase> qsiderule (base_fe_type.default_quadrature_rule(dim-1));
  std::vector<Point> coarse_qpoints;
 
  // The values of the shape functions at the quadrature
  // points
  const std::vector<std::vector<OutputShape>> & phi_values =
    fe->get_phi();
  const std::vector<std::vector<OutputShape>> & phi_coarse =
    fe_coarse->get_phi();
 
  // The gradients of the shape functions at the quadrature
  // points on the child element.
  const std::vector<std::vector<OutputGradient>> * dphi_values =
    nullptr;
  const std::vector<std::vector<OutputGradient>> * dphi_coarse =
    nullptr;
 
  const FEContinuity cont = fe->get_continuity();
 
  if (cont == C_ONE)
    {
      const std::vector<std::vector<OutputGradient>> &
        ref_dphi_values = fe->get_dphi();
      dphi_values = &ref_dphi_values;
      const std::vector<std::vector<OutputGradient>> &
        ref_dphi_coarse = fe_coarse->get_dphi();
      dphi_coarse = &ref_dphi_coarse;
    }
 
  // The Jacobian * quadrature weight at the quadrature points
  const std::vector<Real> & JxW =
    fe->get_JxW();
 
  // The XYZ locations of the quadrature points on the
  // child element
  const std::vector<Point> & xyz_values =
    fe->get_xyz();
 
  // Number of nodes on parent element
  const unsigned int n_nodes = elem->n_nodes();
 
  // Number of dofs on parent element
  const unsigned int new_n_dofs =
    FEInterface::n_dofs(base_fe_type, elem->max_descendant_p_level(), elem);
 
  // Fixed vs. free DoFs on edge/face projections
  std::vector<char> dof_is_fixed(new_n_dofs, false); // bools
  std::vector<int> free_dof(new_n_dofs, 0);
 
  DenseMatrix<Real> Ke;
  DenseVector<Number> Fe;
  Ue.resize(new_n_dofs); Ue.zero();
 
 
  // When coarsening, in general, we need a series of
  // projections to ensure a unique and continuous
  // solution.  We start by interpolating nodes, then
  // hold those fixed and project edges, then
  // hold those fixed and project faces, then
  // hold those fixed and project interiors
 
  // Copy node values first
  {
    std::vector<dof_id_type> node_dof_indices;
    if (use_old_dof_indices)
      dof_map.old_dof_indices (elem, node_dof_indices, var);
    else
      dof_map.dof_indices (elem, node_dof_indices, var);
 
    unsigned int current_dof = 0;
    for (unsigned int n=0; n!= n_nodes; ++n)
      {
        // FIXME: this should go through the DofMap,
        // not duplicate dof_indices code badly!
        const unsigned int my_nc =
          FEInterface::n_dofs_at_node (base_fe_type, elem->max_descendant_p_level(), elem, n);
        if (!elem->is_vertex(n))
          {
            current_dof += my_nc;
            continue;
          }
 
        // We're assuming here that child n shares vertex n,
        // which is wrong on non-simplices right now
        // ... but this code isn't necessary except on elements
        // where p refinement creates more vertex dofs; we have
        // no such elements yet.
        int extra_order = 0;
        // if (elem->child_ptr(n)->p_level() < elem->p_level())
        //   extra_order = elem->child_ptr(n)->p_level();
        const unsigned int nc =
          FEInterface::n_dofs_at_node (base_fe_type, extra_order, elem, n);
        for (unsigned int i=0; i!= nc; ++i)
          {
            Ue(current_dof) =
              old_vector(node_dof_indices[current_dof]);
            dof_is_fixed[current_dof] = true;
            current_dof++;
          }
      }
  }
 
  FEType fe_type = base_fe_type, temp_fe_type;
  fe_type.order = fe_type.order + elem->max_descendant_p_level();
 
  // In 3D, project any edge values next
  if (dim > 2 && cont != DISCONTINUOUS)
    for (auto e : elem->edge_index_range())
      {
        FEInterface::dofs_on_edge(elem, dim, fe_type,
                                  e, new_side_dofs);
 
        const unsigned int n_new_side_dofs =
          cast_int<unsigned int>(new_side_dofs.size());
 
        // Some edge dofs are on nodes and already
        // fixed, others are free to calculate
        unsigned int free_dofs = 0;
        for (unsigned int i=0; i != n_new_side_dofs; ++i)
          if (!dof_is_fixed[new_side_dofs[i]])
            free_dof[free_dofs++] = i;
        Ke.resize (free_dofs, free_dofs); Ke.zero();
        Fe.resize (free_dofs); Fe.zero();
        // The new edge coefficients
        DenseVector<Number> Uedge(free_dofs);
 
        // Add projection terms from each child sharing
        // this edge
        for (unsigned int c=0; c != n_children; ++c)
          {
            if (!elem->is_child_on_edge(c,e))
              continue;
            const Elem * child = elem->child_ptr(c);
 
            std::vector<dof_id_type> child_dof_indices;
            if (use_old_dof_indices)
              dof_map.old_dof_indices (child,
                                       child_dof_indices, var);
            else
              dof_map.dof_indices (child,
                                   child_dof_indices, var);
            const unsigned int child_n_dofs =
              cast_int<unsigned int>
              (child_dof_indices.size());
 
            temp_fe_type = base_fe_type;
            temp_fe_type.order = temp_fe_type.order + child->p_level();
 
            FEInterface::dofs_on_edge(child, dim,
                                      temp_fe_type, e, old_side_dofs);
 
            // Initialize both child and parent FE data
            // on the child's edge
            fe->attach_quadrature_rule (qedgerule.get());
            fe->edge_reinit (child, e);
            const unsigned int n_qp = qedgerule->n_points();
 
            FEMap::inverse_map (dim, elem, xyz_values,
                                coarse_qpoints);
 
            fe_coarse->reinit(elem, &coarse_qpoints);
 
            // Loop over the quadrature points
            for (unsigned int qp=0; qp<n_qp; qp++)
              {
                // solution value at the quadrature point
                OutputNumber fineval = libMesh::zero;
                // solution grad at the quadrature point
                OutputNumberGradient finegrad;
 
                // Sum the solution values * the DOF
                // values at the quadrature point to
                // get the solution value and gradient.
                for (unsigned int i=0; i<child_n_dofs;
                     i++)
                  {
                    fineval +=
                      (old_vector(child_dof_indices[i])*
                       phi_values[i][qp]);
                    if (cont == C_ONE)
                      finegrad += (*dphi_values)[i][qp] *
                        old_vector(child_dof_indices[i]);
                  }
 
                // Form edge projection matrix
                for (unsigned int sidei=0, freei=0; sidei != n_new_side_dofs; ++sidei)
                  {
                    unsigned int i = new_side_dofs[sidei];
                    // fixed DoFs aren't test functions
                    if (dof_is_fixed[i])
                      continue;
                    for (unsigned int sidej=0, freej=0; sidej != n_new_side_dofs; ++sidej)
                      {
                        unsigned int j =
                          new_side_dofs[sidej];
                        if (dof_is_fixed[j])
                          Fe(freei) -=
                            TensorTools::inner_product(phi_coarse[i][qp],
                                                       phi_coarse[j][qp]) *
                            JxW[qp] * Ue(j);
                        else
                          Ke(freei,freej) +=
                            TensorTools::inner_product(phi_coarse[i][qp],
                                                       phi_coarse[j][qp]) *
                            JxW[qp];
                        if (cont == C_ONE)
                          {
                            if (dof_is_fixed[j])
                              Fe(freei) -=
                                TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                           (*dphi_coarse)[j][qp]) *
                                JxW[qp] * Ue(j);
                            else
                              Ke(freei,freej) +=
                                TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                           (*dphi_coarse)[j][qp]) *
                                JxW[qp];
                          }
                        if (!dof_is_fixed[j])
                          freej++;
                      }
                    Fe(freei) += TensorTools::inner_product(phi_coarse[i][qp],
                                                            fineval) * JxW[qp];
                    if (cont == C_ONE)
                      Fe(freei) +=
                        TensorTools::inner_product(finegrad, (*dphi_coarse)[i][qp]) * JxW[qp];
                    freei++;
                  }
              }
          }
        Ke.cholesky_solve(Fe, Uedge);
 
        // Transfer new edge solutions to element
        for (unsigned int i=0; i != free_dofs; ++i)
          {
            Number & ui = Ue(new_side_dofs[free_dof[i]]);
            libmesh_assert(std::abs(ui) < TOLERANCE ||
                           std::abs(ui - Uedge(i)) < TOLERANCE);
            ui = Uedge(i);
            dof_is_fixed[new_side_dofs[free_dof[i]]] = true;
          }
      }
 
  // Project any side values (edges in 2D, faces in 3D)
  if (dim > 1 && cont != DISCONTINUOUS)
    for (auto s : elem->side_index_range())
      {
        FEInterface::dofs_on_side(elem, dim, fe_type,
                                  s, new_side_dofs);
 
        const unsigned int n_new_side_dofs =
          cast_int<unsigned int>(new_side_dofs.size());
 
        // Some side dofs are on nodes/edges and already
        // fixed, others are free to calculate
        unsigned int free_dofs = 0;
        for (unsigned int i=0; i != n_new_side_dofs; ++i)
          if (!dof_is_fixed[new_side_dofs[i]])
            free_dof[free_dofs++] = i;
        Ke.resize (free_dofs, free_dofs); Ke.zero();
        Fe.resize (free_dofs); Fe.zero();
        // The new side coefficients
        DenseVector<Number> Uside(free_dofs);
 
        // Add projection terms from each child sharing
        // this side
        for (unsigned int c=0; c != n_children; ++c)
          {
            if (!elem->is_child_on_side(c,s))
              continue;
            const Elem * child = elem->child_ptr(c);
 
            std::vector<dof_id_type> child_dof_indices;
            if (use_old_dof_indices)
              dof_map.old_dof_indices (child,
                                       child_dof_indices, var);
            else
              dof_map.dof_indices (child,
                                   child_dof_indices, var);
            const unsigned int child_n_dofs =
              cast_int<unsigned int>
              (child_dof_indices.size());
 
            temp_fe_type = base_fe_type;
            temp_fe_type.order = temp_fe_type.order + child->p_level();
 
            FEInterface::dofs_on_side(child, dim,
                                      temp_fe_type, s, old_side_dofs);
 
            // Initialize both child and parent FE data
            // on the child's side
            fe->attach_quadrature_rule (qsiderule.get());
            fe->reinit (child, s);
            const unsigned int n_qp = qsiderule->n_points();
 
            FEMap::inverse_map (dim, elem, xyz_values,
                                coarse_qpoints);
 
            fe_coarse->reinit(elem, &coarse_qpoints);
 
            // Loop over the quadrature points
            for (unsigned int qp=0; qp<n_qp; qp++)
              {
                // solution value at the quadrature point
                OutputNumber fineval = libMesh::zero;
                // solution grad at the quadrature point
                OutputNumberGradient finegrad;
 
                // Sum the solution values * the DOF
                // values at the quadrature point to
                // get the solution value and gradient.
                for (unsigned int i=0; i<child_n_dofs;
                     i++)
                  {
                    fineval +=
                      old_vector(child_dof_indices[i]) *
                      phi_values[i][qp];
                    if (cont == C_ONE)
                      finegrad += (*dphi_values)[i][qp] *
                        old_vector(child_dof_indices[i]);
                  }
 
                // Form side projection matrix
                for (unsigned int sidei=0, freei=0; sidei != n_new_side_dofs; ++sidei)
                  {
                    unsigned int i = new_side_dofs[sidei];
                    // fixed DoFs aren't test functions
                    if (dof_is_fixed[i])
                      continue;
                    for (unsigned int sidej=0, freej=0; sidej != n_new_side_dofs; ++sidej)
                      {
                        unsigned int j =
                          new_side_dofs[sidej];
                        if (dof_is_fixed[j])
                          Fe(freei) -=
                            TensorTools::inner_product(phi_coarse[i][qp],
                                                       phi_coarse[j][qp]) *
                            JxW[qp] * Ue(j);
                        else
                          Ke(freei,freej) +=
                            TensorTools::inner_product(phi_coarse[i][qp],
                                                       phi_coarse[j][qp]) *
                            JxW[qp];
                        if (cont == C_ONE)
                          {
                            if (dof_is_fixed[j])
                              Fe(freei) -=
                                TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                           (*dphi_coarse)[j][qp]) *
                                JxW[qp] * Ue(j);
                            else
                              Ke(freei,freej) +=
                                TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                           (*dphi_coarse)[j][qp]) *
                                JxW[qp];
                          }
                        if (!dof_is_fixed[j])
                          freej++;
                      }
                    Fe(freei) += TensorTools::inner_product(fineval, phi_coarse[i][qp]) * JxW[qp];
                    if (cont == C_ONE)
                      Fe(freei) +=
                        TensorTools::inner_product(finegrad, (*dphi_coarse)[i][qp]) * JxW[qp];
                    freei++;
                  }
              }
          }
        Ke.cholesky_solve(Fe, Uside);
 
        // Transfer new side solutions to element
        for (unsigned int i=0; i != free_dofs; ++i)
          {
            Number & ui = Ue(new_side_dofs[free_dof[i]]);
            libmesh_assert(std::abs(ui) < TOLERANCE ||
                           std::abs(ui - Uside(i)) < TOLERANCE);
            ui = Uside(i);
            dof_is_fixed[new_side_dofs[free_dof[i]]] = true;
          }
      }
 
  // Project the interior values, finally
 
  // Some interior dofs are on nodes/edges/sides and
  // already fixed, others are free to calculate
  unsigned int free_dofs = 0;
  for (unsigned int i=0; i != new_n_dofs; ++i)
    if (!dof_is_fixed[i])
      free_dof[free_dofs++] = i;
  Ke.resize (free_dofs, free_dofs); Ke.zero();
  Fe.resize (free_dofs); Fe.zero();
  // The new interior coefficients
  DenseVector<Number> Uint(free_dofs);
 
  // Add projection terms from each child
  for (auto & child : elem->child_ref_range())
    {
      std::vector<dof_id_type> child_dof_indices;
      if (use_old_dof_indices)
        dof_map.old_dof_indices (&child,
                                 child_dof_indices, var);
      else
        dof_map.dof_indices (&child,
                             child_dof_indices, var);
      const unsigned int child_n_dofs =
        cast_int<unsigned int>
        (child_dof_indices.size());
 
      // Initialize both child and parent FE data
      // on the child's quadrature points
      fe->attach_quadrature_rule (qrule.get());
      fe->reinit (&child);
      const unsigned int n_qp = qrule->n_points();
 
      FEMap::inverse_map (dim, elem, xyz_values, coarse_qpoints);
 
      fe_coarse->reinit(elem, &coarse_qpoints);
 
      // Loop over the quadrature points
      for (unsigned int qp=0; qp<n_qp; qp++)
        {
          // solution value at the quadrature point
          OutputNumber fineval = libMesh::zero;
          // solution grad at the quadrature point
          OutputNumberGradient finegrad;
 
          // Sum the solution values * the DOF
          // values at the quadrature point to
          // get the solution value and gradient.
          for (unsigned int i=0; i<child_n_dofs; i++)
            {
              fineval +=
                (old_vector(child_dof_indices[i]) *
                 phi_values[i][qp]);
              if (cont == C_ONE)
                finegrad += (*dphi_values)[i][qp] *
                  old_vector(child_dof_indices[i]);
            }
 
          // Form interior projection matrix
          for (unsigned int i=0, freei=0;
               i != new_n_dofs; ++i)
            {
              // fixed DoFs aren't test functions
              if (dof_is_fixed[i])
                continue;
              for (unsigned int j=0, freej=0; j !=
                     new_n_dofs; ++j)
                {
                  if (dof_is_fixed[j])
                    Fe(freei) -=
                      TensorTools::inner_product(phi_coarse[i][qp],
                                                 phi_coarse[j][qp]) *
                      JxW[qp] * Ue(j);
                  else
                    Ke(freei,freej) +=
                      TensorTools::inner_product(phi_coarse[i][qp],
                                                 phi_coarse[j][qp]) *
                      JxW[qp];
                  if (cont == C_ONE)
                    {
                      if (dof_is_fixed[j])
                        Fe(freei) -=
                          TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                     (*dphi_coarse)[j][qp]) *
                          JxW[qp] * Ue(j);
                      else
                        Ke(freei,freej) +=
                          TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                     (*dphi_coarse)[j][qp]) *
                          JxW[qp];
                    }
                  if (!dof_is_fixed[j])
                    freej++;
                }
              Fe(freei) += TensorTools::inner_product(phi_coarse[i][qp], fineval) *
                JxW[qp];
              if (cont == C_ONE)
                Fe(freei) += TensorTools::inner_product(finegrad, (*dphi_coarse)[i][qp]) * JxW[qp];
              freei++;
            }
        }
    }
  Ke.cholesky_solve(Fe, Uint);
 
  // Transfer new interior solutions to element
  for (unsigned int i=0; i != free_dofs; ++i)
    {
      Number & ui = Ue(free_dof[i]);
      libmesh_assert(std::abs(ui) < TOLERANCE ||
                     std::abs(ui - Uint(i)) < TOLERANCE);
      ui = Uint(i);
      // We should be fixing all dofs by now; no need to keep track of
      // that unless we're debugging
#ifndef NDEBUG
      dof_is_fixed[free_dof[i]] = true;
#endif
    }
 
#ifndef NDEBUG
  // Make sure every DoF got reached!
  for (unsigned int i=0; i != new_n_dofs; ++i)
    libmesh_assert(dof_is_fixed[i]);
#endif
}

compute_constraints() [1/49]

void libMesh::FE< 2, L2_HIERARCHIC >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 202 of file fe_l2_hierarchic.C.

{ }

compute_constraints() [2/49]

void libMesh::FE< 3, L2_HIERARCHIC >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 209 of file fe_l2_hierarchic.C.

{ }

compute_constraints() [3/49]

void libMesh::FE< 2, L2_LAGRANGE >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 277 of file fe_l2_lagrange.C.

{ }

compute_constraints() [4/49]

void libMesh::FE< 3, L2_LAGRANGE >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 284 of file fe_l2_lagrange.C.

{ }

compute_constraints() [5/49]

void libMesh::FE< 2, MONOMIAL >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 438 of file fe_monomial.C.

{}

compute_constraints() [6/49]

void libMesh::FE< 3, MONOMIAL >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 439 of file fe_monomial.C.

{}

compute_constraints() [7/49]

void libMesh::FE< 2, MONOMIAL_VEC >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 778 of file fe_monomial_vec.C.

{
}

compute_constraints() [8/49]

void libMesh::FE< 3, MONOMIAL_VEC >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 787 of file fe_monomial_vec.C.

{
}

compute_constraints() [9/49]

void libMesh::FE< 0, NEDELEC_ONE >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 427 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

compute_constraints() [10/49]

void libMesh::FE< 1, NEDELEC_ONE >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 434 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

compute_constraints() [11/49]

void libMesh::FE< 0, RAVIART_THOMAS >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 491 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

compute_constraints() [12/49]

void libMesh::FE< 1, RAVIART_THOMAS >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 498 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

compute_constraints() [13/49]

void libMesh::FE< 0, L2_RAVIART_THOMAS >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 519 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

compute_constraints() [14/49]

void libMesh::FE< 1, L2_RAVIART_THOMAS >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 526 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

compute_constraints() [15/49]

void libMesh::FE< 2, SCALAR >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 110 of file fe_scalar.C.

{ }

compute_constraints() [16/49]

void libMesh::FE< 3, SCALAR >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 117 of file fe_scalar.C.

{ }

compute_constraints() [17/49]

void libMesh::FE< 2, XYZ >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 423 of file fe_xyz.C.

{}

compute_constraints() [18/49]

void libMesh::FE< 3, XYZ >::compute_constraints ( DofConstraints &  , DofMap &  , const unsigned int  , const Elem *    )

inherited

Definition at line 424 of file fe_xyz.C.

{}

compute_constraints() [19/49]

static void libMesh::FE< Dim, T >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

staticinherited

Computes the constraint matrix contributions (for non-conforming adapted meshes) corresponding to variable number var_number, using element-specific optimizations if possible.

compute_constraints() [20/49]

void libMesh::FE< 2, BERNSTEIN >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 436 of file fe_bernstein.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [21/49]

void libMesh::FE< 3, BERNSTEIN >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 443 of file fe_bernstein.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [22/49]

void libMesh::FE< 2, CLOUGH >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 284 of file fe_clough.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [23/49]

void libMesh::FE< 3, CLOUGH >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 291 of file fe_clough.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [24/49]

void libMesh::FE< 2, HERMITE >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 327 of file fe_hermite.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [25/49]

void libMesh::FE< 3, HERMITE >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 334 of file fe_hermite.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [26/49]

void libMesh::FE< 2, HIERARCHIC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 490 of file fe_hierarchic.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [27/49]

void libMesh::FE< 3, HIERARCHIC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 497 of file fe_hierarchic.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [28/49]

void libMesh::FE< 2, HIERARCHIC_VEC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 810 of file fe_hierarchic_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [29/49]

void libMesh::FE< 3, HIERARCHIC_VEC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 819 of file fe_hierarchic_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [30/49]

void libMesh::FE< 2, L2_HIERARCHIC_VEC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 828 of file fe_hierarchic_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [31/49]

void libMesh::FE< 3, L2_HIERARCHIC_VEC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 837 of file fe_hierarchic_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [32/49]

void libMesh::FE< 2, LAGRANGE >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 1137 of file fe_lagrange.C.

{ lagrange_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/2); }

compute_constraints() [33/49]

void libMesh::FE< 3, LAGRANGE >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 1144 of file fe_lagrange.C.

{ lagrange_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/3); }

compute_constraints() [34/49]

void libMesh::FE< 2, LAGRANGE_VEC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 1379 of file fe_lagrange_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [35/49]

void libMesh::FE< 3, LAGRANGE_VEC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 1388 of file fe_lagrange_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [36/49]

void libMesh::FE< 2, L2_LAGRANGE_VEC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 1397 of file fe_lagrange_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [37/49]

void libMesh::FE< 3, L2_LAGRANGE_VEC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 1406 of file fe_lagrange_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [38/49]

void libMesh::FE< 2, NEDELEC_ONE >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 441 of file fe_nedelec_one.C.

{ nedelec_one_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/2); }

compute_constraints() [39/49]

void libMesh::FE< 3, NEDELEC_ONE >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 448 of file fe_nedelec_one.C.

{ nedelec_one_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/3); }

compute_constraints() [40/49]

void libMesh::FE< 2, RATIONAL_BERNSTEIN >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 174 of file fe_rational.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [41/49]

void libMesh::FE< 3, RATIONAL_BERNSTEIN >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 181 of file fe_rational.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [42/49]

void libMesh::FE< 2, RAVIART_THOMAS >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 505 of file fe_raviart.C.

{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/2); }

compute_constraints() [43/49]

void libMesh::FE< 3, RAVIART_THOMAS >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 512 of file fe_raviart.C.

{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/3); }

compute_constraints() [44/49]

void libMesh::FE< 2, L2_RAVIART_THOMAS >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 533 of file fe_raviart.C.

{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/2); }

compute_constraints() [45/49]

void libMesh::FE< 3, L2_RAVIART_THOMAS >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 540 of file fe_raviart.C.

{ raviart_thomas_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/3); }

compute_constraints() [46/49]

void libMesh::FE< 2, SIDE_HIERARCHIC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 341 of file fe_side_hierarchic.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [47/49]

void libMesh::FE< 3, SIDE_HIERARCHIC >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 348 of file fe_side_hierarchic.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [48/49]

void libMesh::FE< 2, SZABAB >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 1339 of file fe_szabab.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [49/49]

void libMesh::FE< 3, SZABAB >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

inherited

Definition at line 1346 of file fe_szabab.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_dual_shape_coeffs() [1/3]

void libMesh::FEGenericBase< Real >::compute_dual_shape_coeffs ( const std::vector< Real > &  , const std::vector< std::vector< OutputShape > > &    )

protectedinherited

compute_dual_shape_coeffs() [2/3]

void libMesh::FEGenericBase< FEOutputType< T >::type >::compute_dual_shape_coeffs ( const std::vector< Real > &  JxW, const std::vector< std::vector< OutputShape > > &  phi  )

protectedinherited

Compute the dual basis coefficients dual_coeff we rely on the JxW (or weights) and the phi values, which can come from default or customized qrule.

Definition at line 596 of file fe_base.h.

{
  libmesh_error_msg(
      "Computation of dual shape functions for vector finite element "
      "families is not currently implemented");
}

compute_dual_shape_coeffs() [3/3]

void libMesh::FEGenericBase< Real >::compute_dual_shape_coeffs ( const std::vector< Real > &  JxW, const std::vector< std::vector< OutputShape > > &  phi_vals  )

protectedinherited

Definition at line 804 of file fe_base.C.

{
  // Start logging the dual coeff computation
  LOG_SCOPE("compute_dual_shape_coeffs()", "FE");
 
  const unsigned int sz=phi_vals.size();
  libmesh_error_msg_if(!sz, "ERROR: cannot compute dual shape coefficients with empty phi values");
 
  //compute dual basis coefficient (dual_coeff)
  dual_coeff.resize(sz, sz);
  DenseMatrix<Real> A(sz, sz), D(sz, sz);
 
  for (const auto i : index_range(phi_vals))
    for (const auto qp : index_range(phi_vals[i]))
    {
      D(i,i) += JxW[qp]*phi_vals[i][qp];
      for (const auto j : index_range(phi_vals))
        A(i,j) += JxW[qp]*phi_vals[i][qp]*phi_vals[j][qp];
    }
 
  // dual_coeff = A^-1*D
  for (const auto j : index_range(phi_vals))
  {
    DenseVector<Real> Dcol(sz), coeffcol(sz);
    for (const auto i : index_range(phi_vals))
      Dcol(i) = D(i, j);
    A.cholesky_solve(Dcol, coeffcol);
 
    for (const auto row : index_range(phi_vals))
      dual_coeff(row, j)=coeffcol(row);
  }
}

compute_dual_shape_functions() [1/3]

void libMesh::FEGenericBase< FEOutputType< T >::type >::compute_dual_shape_functions ( )

protectedinherited

Compute dual_phi, dual_dphi, dual_d2phi It is only valid for this to be called after reinit has occurred with a quadrature rule.

Definition at line 603 of file fe_base.h.

{
  libmesh_error_msg(
      "Computation of dual shape functions for vector finite element "
      "families is not currently implemented");
}

compute_dual_shape_functions() [2/3]

void libMesh::FEGenericBase< Real >::compute_dual_shape_functions ( )

protectedinherited

compute_dual_shape_functions() [3/3]

void libMesh::FEGenericBase< Real >::compute_dual_shape_functions ( )

protectedinherited

Definition at line 838 of file fe_base.C.

{
  // Start logging the shape function computation
  LOG_SCOPE("compute_dual_shape_functions()", "FE");
 
  // The dual coeffs matrix should have the same size as phi
  libmesh_assert(dual_coeff.m() == phi.size());
  libmesh_assert(dual_coeff.n() == phi.size());
 
  // initialize dual basis
  for (const auto j : index_range(phi))
    for (const auto qp : index_range(phi[j]))
    {
      dual_phi[j][qp] = 0;
      if (calculate_dphi)
        dual_dphi[j][qp] = 0;
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
      if (calculate_d2phi)
        dual_d2phi[j][qp] = 0;
#endif
    }
 
  // compute dual basis
  for (const auto j : index_range(phi))
    for (const auto i : index_range(phi))
      for (const auto qp : index_range(phi[j]))
      {
        dual_phi[j][qp] += dual_coeff(i, j) * phi[i][qp];
        if (calculate_dphi)
          dual_dphi[j][qp] += dual_coeff(i, j) * dphi[i][qp];
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
        if (calculate_d2phi)
          dual_d2phi[j][qp] += dual_coeff(i, j) * d2phi[i][qp];
#endif
      }
}

compute_node_constraints()

void libMesh::FEAbstract::compute_node_constraints ( NodeConstraints &  constraints, const Elem *  elem  )

staticinherited

Computes the nodal constraint contributions (for non-conforming adapted meshes), using Lagrange geometry.

Definition at line 886 of file fe_abstract.C.

{
  libmesh_assert(elem);
 
  const unsigned int Dim = elem->dim();
 
  // Only constrain elements in 2,3D.
  if (Dim == 1)
    return;
 
  // Only constrain active and ancestor elements
  if (elem->subactive())
    return;
 
 
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
  if (elem->infinite())
    {
      const FEType fe_t(elem->default_order(), FEMap::map_fe_type(*elem));
 
      // expand the infinite_compute_constraint in its template-arguments.
      switch(Dim)
      {
         case 2:
            {
            inf_fe_family_mapping_switch(2, inf_compute_node_constraints (constraints, elem) , ,; break;);
            break;
          }
         case 3:
            {
            inf_fe_family_mapping_switch(3, inf_compute_node_constraints (constraints, elem) , ,; break;);
            break;
            }
         default:
           libmesh_error_msg("Invalid dim = " << Dim);
      }
      return;
    }
 
#endif
  const FEFamily mapping_family = FEMap::map_fe_type(*elem);
  const FEType fe_type(elem->default_side_order(), mapping_family);
 
  // Pull objects out of the loop to reduce heap operations
  std::vector<const Node *> my_nodes, parent_nodes;
  std::unique_ptr<const Elem> my_side, parent_side;
 
  // Look at the element faces.  Check to see if we need to
  // build constraints.
  for (auto s : elem->side_index_range())
    if (elem->neighbor_ptr(s) != nullptr &&
        elem->neighbor_ptr(s) != remote_elem)
      if (elem->neighbor_ptr(s)->level() < elem->level()) // constrain dofs shared between
        {                                                 // this element and ones coarser
          // than this element.
          // Get pointers to the elements of interest and its parent.
          const Elem * parent = elem->parent();
 
          // This can't happen...  Only level-0 elements have nullptr
          // parents, and no level-0 elements can be at a higher
          // level than their neighbors!
          libmesh_assert(parent);
 
          elem->build_side_ptr(my_side, s);
          parent->build_side_ptr(parent_side, s);
 
          const unsigned int n_side_nodes = my_side->n_nodes();
 
          my_nodes.clear();
          my_nodes.reserve (n_side_nodes);
          parent_nodes.clear();
          parent_nodes.reserve (n_side_nodes);
 
          for (unsigned int n=0; n != n_side_nodes; ++n)
            my_nodes.push_back(my_side->node_ptr(n));
 
          for (unsigned int n=0; n != n_side_nodes; ++n)
            parent_nodes.push_back(parent_side->node_ptr(n));
 
          for (unsigned int my_side_n=0;
               my_side_n < n_side_nodes;
               my_side_n++)
            {
              // We can have an FE type that supports an order
              // partially, such that sides do not support the same
              // order.  E.g. we say that a LAGRANGE PRISM21 supports
              // "third" order to distinguish its shape functions from
              // a PRISM18, but the QUAD9 sides will still only
              // support second order.
              FEType side_fe_type = fe_type;
              const int side_max_order =
                FEInterface::max_order(fe_type, my_side->type());
 
              if ((int)fe_type.order > side_max_order)
                side_fe_type.order = side_max_order;
 
              // Do not use the p_level(), if any, that is inherited by the side.
              libmesh_assert_less
                (my_side_n,
                 FEInterface::n_dofs(side_fe_type, /*extra_order=*/0,
                                     my_side.get()));
 
              const Node * my_node = my_nodes[my_side_n];
 
              // The support point of the DOF
              const Point & support_point = *my_node;
 
              // Figure out where my node lies on their reference element.
              const Point mapped_point = FEMap::inverse_map(Dim-1,
                                                            parent_side.get(),
                                                            support_point);
 
              // Compute the parent's side shape function values.
              for (unsigned int their_side_n=0;
                   their_side_n < n_side_nodes;
                   their_side_n++)
                {
                  // Do not use the p_level(), if any, that is inherited by the side.
                  libmesh_assert_less
                    (their_side_n,
                     FEInterface::n_dofs(side_fe_type,
                                         /*extra_order=*/0,
                                         parent_side.get()));
 
                  const Node * their_node = parent_nodes[their_side_n];
                  libmesh_assert(their_node);
 
                  // Do not use the p_level(), if any, that is inherited by the side.
                  const Real their_value = FEInterface::shape(side_fe_type,
                                                              /*extra_order=*/0,
                                                              parent_side.get(),
                                                              their_side_n,
                                                              mapped_point);
 
                  const Real their_mag = std::abs(their_value);
#ifdef DEBUG
                  // Protect for the case u_i ~= u_j,
                  // in which case i better equal j.
                  if (their_mag > 0.999)
                    {
                      libmesh_assert_equal_to (my_node, their_node);
                      libmesh_assert_less (std::abs(their_value - 1.), 0.001);
                    }
                  else
#endif
                    // To make nodal constraints useful for constructing
                    // sparsity patterns faster, we need to get EVERY
                    // POSSIBLE constraint coupling identified, even if
                    // there is no coupling in the isoparametric
                    // Lagrange case.
                    if (their_mag < 1.e-5)
                      {
                        // since we may be running this method concurrently
                        // on multiple threads we need to acquire a lock
                        // before modifying the shared constraint_row object.
                        Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
 
                        // A reference to the constraint row.
                        NodeConstraintRow & constraint_row = constraints[my_node].first;
 
                        constraint_row.emplace(their_node, 0.);
                      }
                  // To get nodal coordinate constraints right, only
                  // add non-zero and non-identity values for Lagrange
                  // basis functions.
                    else // (1.e-5 <= their_mag <= .999)
                      {
                        // since we may be running this method concurrently
                        // on multiple threads we need to acquire a lock
                        // before modifying the shared constraint_row object.
                        Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
 
                        // A reference to the constraint row.
                        NodeConstraintRow & constraint_row = constraints[my_node].first;
 
                        constraint_row.emplace(their_node, their_value);
                      }
                }
            }
        }
}

References libMesh::Elem::build_side_ptr(), libMesh::Elem::default_order(), libMesh::Elem::default_side_order(), libMesh::Elem::dim(), libMesh::FEAbstract::fe_type, libMesh::Elem::infinite(), libMesh::FEMap::inverse_map(), libMesh::Elem::level(), libMesh::libmesh_assert(), libMesh::FEMap::map_fe_type(), libMesh::FEInterface::max_order(), libMesh::FEInterface::n_dofs(), libMesh::Elem::neighbor_ptr(), libMesh::FEType::order, libMesh::Elem::parent(), libMesh::Real, libMesh::remote_elem, libMesh::FEInterface::shape(), libMesh::Elem::side_index_range(), libMesh::Threads::spin_mtx, and libMesh::Elem::subactive().

compute_periodic_constraints()

void libMesh::FEGenericBase< FEOutputType< T >::type >::compute_periodic_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const PeriodicBoundaries &  boundaries, const MeshBase &  mesh, const PointLocatorBase *  point_locator, const unsigned int  variable_number, const Elem *  elem  )

staticinherited

Computes the constraint matrix contributions (for meshes with periodic boundary conditions) corresponding to variable number var_number, using generic projections.

Definition at line 193 of file fe_base.C.

{
  // Only bother if we truly have periodic boundaries
  if (boundaries.empty())
    return;
 
  libmesh_assert(elem);
 
  // Only constrain active elements with this method
  if (!elem->active())
    return;
 
  if (elem->infinite())
    libmesh_not_implemented();
 
  const unsigned int Dim = elem->dim();
 
  // We need sys_number and variable_number for DofObject methods
  // later
  const unsigned int sys_number = dof_map.sys_number();
 
  const FEType & base_fe_type = dof_map.variable_type(variable_number);
 
  // Construct FE objects for this element and its pseudo-neighbors.
  std::unique_ptr<FEGenericBase<OutputShape>> my_fe
    (FEGenericBase<OutputShape>::build(Dim, base_fe_type));
  const FEContinuity cont = my_fe->get_continuity();
 
  // We don't need to constrain discontinuous elements
  if (cont == DISCONTINUOUS)
    return;
  libmesh_assert (cont == C_ZERO || cont == C_ONE);
 
  // We'll use element size to generate relative tolerances later
  const Real primary_hmin = elem->hmin();
 
  std::unique_ptr<FEGenericBase<OutputShape>> neigh_fe
    (FEGenericBase<OutputShape>::build(Dim, base_fe_type));
 
  QGauss my_qface(Dim-1, base_fe_type.default_quadrature_order());
  my_fe->attach_quadrature_rule (&my_qface);
  std::vector<Point> neigh_qface;
 
  const std::vector<Real> & JxW = my_fe->get_JxW();
  const std::vector<Point> & q_point = my_fe->get_xyz();
  const std::vector<std::vector<OutputShape>> & phi = my_fe->get_phi();
  const std::vector<std::vector<OutputShape>> & neigh_phi =
    neigh_fe->get_phi();
  const std::vector<Point> * face_normals = nullptr;
  const std::vector<std::vector<OutputGradient>> * dphi = nullptr;
  const std::vector<std::vector<OutputGradient>> * neigh_dphi = nullptr;
  std::vector<dof_id_type> my_dof_indices, neigh_dof_indices;
  std::vector<unsigned int> my_side_dofs, neigh_side_dofs;
 
  if (cont != C_ZERO)
    {
      const std::vector<Point> & ref_face_normals =
        my_fe->get_normals();
      face_normals = &ref_face_normals;
      const std::vector<std::vector<OutputGradient>> & ref_dphi =
        my_fe->get_dphi();
      dphi = &ref_dphi;
      const std::vector<std::vector<OutputGradient>> & ref_neigh_dphi =
        neigh_fe->get_dphi();
      neigh_dphi = &ref_neigh_dphi;
    }
 
  DenseMatrix<Real> Ke;
  DenseVector<Real> Fe;
  std::vector<DenseVector<Real>> Ue;
 
  // Container to catch the boundary ids that BoundaryInfo hands us.
  std::vector<boundary_id_type> bc_ids;
 
  // Look at the element faces.  Check to see if we need to
  // build constraints.
  const unsigned short int max_ns = elem->n_sides();
  for (unsigned short int s = 0; s != max_ns; ++s)
    {
      if (elem->neighbor_ptr(s))
        continue;
 
      mesh.get_boundary_info().boundary_ids (elem, s, bc_ids);
 
      for (const auto & boundary_id : bc_ids)
        {
          const PeriodicBoundaryBase * periodic = boundaries.boundary(boundary_id);
          if (!periodic || !periodic->is_my_variable(variable_number))
            continue;
 
          libmesh_assert(point_locator);
 
          // Get pointers to the element's neighbor.
          unsigned int s_neigh;
          const Elem * neigh = boundaries.neighbor(boundary_id, *point_locator, elem, s, &s_neigh);
 
          libmesh_error_msg_if(neigh == nullptr,
                               "PeriodicBoundaries point locator object returned nullptr!");
 
          // periodic (and possibly h refinement) constraints:
          // constrain dofs shared between
          // this element and ones as coarse
          // as or coarser than this element.
          if (neigh->level() <= elem->level())
            {
#ifdef LIBMESH_ENABLE_AMR
              // Find the minimum p level; we build the h constraint
              // matrix with this and then constrain away all higher p
              // DoFs.
              libmesh_assert(neigh->active());
              const unsigned int min_p_level =
                std::min(elem->p_level(), neigh->p_level());
 
              // we may need to make the FE objects reinit with the
              // minimum shared p_level
              // FIXME - I hate using const_cast<> and avoiding
              // accessor functions; there's got to be a
              // better way to do this!
              const unsigned int old_elem_level = elem->p_level();
              if (old_elem_level != min_p_level)
                (const_cast<Elem *>(elem))->hack_p_level(min_p_level);
              const unsigned int old_neigh_level = neigh->p_level();
              if (old_neigh_level != min_p_level)
                (const_cast<Elem *>(neigh))->hack_p_level(min_p_level);
#endif // #ifdef LIBMESH_ENABLE_AMR
 
              // We can do a projection with a single integration,
              // due to the assumption of nested finite element
              // subspaces.
              // FIXME: it might be more efficient to do nodes,
              // then edges, then side, to reduce the size of the
              // Cholesky factorization(s)
              my_fe->reinit(elem, s);
 
              dof_map.dof_indices (elem, my_dof_indices,
                                   variable_number);
              dof_map.dof_indices (neigh, neigh_dof_indices,
                                   variable_number);
 
              // We use neigh_dof_indices_all_variables in the case that the
              // periodic boundary condition involves mappings between multiple
              // variables.
              std::vector<std::vector<dof_id_type>> neigh_dof_indices_all_variables;
              if(periodic->has_transformation_matrix())
                {
                  const std::set<unsigned int> & variables = periodic->get_variables();
                  neigh_dof_indices_all_variables.resize(variables.size());
                  unsigned int index = 0;
                  for(unsigned int var : variables)
                    {
                      dof_map.dof_indices (neigh, neigh_dof_indices_all_variables[index],
                                           var);
                      index++;
                    }
                }
 
              const unsigned int n_qp = my_qface.n_points();
 
              // Translate the quadrature points over to the
              // neighbor's boundary
              std::vector<Point> neigh_point(q_point.size());
              for (auto i : index_range(neigh_point))
                neigh_point[i] = periodic->get_corresponding_pos(q_point[i]);
 
              FEMap::inverse_map (Dim, neigh, neigh_point,
                                  neigh_qface);
 
              neigh_fe->reinit(neigh, &neigh_qface);
 
              // We're only concerned with DOFs whose values (and/or first
              // derivatives for C1 elements) are supported on side nodes
              FEInterface::dofs_on_side(elem, Dim, base_fe_type, s, my_side_dofs);
              FEInterface::dofs_on_side(neigh, Dim, base_fe_type, s_neigh, neigh_side_dofs);
 
              // We're done with functions that examine Elem::p_level(),
              // so let's unhack those levels
#ifdef LIBMESH_ENABLE_AMR
              if (elem->p_level() != old_elem_level)
                (const_cast<Elem *>(elem))->hack_p_level(old_elem_level);
              if (neigh->p_level() != old_neigh_level)
                (const_cast<Elem *>(neigh))->hack_p_level(old_neigh_level);
#endif // #ifdef LIBMESH_ENABLE_AMR
 
              const unsigned int n_side_dofs =
                cast_int<unsigned int>
                (my_side_dofs.size());
              libmesh_assert_equal_to (n_side_dofs, neigh_side_dofs.size());
 
              Ke.resize (n_side_dofs, n_side_dofs);
              Ue.resize(n_side_dofs);
 
              // Form the projection matrix, (inner product of fine basis
              // functions against fine test functions)
              for (unsigned int is = 0; is != n_side_dofs; ++is)
                {
                  const unsigned int i = my_side_dofs[is];
                  for (unsigned int js = 0; js != n_side_dofs; ++js)
                    {
                      const unsigned int j = my_side_dofs[js];
                      for (unsigned int qp = 0; qp != n_qp; ++qp)
                        {
                          Ke(is,js) += JxW[qp] *
                            TensorTools::inner_product(phi[i][qp],
                                                       phi[j][qp]);
                          if (cont != C_ZERO)
                            Ke(is,js) += JxW[qp] *
                              TensorTools::inner_product((*dphi)[i][qp] *
                                                         (*face_normals)[qp],
                                                         (*dphi)[j][qp] *
                                                         (*face_normals)[qp]);
                        }
                    }
                }
 
              // Form the right hand sides, (inner product of coarse basis
              // functions against fine test functions)
              for (unsigned int is = 0; is != n_side_dofs; ++is)
                {
                  const unsigned int i = neigh_side_dofs[is];
                  Fe.resize (n_side_dofs);
                  for (unsigned int js = 0; js != n_side_dofs; ++js)
                    {
                      const unsigned int j = my_side_dofs[js];
                      for (unsigned int qp = 0; qp != n_qp; ++qp)
                        {
                          Fe(js) += JxW[qp] *
                            TensorTools::inner_product(neigh_phi[i][qp],
                                                       phi[j][qp]);
                          if (cont != C_ZERO)
                            Fe(js) += JxW[qp] *
                              TensorTools::inner_product((*neigh_dphi)[i][qp] *
                                                         (*face_normals)[qp],
                                                         (*dphi)[j][qp] *
                                                         (*face_normals)[qp]);
                        }
                    }
                  Ke.cholesky_solve(Fe, Ue[is]);
                }
 
              // Make sure we're not adding recursive constraints
              // due to the redundancy in the way we add periodic
              // boundary constraints
              //
              // In order for this to work while threaded or on
              // distributed meshes, we need a rigorous way to
              // avoid recursive constraints.  Here it is:
              //
              // For vertex DoFs, if there is a "prior" element
              // (i.e. a coarser element or an equally refined
              // element with a lower id) on this boundary which
              // contains the vertex point, then we will avoid
              // generating constraints; the prior element (or
              // something prior to it) may do so.  If we are the
              // most prior (or "primary") element on this
              // boundary sharing this point, then we look at the
              // boundary periodic to us, we find the primary
              // element there, and if that primary is coarser or
              // equal-but-lower-id, then our vertex dofs are
              // constrained in terms of that element.
              //
              // For edge DoFs, if there is a coarser element
              // on this boundary sharing this edge, then we will
              // avoid generating constraints (we will be
              // constrained indirectly via AMR constraints
              // connecting us to the coarser element's DoFs).  If
              // we are the coarsest element sharing this edge,
              // then we generate constraints if and only if we
              // are finer than the coarsest element on the
              // boundary periodic to us sharing the corresponding
              // periodic edge, or if we are at equal level but
              // our edge nodes have higher ids than the periodic
              // edge nodes (sorted from highest to lowest, then
              // compared lexicographically)
              //
              // For face DoFs, we generate constraints if we are
              // finer than our periodic neighbor, or if we are at
              // equal level but our element id is higher than its
              // element id.
              //
              // If the primary neighbor is also the current elem
              // (a 1-element-thick mesh) then we choose which
              // vertex dofs to constrain via lexicographic
              // ordering on point locations
 
              // FIXME: This code doesn't yet properly handle
              // cases where multiple different periodic BCs
              // intersect.
              std::set<dof_id_type> my_constrained_dofs;
 
              // Container to catch boundary IDs handed back by BoundaryInfo.
              std::vector<boundary_id_type> new_bc_ids;
 
              for (auto n : elem->node_index_range())
                {
                  if (!elem->is_node_on_side(n,s))
                    continue;
 
                  const Node & my_node = elem->node_ref(n);
 
                  if (elem->is_vertex(n))
                    {
                      // Find all boundary ids that include this
                      // point and have periodic boundary
                      // conditions for this variable
                      std::set<boundary_id_type> point_bcids;
 
                      for (unsigned int new_s = 0;
                           new_s != max_ns; ++new_s)
                        {
                          if (!elem->is_node_on_side(n,new_s))
                            continue;
 
                          mesh.get_boundary_info().boundary_ids (elem, s, new_bc_ids);
 
                          for (const auto & new_boundary_id : new_bc_ids)
                            {
                              const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
                              if (new_periodic && new_periodic->is_my_variable(variable_number))
                            point_bcids.insert(new_boundary_id);
                            }
                        }
 
                      // See if this vertex has point neighbors to
                      // defer to
                      if (primary_boundary_point_neighbor
                          (elem, my_node, mesh.get_boundary_info(), point_bcids)
                          != elem)
                        continue;
 
                      // Find the complementary boundary id set
                      std::set<boundary_id_type> point_pairedids;
                      for (const auto & new_boundary_id : point_bcids)
                        {
                          const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
                          point_pairedids.insert(new_periodic->pairedboundary);
                        }
 
                      // What do we want to constrain against?
                      const Elem * primary_elem = nullptr;
                      const Elem * main_neigh = nullptr;
                      Point main_pt = my_node,
                        primary_pt = my_node;
 
                      for (const auto & new_boundary_id : point_bcids)
                        {
                          // Find the corresponding periodic point and
                          // its primary neighbor
                          const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
 
                          const Point neigh_pt =
                            new_periodic->get_corresponding_pos(my_node);
 
                          // If the point is getting constrained
                          // to itself by this PBC then we don't
                          // generate any constraints
                          if (neigh_pt.absolute_fuzzy_equals
                              (my_node, primary_hmin*TOLERANCE))
                            continue;
 
                          // Otherwise we'll have a constraint in
                          // one direction or another
                          if (!primary_elem)
                            primary_elem = elem;
 
                          const Elem * primary_neigh =
                            primary_boundary_point_neighbor(neigh, neigh_pt,
                                                            mesh.get_boundary_info(),
                                                            point_pairedids);
 
                          libmesh_assert(primary_neigh);
 
                          if (new_boundary_id == boundary_id)
                            {
                              main_neigh = primary_neigh;
                              main_pt = neigh_pt;
                            }
 
                          // Finer elements will get constrained in
                          // terms of coarser neighbors, not the
                          // other way around
                          if ((primary_neigh->level() > primary_elem->level()) ||
 
                              // For equal-level elements, the one with
                              // higher id gets constrained in terms of
                              // the one with lower id
                              (primary_neigh->level() == primary_elem->level() &&
                               primary_neigh->id() > primary_elem->id()) ||
 
                              // On a one-element-thick mesh, we compare
                              // points to see what side gets constrained
                              (primary_neigh == primary_elem &&
                               (neigh_pt > primary_pt)))
                            continue;
 
                          primary_elem = primary_neigh;
                          primary_pt = neigh_pt;
                        }
 
                      if (!primary_elem ||
                          primary_elem != main_neigh ||
                          primary_pt != main_pt)
                        continue;
                    }
                  else if (elem->is_edge(n))
                    {
                      // Find which edge we're on
                      unsigned int e=0, ne = elem->n_edges();
                      for (; e != ne; ++e)
                        {
                          if (elem->is_node_on_edge(n,e))
                            break;
                        }
                      libmesh_assert_less (e, elem->n_edges());
 
                      // Find the edge end nodes
                      const Node
                        * e1 = nullptr,
                        * e2 = nullptr;
                      for (auto nn : elem->node_index_range())
                        {
                          if (nn == n)
                            continue;
 
                          if (elem->is_node_on_edge(nn, e))
                            {
                              if (e1 == nullptr)
                                {
                                  e1 = elem->node_ptr(nn);
                                }
                              else
                                {
                                  e2 = elem->node_ptr(nn);
                                  break;
                                }
                            }
                        }
                      libmesh_assert (e1 && e2);
 
                      // Find all boundary ids that include this
                      // edge and have periodic boundary
                      // conditions for this variable
                      std::set<boundary_id_type> edge_bcids;
 
                      for (unsigned int new_s = 0;
                           new_s != max_ns; ++new_s)
                        {
                          if (!elem->is_node_on_side(n,new_s))
                            continue;
 
                          // We're reusing the new_bc_ids vector created outside the loop over nodes.
                          mesh.get_boundary_info().boundary_ids (elem, s, new_bc_ids);
 
                          for (const auto & new_boundary_id : new_bc_ids)
                            {
                              const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
                              if (new_periodic && new_periodic->is_my_variable(variable_number))
                                edge_bcids.insert(new_boundary_id);
                            }
                        }
 
 
                      // See if this edge has neighbors to defer to
                      if (primary_boundary_edge_neighbor
                          (elem, *e1, *e2, mesh.get_boundary_info(), edge_bcids)
                          != elem)
                        continue;
 
                      // Find the complementary boundary id set
                      std::set<boundary_id_type> edge_pairedids;
                      for (const auto & new_boundary_id : edge_bcids)
                        {
                          const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
                          edge_pairedids.insert(new_periodic->pairedboundary);
                        }
 
                      // What do we want to constrain against?
                      const Elem * primary_elem = nullptr;
                      const Elem * main_neigh = nullptr;
                      Point main_pt1 = *e1,
                        main_pt2 = *e2,
                        primary_pt1 = *e1,
                        primary_pt2 = *e2;
 
                      for (const auto & new_boundary_id : edge_bcids)
                        {
                          // Find the corresponding periodic edge and
                          // its primary neighbor
                          const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
 
                          Point neigh_pt1 = new_periodic->get_corresponding_pos(*e1),
                            neigh_pt2 = new_periodic->get_corresponding_pos(*e2);
 
                          // If the edge is getting constrained
                          // to itself by this PBC then we don't
                          // generate any constraints
                          if (neigh_pt1.absolute_fuzzy_equals
                              (*e1, primary_hmin*TOLERANCE) &&
                              neigh_pt2.absolute_fuzzy_equals
                              (*e2, primary_hmin*TOLERANCE))
                            continue;
 
                          // Otherwise we'll have a constraint in
                          // one direction or another
                          if (!primary_elem)
                            primary_elem = elem;
 
                          const Elem * primary_neigh = primary_boundary_edge_neighbor
                            (neigh, neigh_pt1, neigh_pt2,
                             mesh.get_boundary_info(), edge_pairedids);
 
                          libmesh_assert(primary_neigh);
 
                          if (new_boundary_id == boundary_id)
                            {
                              main_neigh = primary_neigh;
                              main_pt1 = neigh_pt1;
                              main_pt2 = neigh_pt2;
                            }
 
                          // If we have a one-element thick mesh,
                          // we'll need to sort our points to get a
                          // consistent ordering rule
                          //
                          // Use >= in this test to make sure that,
                          // for angular constraints, no node gets
                          // constrained to itself.
                          if (primary_neigh == primary_elem)
                            {
                              if (primary_pt1 > primary_pt2)
                                std::swap(primary_pt1, primary_pt2);
                              if (neigh_pt1 > neigh_pt2)
                                std::swap(neigh_pt1, neigh_pt2);
 
                              if (neigh_pt2 >= primary_pt2)
                                continue;
                            }
 
                          // Otherwise:
                          // Finer elements will get constrained in
                          // terms of coarser ones, not the other way
                          // around
                          if ((primary_neigh->level() > primary_elem->level()) ||
 
                              // For equal-level elements, the one with
                              // higher id gets constrained in terms of
                              // the one with lower id
                              (primary_neigh->level() == primary_elem->level() &&
                               primary_neigh->id() > primary_elem->id()))
                            continue;
 
                          primary_elem = primary_neigh;
                          primary_pt1 = neigh_pt1;
                          primary_pt2 = neigh_pt2;
                        }
 
                      if (!primary_elem ||
                          primary_elem != main_neigh ||
                          primary_pt1 != main_pt1 ||
                          primary_pt2 != main_pt2)
                        continue;
                    }
                  else if (elem->is_face(n))
                    {
                      // If we have a one-element thick mesh,
                      // use the ordering of the face node and its
                      // periodic counterpart to determine what
                      // gets constrained
                      if (neigh == elem)
                        {
                          const Point neigh_pt =
                            periodic->get_corresponding_pos(my_node);
                          if (neigh_pt > my_node)
                            continue;
                        }
 
                      // Otherwise:
                      // Finer elements will get constrained in
                      // terms of coarser ones, not the other way
                      // around
                      if ((neigh->level() > elem->level()) ||
 
                          // For equal-level elements, the one with
                          // higher id gets constrained in terms of
                          // the one with lower id
                          (neigh->level() == elem->level() &&
                           neigh->id() > elem->id()))
                        continue;
                    }
 
                  // If we made it here without hitting a continue
                  // statement, then we're at a node whose dofs
                  // should be constrained by this element's
                  // calculations.
                  const unsigned int n_comp =
                    my_node.n_comp(sys_number, variable_number);
 
                  for (unsigned int i=0; i != n_comp; ++i)
                    my_constrained_dofs.insert
                      (my_node.dof_number
                       (sys_number, variable_number, i));
                }
 
              // FIXME: old code for disambiguating periodic BCs:
              // this is not threadsafe nor safe to run on a
              // non-serialized mesh.
              /*
                std::vector<bool> recursive_constraint(n_side_dofs, false);
 
                for (unsigned int is = 0; is != n_side_dofs; ++is)
                {
                const unsigned int i = neigh_side_dofs[is];
                const dof_id_type their_dof_g = neigh_dof_indices[i];
                libmesh_assert_not_equal_to (their_dof_g, DofObject::invalid_id);
 
                {
                Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
 
                if (!dof_map.is_constrained_dof(their_dof_g))
                continue;
                }
 
                DofConstraintRow & their_constraint_row =
                constraints[their_dof_g].first;
 
                for (unsigned int js = 0; js != n_side_dofs; ++js)
                {
                const unsigned int j = my_side_dofs[js];
                const dof_id_type my_dof_g = my_dof_indices[j];
                libmesh_assert_not_equal_to (my_dof_g, DofObject::invalid_id);
 
                if (their_constraint_row.count(my_dof_g))
                recursive_constraint[js] = true;
                }
                }
              */
 
              for (unsigned int js = 0; js != n_side_dofs; ++js)
                {
                  // FIXME: old code path
                  // if (recursive_constraint[js])
                  //  continue;
 
                  const unsigned int j = my_side_dofs[js];
                  const dof_id_type my_dof_g = my_dof_indices[j];
                  libmesh_assert_not_equal_to (my_dof_g, DofObject::invalid_id);
 
                  // FIXME: new code path
                  if (!my_constrained_dofs.count(my_dof_g))
                    continue;
 
                  DofConstraintRow * constraint_row;
 
                  // we may be running constraint methods concurrently
                  // on multiple threads, so we need a lock to
                  // ensure that this constraint is "ours"
                  {
                    Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
 
                    if (dof_map.is_constrained_dof(my_dof_g))
                      continue;
 
                    constraint_row = &(constraints[my_dof_g]);
                    libmesh_assert(constraint_row->empty());
                  }
 
                  for (unsigned int is = 0; is != n_side_dofs; ++is)
                    {
                      const unsigned int i = neigh_side_dofs[is];
                      const dof_id_type their_dof_g = neigh_dof_indices[i];
                      libmesh_assert_not_equal_to (their_dof_g, DofObject::invalid_id);
 
                      // Periodic constraints should never be
                      // self-constraints
                      // libmesh_assert_not_equal_to (their_dof_g, my_dof_g);
 
                      const Real their_dof_value = Ue[is](js);
 
                      if (their_dof_g == my_dof_g)
                        {
                          libmesh_assert_less (std::abs(their_dof_value-1.), 1.e-5);
                          for (unsigned int k = 0; k != n_side_dofs; ++k)
                            libmesh_assert(k == is || std::abs(Ue[k](js)) < 1.e-5);
                          continue;
                        }
 
                      if (std::abs(their_dof_value) < 10*TOLERANCE)
                        continue;
 
                      if(!periodic->has_transformation_matrix())
                        {
                          constraint_row->emplace(their_dof_g, their_dof_value);
                        }
                      else
                        {
                          // In this case the current variable is constrained in terms of other variables.
                          // We assume that all variables in this constraint have the same FE type (this
                          // is asserted below), and hence we can create the constraint row contribution
                          // by multiplying their_dof_value by the corresponding row of the transformation
                          // matrix.
 
                          const std::set<unsigned int> & variables = periodic->get_variables();
                          neigh_dof_indices_all_variables.resize(variables.size());
                          unsigned int index = 0;
                          for(unsigned int other_var : variables)
                            {
                              libmesh_assert_msg(base_fe_type == dof_map.variable_type(other_var), "FE types must match for all variables involved in constraint");
 
                              Real var_weighting = periodic->get_transformation_matrix()(variable_number, other_var);
                              constraint_row->emplace(neigh_dof_indices_all_variables[index][i],
                                                      var_weighting*their_dof_value);
                              index++;
                            }
                        }
 
                    }
                }
            }
          // p refinement constraints:
          // constrain dofs shared between
          // active elements and neighbors with
          // lower polynomial degrees
#ifdef LIBMESH_ENABLE_AMR
          const unsigned int min_p_level =
            neigh->min_p_level_by_neighbor(elem, elem->p_level());
          if (min_p_level < elem->p_level())
            {
              // Adaptive p refinement of non-hierarchic bases will
              // require more coding
              libmesh_assert(my_fe->is_hierarchic());
              dof_map.constrain_p_dofs(variable_number, elem,
                                       s, min_p_level);
            }
#endif // #ifdef LIBMESH_ENABLE_AMR
        }
    }
}

compute_periodic_node_constraints()

void libMesh::FEAbstract::compute_periodic_node_constraints ( NodeConstraints &  constraints, const PeriodicBoundaries &  boundaries, const MeshBase &  mesh, const PointLocatorBase *  point_locator, const Elem *  elem  )

staticinherited

Computes the node position constraint equation contributions (for meshes with periodic boundary conditions)

Definition at line 1078 of file fe_abstract.C.

{
  // Only bother if we truly have periodic boundaries
  if (boundaries.empty())
    return;
 
  libmesh_assert(elem);
 
  // Only constrain active elements with this method
  if (!elem->active())
    return;
 
  const unsigned int Dim = elem->dim();
 
  const FEFamily mapping_family = FEMap::map_fe_type(*elem);
  const FEType fe_type(elem->default_side_order(), mapping_family);
 
  // Pull objects out of the loop to reduce heap operations
  std::vector<const Node *> my_nodes, neigh_nodes;
  std::unique_ptr<const Elem> my_side, neigh_side;
 
  // Look at the element faces.  Check to see if we need to
  // build constraints.
  std::vector<boundary_id_type> bc_ids;
  for (auto s : elem->side_index_range())
    {
      if (elem->neighbor_ptr(s))
        continue;
 
      mesh.get_boundary_info().boundary_ids (elem, s, bc_ids);
      for (const auto & boundary_id : bc_ids)
        {
          const PeriodicBoundaryBase * periodic = boundaries.boundary(boundary_id);
          if (periodic)
            {
              libmesh_assert(point_locator);
 
              // Get pointers to the element's neighbor.
              unsigned int s_neigh;
              const Elem * neigh = boundaries.neighbor(boundary_id, *point_locator, elem, s, &s_neigh);
 
              libmesh_error_msg_if
                (!neigh, "PeriodicBoundaries can't find a periodic neighbor for element " <<
                         elem->id() << " side " << s);
 
              // h refinement constraints:
              // constrain dofs shared between
              // this element and ones as coarse
              // as or coarser than this element.
              if (neigh->level() <= elem->level())
                {
#ifdef LIBMESH_ENABLE_AMR
                  libmesh_assert(neigh->active());
#endif // #ifdef LIBMESH_ENABLE_AMR
 
                  elem->build_side_ptr(my_side, s);
                  neigh->build_side_ptr(neigh_side, s_neigh);
 
                  const unsigned int n_side_nodes = my_side->n_nodes();
 
                  my_nodes.clear();
                  my_nodes.reserve (n_side_nodes);
                  neigh_nodes.clear();
                  neigh_nodes.reserve (n_side_nodes);
 
                  for (unsigned int n=0; n != n_side_nodes; ++n)
                    my_nodes.push_back(my_side->node_ptr(n));
 
                  for (unsigned int n=0; n != n_side_nodes; ++n)
                    neigh_nodes.push_back(neigh_side->node_ptr(n));
 
                  // Make sure we're not adding recursive constraints
                  // due to the redundancy in the way we add periodic
                  // boundary constraints, or adding constraints to
                  // nodes that already have AMR constraints
                  std::vector<bool> skip_constraint(n_side_nodes, false);
 
                  for (unsigned int my_side_n=0;
                       my_side_n < n_side_nodes;
                       my_side_n++)
                    {
                      // Do not use the p_level(), if any, that is inherited by the side.
                      libmesh_assert_less (my_side_n, FEInterface::n_dofs(fe_type, /*extra_order=*/0, my_side.get()));
 
                      const Node * my_node = my_nodes[my_side_n];
 
                      // If we've already got a constraint on this
                      // node, then the periodic constraint is
                      // redundant
                      {
                        Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
 
                        if (constraints.count(my_node))
                          {
                            skip_constraint[my_side_n] = true;
                            continue;
                          }
                      }
 
                      // Compute the neighbors's side shape function values.
                      for (unsigned int their_side_n=0;
                           their_side_n < n_side_nodes;
                           their_side_n++)
                        {
                          // Do not use the p_level(), if any, that is inherited by the side.
                          libmesh_assert_less (their_side_n, FEInterface::n_dofs(fe_type, /*extra_order=*/0, neigh_side.get()));
 
                          const Node * their_node = neigh_nodes[their_side_n];
 
                          // If there's a constraint on an opposing node,
                          // we need to see if it's constrained by
                          // *our side* making any periodic constraint
                          // on us recursive
                          {
                            Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
 
                            if (!constraints.count(their_node))
                              continue;
 
                            const NodeConstraintRow & their_constraint_row =
                              constraints[their_node].first;
 
                            for (unsigned int orig_side_n=0;
                                 orig_side_n < n_side_nodes;
                                 orig_side_n++)
                              {
                                // Do not use the p_level(), if any, that is inherited by the side.
                                libmesh_assert_less (orig_side_n, FEInterface::n_dofs(fe_type, /*extra_order=*/0, my_side.get()));
 
                                const Node * orig_node = my_nodes[orig_side_n];
 
                                if (their_constraint_row.count(orig_node))
                                  skip_constraint[orig_side_n] = true;
                              }
                          }
                        }
                    }
                  for (unsigned int my_side_n=0;
                       my_side_n < n_side_nodes;
                       my_side_n++)
                    {
                      // Do not use the p_level(), if any, that is inherited by the side.
                      libmesh_assert_less (my_side_n, FEInterface::n_dofs(fe_type, /*extra_order=*/0, my_side.get()));
 
                      if (skip_constraint[my_side_n])
                        continue;
 
                      const Node * my_node = my_nodes[my_side_n];
 
                      // Figure out where my node lies on their reference element.
                      const Point neigh_point = periodic->get_corresponding_pos(*my_node);
 
                      // Figure out where my node lies on their reference element.
                      const Point mapped_point =
                        FEMap::inverse_map(Dim-1, neigh_side.get(),
                                           neigh_point);
 
                      for (unsigned int their_side_n=0;
                           their_side_n < n_side_nodes;
                           their_side_n++)
                        {
                          // Do not use the p_level(), if any, that is inherited by the side.
                          libmesh_assert_less (their_side_n, FEInterface::n_dofs(fe_type, /*extra_order=*/0, neigh_side.get()));
 
                          const Node * their_node = neigh_nodes[their_side_n];
                          libmesh_assert(their_node);
 
                          // Do not use the p_level(), if any, that is inherited by the side.
                          const Real their_value = FEInterface::shape(fe_type,
                                                                      /*extra_order=*/0,
                                                                      neigh_side.get(),
                                                                      their_side_n,
                                                                      mapped_point);
 
                          // since we may be running this method concurrently
                          // on multiple threads we need to acquire a lock
                          // before modifying the shared constraint_row object.
                          {
                            Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
 
                            NodeConstraintRow & constraint_row =
                              constraints[my_node].first;
 
                            constraint_row.emplace(their_node, their_value);
                          }
                        }
                    }
                }
            }
        }
    }
}

References libMesh::Elem::active(), libMesh::PeriodicBoundaries::boundary(), libMesh::Elem::build_side_ptr(), libMesh::Elem::default_side_order(), libMesh::Elem::dim(), libMesh::FEAbstract::fe_type, libMesh::PeriodicBoundaryBase::get_corresponding_pos(), libMesh::DofObject::id(), libMesh::FEMap::inverse_map(), libMesh::Elem::level(), libMesh::libmesh_assert(), libMesh::FEMap::map_fe_type(), mesh, libMesh::FEInterface::n_dofs(), libMesh::PeriodicBoundaries::neighbor(), libMesh::Elem::neighbor_ptr(), libMesh::Real, libMesh::FEInterface::shape(), libMesh::Elem::side_index_range(), and libMesh::Threads::spin_mtx.

compute_proj_constraints()

void libMesh::FEGenericBase< FEOutputType< T >::type >::compute_proj_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

staticinherited

Computes the constraint matrix contributions (for non-conforming adapted meshes) corresponding to variable number var_number, using generic projections.

Definition at line 153 of file fe_base.C.

{
  libmesh_assert(elem);
 
  const unsigned int Dim = elem->dim();
 
  // Only constrain elements in 2,3D.
  if (Dim == 1)
    return;
 
  // Only constrain active elements with this method
  if (!elem->active())
    return;
 
  const Variable & var = dof_map.variable(variable_number);
  const FEType & base_fe_type = var.type();
  const bool add_p_level = base_fe_type.p_refinement;
 
  // Construct FE objects for this element and its neighbors.
  std::unique_ptr<FEGenericBase<OutputShape>> my_fe
    (FEGenericBase<OutputShape>::build(Dim, base_fe_type));
  my_fe->add_p_level_in_reinit(add_p_level);
  const FEContinuity cont = my_fe->get_continuity();
 
  // We don't need to constrain discontinuous elements
  if (cont == DISCONTINUOUS)
    return;
  libmesh_assert (cont == C_ZERO || cont == C_ONE ||
                  cont == SIDE_DISCONTINUOUS);
 
  // this would require some generalisation:
  //  - e.g. the 'my_fe'-object needs generalisation
  //  - due to lack of one-to-one correspondence of DOFs and nodes,
  //    this doesn't work easily.
  if (elem->infinite())
    libmesh_not_implemented();
 
  std::unique_ptr<FEGenericBase<OutputShape>> neigh_fe
    (FEGenericBase<OutputShape>::build(Dim, base_fe_type));
  neigh_fe->add_p_level_in_reinit(add_p_level);
 
  QGauss my_qface(Dim-1, base_fe_type.default_quadrature_order());
  my_fe->attach_quadrature_rule (&my_qface);
  std::vector<Point> neigh_qface;
 
  const std::vector<Real> & JxW = my_fe->get_JxW();
  const std::vector<Point> & q_point = my_fe->get_xyz();
  const std::vector<std::vector<OutputShape>> & phi = my_fe->get_phi();
  const std::vector<std::vector<OutputShape>> & neigh_phi =
    neigh_fe->get_phi();
  const std::vector<Point> * face_normals = nullptr;
  const std::vector<std::vector<OutputGradient>> * dphi = nullptr;
  const std::vector<std::vector<OutputGradient>> * neigh_dphi = nullptr;
 
  std::vector<dof_id_type> my_dof_indices, neigh_dof_indices;
  std::vector<unsigned int> my_side_dofs, neigh_side_dofs;
 
  if (cont == C_ONE)
    {
      const std::vector<Point> & ref_face_normals =
        my_fe->get_normals();
      face_normals = &ref_face_normals;
      const std::vector<std::vector<OutputGradient>> & ref_dphi =
        my_fe->get_dphi();
      dphi = &ref_dphi;
      const std::vector<std::vector<OutputGradient>> & ref_neigh_dphi =
        neigh_fe->get_dphi();
      neigh_dphi = &ref_neigh_dphi;
    }
 
  DenseMatrix<Real> Ke;
  DenseVector<Real> Fe;
  std::vector<DenseVector<Real>> Ue;
 
  // Look at the element faces.  Check to see if we need to
  // build constraints.
  for (auto s : elem->side_index_range())
    {
      // Get pointers to the element's neighbor.
      const Elem * neigh = elem->neighbor_ptr(s);
 
      if (!neigh)
        continue;
 
      if (!var.active_on_subdomain(neigh->subdomain_id()))
        continue;
 
      // h refinement constraints:
      // constrain dofs shared between
      // this element and ones coarser
      // than this element.
      if (neigh->level() < elem->level())
        {
          unsigned int s_neigh = neigh->which_neighbor_am_i(elem);
          libmesh_assert_less (s_neigh, neigh->n_neighbors());
 
          // Find the minimum p level; we build the h constraint
          // matrix with this and then constrain away all higher p
          // DoFs.
          libmesh_assert(neigh->active());
          const unsigned int min_p_level = add_p_level *
            std::min(elem->p_level(), neigh->p_level());
          // we may need to make the FE objects reinit with the
          // minimum shared p_level
          const unsigned int old_elem_level = add_p_level * elem->p_level();
          if (old_elem_level != min_p_level)
            my_fe->set_fe_order(my_fe->get_fe_type().order.get_order() + min_p_level - old_elem_level);
          const unsigned int old_neigh_level = add_p_level * neigh->p_level();
          if (old_neigh_level != min_p_level)
            neigh_fe->set_fe_order(neigh_fe->get_fe_type().order.get_order() + min_p_level - old_neigh_level);
 
          my_fe->reinit(elem, s);
 
          // This function gets called element-by-element, so there
          // will be a lot of memory allocation going on.  We can
          // at least minimize this for the case of the dof indices
          // by efficiently preallocating the requisite storage.
          // n_nodes is not necessarily n_dofs, but it is better
          // than nothing!
          my_dof_indices.reserve    (elem->n_nodes());
          neigh_dof_indices.reserve (neigh->n_nodes());
 
          dof_map.dof_indices (elem, my_dof_indices,
                               variable_number,
                               min_p_level);
          dof_map.dof_indices (neigh, neigh_dof_indices,
                               variable_number,
                               min_p_level);
 
          const unsigned int n_qp = my_qface.n_points();
 
          FEMap::inverse_map (Dim, neigh, q_point, neigh_qface);
 
          neigh_fe->reinit(neigh, &neigh_qface);
 
          // We're only concerned with DOFs whose values (and/or first
          // derivatives for C1 elements) are supported on side nodes
          FEType elem_fe_type = base_fe_type;
          if (old_elem_level != min_p_level)
            elem_fe_type.order = base_fe_type.order.get_order() + min_p_level - old_elem_level;
          FEType neigh_fe_type = base_fe_type;
          if (old_neigh_level != min_p_level)
            neigh_fe_type.order = base_fe_type.order.get_order() + min_p_level - old_neigh_level;
          FEInterface::dofs_on_side(elem,  Dim, elem_fe_type,  s,       my_side_dofs);
          FEInterface::dofs_on_side(neigh, Dim, neigh_fe_type, s_neigh, neigh_side_dofs);
 
          const unsigned int n_side_dofs =
            cast_int<unsigned int>(my_side_dofs.size());
          libmesh_assert_equal_to (n_side_dofs, neigh_side_dofs.size());
 
#ifndef NDEBUG
          for (auto i : my_side_dofs)
            libmesh_assert_less(i, my_dof_indices.size());
          for (auto i : neigh_side_dofs)
            libmesh_assert_less(i, neigh_dof_indices.size());
#endif
 
          Ke.resize (n_side_dofs, n_side_dofs);
          Ue.resize(n_side_dofs);
 
          // Form the projection matrix, (inner product of fine basis
          // functions against fine test functions)
          for (unsigned int is = 0; is != n_side_dofs; ++is)
            {
              const unsigned int i = my_side_dofs[is];
              for (unsigned int js = 0; js != n_side_dofs; ++js)
                {
                  const unsigned int j = my_side_dofs[js];
                  for (unsigned int qp = 0; qp != n_qp; ++qp)
                    {
                      Ke(is,js) += JxW[qp] * TensorTools::inner_product(phi[i][qp], phi[j][qp]);
                      if (cont == C_ONE)
                        Ke(is,js) += JxW[qp] *
                          TensorTools::inner_product((*dphi)[i][qp] *
                                                     (*face_normals)[qp],
                                                     (*dphi)[j][qp] *
                                                     (*face_normals)[qp]);
                    }
                }
            }
 
          // Form the right hand sides, (inner product of coarse basis
          // functions against fine test functions)
          for (unsigned int is = 0; is != n_side_dofs; ++is)
            {
              const unsigned int i = neigh_side_dofs[is];
              Fe.resize (n_side_dofs);
              for (unsigned int js = 0; js != n_side_dofs; ++js)
                {
                  const unsigned int j = my_side_dofs[js];
                  for (unsigned int qp = 0; qp != n_qp; ++qp)
                    {
                      Fe(js) += JxW[qp] *
                        TensorTools::inner_product(neigh_phi[i][qp],
                                                   phi[j][qp]);
                      if (cont == C_ONE)
                        Fe(js) += JxW[qp] *
                          TensorTools::inner_product((*neigh_dphi)[i][qp] *
                                                     (*face_normals)[qp],
                                                     (*dphi)[j][qp] *
                                                     (*face_normals)[qp]);
                    }
                }
              Ke.cholesky_solve(Fe, Ue[is]);
            }
 
          for (unsigned int js = 0; js != n_side_dofs; ++js)
            {
              const unsigned int j = my_side_dofs[js];
              const dof_id_type my_dof_g = my_dof_indices[j];
              libmesh_assert_not_equal_to (my_dof_g, DofObject::invalid_id);
 
              // Hunt for "constraining against myself" cases before
              // we bother creating a constraint row
              bool self_constraint = false;
              for (unsigned int is = 0; is != n_side_dofs; ++is)
                {
                  const unsigned int i = neigh_side_dofs[is];
                  const dof_id_type their_dof_g = neigh_dof_indices[i];
                  libmesh_assert_not_equal_to (their_dof_g, DofObject::invalid_id);
 
                  if (their_dof_g == my_dof_g)
                    {
#ifndef NDEBUG
                      const Real their_dof_value = Ue[is](js);
                      libmesh_assert_less (std::abs(their_dof_value-1.),
                                           10*TOLERANCE);
 
                      for (unsigned int k = 0; k != n_side_dofs; ++k)
                        libmesh_assert(k == is ||
                                       std::abs(Ue[k](js)) <
                                       10*TOLERANCE);
#endif
 
                      self_constraint = true;
                      break;
                    }
                }
 
              if (self_constraint)
                continue;
 
              DofConstraintRow * constraint_row;
 
              // we may be running constraint methods concurrently
              // on multiple threads, so we need a lock to
              // ensure that this constraint is "ours"
              {
                Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
 
                if (dof_map.is_constrained_dof(my_dof_g))
                  continue;
 
                constraint_row = &(constraints[my_dof_g]);
                libmesh_assert(constraint_row->empty());
              }
 
              for (unsigned int is = 0; is != n_side_dofs; ++is)
                {
                  const unsigned int i = neigh_side_dofs[is];
                  const dof_id_type their_dof_g = neigh_dof_indices[i];
                  libmesh_assert_not_equal_to (their_dof_g, DofObject::invalid_id);
                  libmesh_assert_not_equal_to (their_dof_g, my_dof_g);
 
                  const Real their_dof_value = Ue[is](js);
 
                  if (std::abs(their_dof_value) < 10*TOLERANCE)
                    continue;
 
                  constraint_row->emplace(their_dof_g, their_dof_value);
                }
            }
 
          my_fe->set_fe_order(my_fe->get_fe_type().order.get_order() + old_elem_level - min_p_level);
          neigh_fe->set_fe_order(neigh_fe->get_fe_type().order.get_order() + old_neigh_level - min_p_level);
        }
 
      if (add_p_level)
      {
        // p refinement constraints:
        // constrain dofs shared between
        // active elements and neighbors with
        // lower polynomial degrees
        const unsigned int min_p_level =
          neigh->min_p_level_by_neighbor(elem, elem->p_level());
        if (min_p_level < elem->p_level())
        {
          // Adaptive p refinement of non-hierarchic bases will
          // require more coding
          libmesh_assert(my_fe->is_hierarchic());
          dof_map.constrain_p_dofs(variable_number, elem,
                                   s, min_p_level);
        }
      }
    }
}

compute_shape_functions()

void libMesh::FEGenericBase< FEOutputType< T >::type >::compute_shape_functions ( const Elem *  elem, const std::vector< Point > &  qp  )

overrideprotectedvirtualinherited

After having updated the jacobian and the transformation from local to global coordinates in FEMap::compute_map(), the first derivatives of the shape functions are transformed to global coordinates, giving dphi, dphidx, dphidy, and dphidz.

This method should rarely be re-defined in derived classes, but still should be usable for children. Therefore, keep it protected.

Implements libMesh::FEAbstract.

Reimplemented in libMesh::FEXYZ< Dim >.

Definition at line 589 of file fe_base.C.

{
  //-------------------------------------------------------------------------
  // Compute the shape function values (and derivatives)
  // at the Quadrature points.  Note that the actual values
  // have already been computed via init_shape_functions
 
  // Start logging the shape function computation
  LOG_SCOPE("compute_shape_functions()", "FE");
 
  this->determine_calculations();
 
  if (calculate_phi)
    this->_fe_trans->map_phi(this->dim, elem, qp, (*this), this->phi, this->_add_p_level_in_reinit);
 
  if (calculate_dphi)
    this->_fe_trans->map_dphi(this->dim, elem, qp, (*this), this->dphi,
                              this->dphidx, this->dphidy, this->dphidz);
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
  if (calculate_d2phi)
    this->_fe_trans->map_d2phi(this->dim, qp, (*this), this->d2phi,
                               this->d2phidx2, this->d2phidxdy, this->d2phidxdz,
                               this->d2phidy2, this->d2phidydz, this->d2phidz2);
#endif //LIBMESH_ENABLE_SECOND_DERIVATIVES
 
  // Only compute curl for vector-valued elements
  if (calculate_curl_phi && TypesEqual<OutputType,RealGradient>::value)
    this->_fe_trans->map_curl(this->dim, elem, qp, (*this), this->curl_phi);
 
  // Only compute div for vector-valued elements
  if (calculate_div_phi && TypesEqual<OutputType,RealGradient>::value)
    this->_fe_trans->map_div(this->dim, elem, qp, (*this), this->div_phi);
}

default_all_shape_derivs()

void libMesh::FE< Dim, T >::default_all_shape_derivs ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< OutputShape > > *  comps[3], const bool  add_p_level = true  )

staticprotectedinherited

A default implementation for all_shape_derivs.

Definition at line 712 of file fe.C.

{
  for (unsigned int d=0; d != Dim; ++d)
    {
      auto & comps_d = *comps[d];
      for (auto i : index_range(comps_d))
        FE<Dim,T>::shape_derivs
          (elem,o,i,d,p,comps_d[i],add_p_level);
    }
}

default_all_shapes()

static void libMesh::FE< Dim, T >::default_all_shapes ( const Elem *  elem, const Order  o, const std::vector< Point > &  p, std::vector< std::vector< OutputShape > > &  v, const bool  add_p_level = true  )

inlinestaticprotectedinherited

A default implementation for all_shapes.

Definition at line 753 of file fe.h.

    {
      for (auto i : index_range(v))
        {
          libmesh_assert_equal_to ( p.size(), v[i].size() );
          FE<Dim,T>::shapes (elem, o, i, p, v[i], add_p_level);
        }
    }

default_shape_derivs()

static void libMesh::FE< Dim, T >::default_shape_derivs ( const Elem *  elem, const Order  o, const unsigned int  i, const unsigned int  j, const std::vector< Point > &  p, std::vector< OutputShape > &  v, const bool  add_p_level = true  )

inlinestaticprotectedinherited

A default implementation for shape_derivs.

Definition at line 769 of file fe.h.

    {
      libmesh_assert_equal_to(p.size(), v.size());
      for (auto vi : index_range(v))
        v[vi] = FE<Dim,T>::shape_deriv (elem, o, i, j, p[vi], add_p_level);
    }

default_shapes()

static void libMesh::FE< Dim, T >::default_shapes ( const Elem *  elem, const Order  o, const unsigned int  i, const std::vector< Point > &  p, std::vector< OutputShape > &  v, const bool  add_p_level = true  )

inlinestaticprotectedinherited

A default implementation for shapes.

Definition at line 738 of file fe.h.

    {
      libmesh_assert_equal_to(p.size(), v.size());
      for (auto vi : index_range(v))
        v[vi] = FE<Dim,T>::shape (elem, o, i, p[vi], add_p_level);
    }

default_side_nodal_soln()

void libMesh::FE< Dim, T >::default_side_nodal_soln ( const Elem *  elem, const Order  o, const unsigned int  side, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln_on_side, bool  add_p_level = true, const unsigned  vdim = 1  )

staticprotectedinherited

A default implementation for side_nodal_soln.

Definition at line 785 of file fe.C.

{
  std::vector<Number> full_nodal_soln;
  nodal_soln(elem, o, elem_soln, full_nodal_soln, add_p_level, vdim);
  const std::vector<unsigned int> side_nodes =
    elem->nodes_on_side(side);
 
  std::size_t n_side_nodes = side_nodes.size();
  nodal_soln_on_side.resize(n_side_nodes);
  for (auto n : make_range(n_side_nodes))
    nodal_soln_on_side[n] = full_nodal_soln[side_nodes[n]];
}

determine_calculations()

void libMesh::FEGenericBase< FEOutputType< T >::type >::determine_calculations ( )

protectedinherited

Determine which values are to be calculated, for both the FE itself and for the FEMap.

Definition at line 562 of file fe_base.C.

{
  this->calculations_started = true;
 
  // If the user did not explicitly pre-request something (or nothing)
  // to be computed, then we throw an error here.
  bool requested_ok =
    this->calculate_nothing || this->calculate_phi || this->calculate_dphi ||
    this->calculate_dphiref || this->calculate_curl_phi || this->calculate_div_phi ||
    this->calculate_map;
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
  requested_ok = requested_ok || this->calculate_d2phi;
#endif
 
  libmesh_error_msg_if(
    !requested_ok,
    "You must call one or more of the FE accessors "
    "(e.g. get_phi(), get_dphi(), get_nothing()) "
    "_before_ calling reinit()!");
 
  // Request whichever terms are necessary from the FEMap
  if (this->calculate_phi)
    this->_fe_trans->init_map_phi(*this);
 
  if (this->calculate_dphiref)
    this->_fe_trans->init_map_dphi(*this);
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
  if (this->calculate_d2phi)
    this->_fe_trans->init_map_d2phi(*this);
#endif //LIBMESH_ENABLE_SECOND_DERIVATIVES
}

disable_print_counter_info()

void libMesh::ReferenceCounter::disable_print_counter_info ( )

staticinherited

Definition at line 100 of file reference_counter.C.

{
  _enable_print_counter = false;
  return;
}

References libMesh::ReferenceCounter::_enable_print_counter.

dofs_on_edge() [1/2]

void libMesh::FE< Dim, T >::dofs_on_edge ( const Elem *const  elem, const Order  o, unsigned int  e, std::vector< unsigned int > &  di, bool  add_p_level = true  )

staticinherited

Fills the vector di with the local degree of freedom indices associated with edge e of element elem.

On a p-refined element, o should be the base order of the element.

Definition at line 528 of file fe.C.

{
  libmesh_assert(elem);
  libmesh_assert_less (e, elem->n_edges());
 
  di.clear();
  unsigned int nodenum = 0;
  const unsigned int n_nodes = elem->n_nodes();
  for (unsigned int n = 0; n != n_nodes; ++n)
    {
      const unsigned int n_dofs =
          n_dofs_at_node(*elem, static_cast<Order>(o + add_p_level*elem->p_level()), n);
      if (elem->is_node_on_edge(n, e))
        for (unsigned int i = 0; i != n_dofs; ++i)
          di.push_back(nodenum++);
      else
        nodenum += n_dofs;
    }
}

dofs_on_edge() [2/2]

void libMesh::FE< 2, SUBDIVISION >::dofs_on_edge ( const Elem * const  , const Order  , unsigned int  , std::vector< unsigned int > &  di, bool    )

inherited

Definition at line 971 of file fe_subdivision_2D.C.

{ di.resize(0); }

dofs_on_side() [1/2]

void libMesh::FE< Dim, T >::dofs_on_side ( const Elem *const  elem, const Order  o, unsigned int  s, std::vector< unsigned int > &  di, bool  add_p_level = true  )

staticinherited

Fills the vector di with the local degree of freedom indices associated with side s of element elem.

On a p-refined element, o should be the base order of the element.

Definition at line 517 of file fe.C.

{
  libmesh_assert(elem);
  libmesh_assert_less (s, elem->n_sides());
 
  di.clear();
  unsigned int nodenum = 0;
  const unsigned int n_nodes = elem->n_nodes();
  for (unsigned int n = 0; n != n_nodes; ++n)
    {
      const unsigned int n_dofs =
          n_dofs_at_node(*elem, static_cast<Order>(o + add_p_level*elem->p_level()), n);
      if (elem->is_node_on_side(n, s))
        for (unsigned int i = 0; i != n_dofs; ++i)
          di.push_back(nodenum++);
      else
        nodenum += n_dofs;
    }
}

dofs_on_side() [2/2]

void libMesh::FE< 2, SUBDIVISION >::dofs_on_side ( const Elem * const  , const Order  , unsigned int  , std::vector< unsigned int > &  di, bool    )

inherited

Definition at line 970 of file fe_subdivision_2D.C.

{ di.resize(0); }

edge_map()

void libMesh::FE< Dim, T >::edge_map ( const Elem *  elem, const Elem *  edge, const unsigned int  e, const std::vector< Point > &  reference_edge_points, std::vector< Point > &  reference_points  )

virtualinherited

Computes the reference space quadrature points on the side of an element based on the edge quadrature points.

Definition at line 626 of file fe_boundary.C.

{
  // We're calculating mappings - we need at least first order info
  this->calculate_phi = true;
  this->determine_calculations();
 
  unsigned int edge_p_level = elem->p_level();
 
  if (edge->type() != last_edge           ||
      (elem->runtime_topology() &&
       this->_elem != elem)               ||
      edge_p_level != this->_elem_p_level ||
      !this->shapes_on_quadrature)
    {
      // Set the element type
      this->_elem = elem;
      this->_elem_type = elem->type();
      this->_elem_p_level = edge_p_level;
      this->_p_level = this->_add_p_level_in_reinit * edge_p_level;
 
      // Set the last_edge
      last_edge = edge->type();
 
      // Initialize the edge shape functions
      this->_fe_map->template init_edge_shape_functions<Dim>(reference_edge_points, edge);
    }
  else
    this->_elem = elem;
 
  const unsigned int n_points =
    cast_int<unsigned int>(reference_edge_points.size());
  reference_points.resize(n_points);
  for (unsigned int i = 0; i < n_points; i++)
    reference_points[i].zero();
 
  std::vector<Point> refspace_nodes;
  this->get_refspace_nodes(elem->type(), refspace_nodes);
 
  const std::vector<std::vector<Real>> & psi_map = this->_fe_map->get_psi();
 
  // sum over the nodes
  for (auto i : index_range(psi_map))
    {
      const Point & edge_node = refspace_nodes[elem->local_edge_node(e,i)];
      for (unsigned int p=0; p<n_points; p++)
        reference_points[p].add_scaled (edge_node, psi_map[i][p]);
    }
}

edge_reinit() [1/2]

void libMesh::FE< Dim, T >::edge_reinit ( const Elem *  elem, const unsigned int  edge, const Real  tolerance = TOLERANCE, const std::vector< Point > *const  pts = nullptr, const std::vector< Real > *const  weights = nullptr  )

overridevirtualinherited

Reinitializes all the physical element-dependent data based on the edge.

The tolerance parameter is passed to the involved call to inverse_map(). By default the shape functions and associated data are computed at the quadrature points specified by the quadrature rule qrule, but may be any points specified on the reference side element specified in the optional argument pts.

Implements libMesh::FEAbstract.

Definition at line 606 of file fe_boundary.C.

{
  libmesh_assert(elem);
  libmesh_assert (this->qrule != nullptr || pts != nullptr);
  // We don't do this for 1D elements!
  libmesh_assert_not_equal_to (Dim, 1);
 
  // We're (possibly re-) calculating now!  Time to determine what.
  // FIXME - we currently just assume that we're using JxW and calling
  // edge_map later.
  this->_fe_map->add_calculations();
  this->_fe_map->get_JxW();
  this->_fe_map->get_xyz();
  this->determine_calculations();
 
  // Build the side of interest
  const std::unique_ptr<const Elem> edge(elem->build_edge_ptr(e));
 
  // Initialize the shape functions at the user-specified
  // points
  if (pts != nullptr)
    {
      // The shape functions do not correspond to the qrule
      this->shapes_on_quadrature = false;
 
      // Initialize the edge shape functions
      this->_fe_map->template init_edge_shape_functions<Dim> (*pts, edge.get());
 
      // Compute the Jacobian*Weight on the face for integration
      if (weights != nullptr)
        {
          this->_fe_map->compute_edge_map (Dim, *weights, edge.get());
        }
      else
        {
          std::vector<Real> dummy_weights (pts->size(), 1.);
          this->_fe_map->compute_edge_map (Dim, dummy_weights, edge.get());
        }
    }
  // If there are no user specified points, we use the
  // quadrature rule
  else
    {
      // initialize quadrature rule
      this->qrule->init(*edge, elem->p_level());
 
      if (this->qrule->shapes_need_reinit())
        this->shapes_on_quadrature = false;
 
      // We might not need to reinitialize the shape functions
      if ((this->get_type() != elem->type())      ||
          (elem->runtime_topology() &&
           this->_elem != elem)                   ||
          (edge->type() != last_edge)             ||
          this->shapes_need_reinit()              ||
          !this->shapes_on_quadrature)
        {
          // Set the element
          this->_elem = elem;
          this->_elem_type = elem->type();
 
          // Set the last_edge
          last_edge = edge->type();
 
          // Initialize the edge shape functions
          this->_fe_map->template init_edge_shape_functions<Dim> (this->qrule->get_points(), edge.get());
        }
      else
        this->_elem = elem;
 
      // Compute the Jacobian*Weight on the face for integration
      this->_fe_map->compute_edge_map (Dim, this->qrule->get_weights(), edge.get());
 
      // The shape functions correspond to the qrule
      this->shapes_on_quadrature = true;
    }
 
  // make a copy of the Jacobian for integration
  const std::vector<Real> JxW_int(this->_fe_map->get_JxW());
 
  // Find where the integration points are located on the
  // full element.
  const std::vector<Point> * ref_qp;
  if (pts != nullptr)
    ref_qp = pts;
  else
    ref_qp = & this->qrule->get_points();
 
  std::vector<Point> qp;
  this->edge_map(elem, edge.get(), e, *ref_qp, qp);
 
  // compute the shape function and derivative values
  // at the points qp
  this->reinit  (elem, &qp);
 
  // copy back old data
  this->_fe_map->get_JxW() = JxW_int;
}

edge_reinit() [2/2]

void libMesh::FE< 2, SUBDIVISION >::edge_reinit ( Elem const *  , unsigned int  , Real  , const std::vector< Point > * const  , const std::vector< Real > * const    )

virtualinherited

Reinitializes all the physical element-dependent data based on the edge of the element elem.

The tolerance parameter is passed to the involved call to inverse_map(). By default the element data are computed at the quadrature points specified by the quadrature rule qrule, but any set of points on the reference edge element may be specified in the optional argument pts.

Implements libMesh::FEAbstract.

Definition at line 927 of file fe_subdivision_2D.C.

{
  libmesh_not_implemented();
}

enable_print_counter_info()

void libMesh::ReferenceCounter::enable_print_counter_info ( )

staticinherited

Methods to enable/disable the reference counter output from print_info().

Enabled by default.

Definition at line 94 of file reference_counter.C.

{
  _enable_print_counter = true;
  return;
}

References libMesh::ReferenceCounter::_enable_print_counter.

Referenced by libMesh::LibMeshInit::~LibMeshInit().

get_continuity() [1/82]

FEContinuity libMesh::FE< 1, BERNSTEIN >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 423 of file fe_bernstein.C.

{ return C_ZERO; }

get_continuity() [2/82]

FEContinuity libMesh::FE< 2, BERNSTEIN >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 424 of file fe_bernstein.C.

{ return C_ZERO; }

get_continuity() [3/82]

FEContinuity libMesh::FE< 3, BERNSTEIN >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 425 of file fe_bernstein.C.

{ return C_ZERO; }

get_continuity() [4/82]

FEContinuity libMesh::FE< 1, CLOUGH >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 271 of file fe_clough.C.

{ return C_ONE; }

get_continuity() [5/82]

FEContinuity libMesh::FE< 2, CLOUGH >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 272 of file fe_clough.C.

{ return C_ONE; }

get_continuity() [6/82]

FEContinuity libMesh::FE< 3, CLOUGH >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 273 of file fe_clough.C.

{ return C_ONE; }

get_continuity() [7/82]

FEContinuity libMesh::FE< 1, HERMITE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 313 of file fe_hermite.C.

{ return C_ONE; }

get_continuity() [8/82]

FEContinuity libMesh::FE< 2, HERMITE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 314 of file fe_hermite.C.

{ return C_ONE; }

get_continuity() [9/82]

FEContinuity libMesh::FE< 3, HERMITE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 315 of file fe_hermite.C.

{ return C_ONE; }

get_continuity() [10/82]

FEContinuity libMesh::FE< 1, HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 477 of file fe_hierarchic.C.

{ return C_ZERO; }

get_continuity() [11/82]

FEContinuity libMesh::FE< 2, HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 478 of file fe_hierarchic.C.

{ return C_ZERO; }

get_continuity() [12/82]

FEContinuity libMesh::FE< 3, HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 479 of file fe_hierarchic.C.

{ return C_ZERO; }

get_continuity() [13/82]

FEContinuity libMesh::FE< 0, HIERARCHIC_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 773 of file fe_hierarchic_vec.C.

{ return C_ZERO; }

get_continuity() [14/82]

FEContinuity libMesh::FE< 1, HIERARCHIC_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 774 of file fe_hierarchic_vec.C.

{ return C_ZERO; }

get_continuity() [15/82]

FEContinuity libMesh::FE< 2, HIERARCHIC_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 775 of file fe_hierarchic_vec.C.

{ return C_ZERO; }

get_continuity() [16/82]

FEContinuity libMesh::FE< 3, HIERARCHIC_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 776 of file fe_hierarchic_vec.C.

{ return C_ZERO; }

get_continuity() [17/82]

FEContinuity libMesh::FE< 0, L2_HIERARCHIC_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 779 of file fe_hierarchic_vec.C.

{ return DISCONTINUOUS; }

get_continuity() [18/82]

FEContinuity libMesh::FE< 1, L2_HIERARCHIC_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 780 of file fe_hierarchic_vec.C.

{ return DISCONTINUOUS; }

get_continuity() [19/82]

FEContinuity libMesh::FE< 2, L2_HIERARCHIC_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 781 of file fe_hierarchic_vec.C.

{ return DISCONTINUOUS; }

get_continuity() [20/82]

FEContinuity libMesh::FE< 3, L2_HIERARCHIC_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 782 of file fe_hierarchic_vec.C.

{ return DISCONTINUOUS; }

get_continuity() [21/82]

FEContinuity libMesh::FE< 0, L2_HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 188 of file fe_l2_hierarchic.C.

{ return DISCONTINUOUS; }

get_continuity() [22/82]

FEContinuity libMesh::FE< 1, L2_HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 189 of file fe_l2_hierarchic.C.

{ return DISCONTINUOUS; }

get_continuity() [23/82]

FEContinuity libMesh::FE< 2, L2_HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 190 of file fe_l2_hierarchic.C.

{ return DISCONTINUOUS; }

get_continuity() [24/82]

FEContinuity libMesh::FE< 3, L2_HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 191 of file fe_l2_hierarchic.C.

{ return DISCONTINUOUS; }

get_continuity() [25/82]

FEContinuity libMesh::FE< 0, L2_LAGRANGE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 256 of file fe_l2_lagrange.C.

{ return DISCONTINUOUS; }

get_continuity() [26/82]

FEContinuity libMesh::FE< 1, L2_LAGRANGE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 257 of file fe_l2_lagrange.C.

{ return DISCONTINUOUS; }

get_continuity() [27/82]

FEContinuity libMesh::FE< 2, L2_LAGRANGE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 258 of file fe_l2_lagrange.C.

{ return DISCONTINUOUS; }

get_continuity() [28/82]

FEContinuity libMesh::FE< 3, L2_LAGRANGE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 259 of file fe_l2_lagrange.C.

{ return DISCONTINUOUS; }

get_continuity() [29/82]

FEContinuity libMesh::FE< 0, LAGRANGE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1114 of file fe_lagrange.C.

{ return C_ZERO; }

get_continuity() [30/82]

FEContinuity libMesh::FE< 1, LAGRANGE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1115 of file fe_lagrange.C.

{ return C_ZERO; }

get_continuity() [31/82]

FEContinuity libMesh::FE< 2, LAGRANGE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1116 of file fe_lagrange.C.

{ return C_ZERO; }

get_continuity() [32/82]

FEContinuity libMesh::FE< 3, LAGRANGE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1117 of file fe_lagrange.C.

{ return C_ZERO; }

get_continuity() [33/82]

FEContinuity libMesh::FE< 0, LAGRANGE_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1342 of file fe_lagrange_vec.C.

{ return C_ZERO; }

get_continuity() [34/82]

FEContinuity libMesh::FE< 1, LAGRANGE_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1343 of file fe_lagrange_vec.C.

{ return C_ZERO; }

get_continuity() [35/82]

FEContinuity libMesh::FE< 2, LAGRANGE_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1344 of file fe_lagrange_vec.C.

{ return C_ZERO; }

get_continuity() [36/82]

FEContinuity libMesh::FE< 3, LAGRANGE_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1345 of file fe_lagrange_vec.C.

{ return C_ZERO; }

get_continuity() [37/82]

FEContinuity libMesh::FE< 0, L2_LAGRANGE_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1348 of file fe_lagrange_vec.C.

{ return DISCONTINUOUS; }

get_continuity() [38/82]

FEContinuity libMesh::FE< 1, L2_LAGRANGE_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1349 of file fe_lagrange_vec.C.

{ return DISCONTINUOUS; }

get_continuity() [39/82]

FEContinuity libMesh::FE< 2, L2_LAGRANGE_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1350 of file fe_lagrange_vec.C.

{ return DISCONTINUOUS; }

get_continuity() [40/82]

FEContinuity libMesh::FE< 3, L2_LAGRANGE_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1351 of file fe_lagrange_vec.C.

{ return DISCONTINUOUS; }

get_continuity() [41/82]

FEContinuity libMesh::FE< 0, MONOMIAL >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 421 of file fe_monomial.C.

{ return DISCONTINUOUS; }

get_continuity() [42/82]

FEContinuity libMesh::FE< 1, MONOMIAL >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 422 of file fe_monomial.C.

{ return DISCONTINUOUS; }

get_continuity() [43/82]

FEContinuity libMesh::FE< 2, MONOMIAL >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 423 of file fe_monomial.C.

{ return DISCONTINUOUS; }

get_continuity() [44/82]

FEContinuity libMesh::FE< 3, MONOMIAL >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 424 of file fe_monomial.C.

{ return DISCONTINUOUS; }

get_continuity() [45/82]

FEContinuity libMesh::FE< 0, MONOMIAL_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 697 of file fe_monomial_vec.C.

{
  return DISCONTINUOUS;
}

get_continuity() [46/82]

FEContinuity libMesh::FE< 1, MONOMIAL_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 703 of file fe_monomial_vec.C.

{
  return DISCONTINUOUS;
}

get_continuity() [47/82]

FEContinuity libMesh::FE< 2, MONOMIAL_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 709 of file fe_monomial_vec.C.

{
  return DISCONTINUOUS;
}

get_continuity() [48/82]

FEContinuity libMesh::FE< 3, MONOMIAL_VEC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 715 of file fe_monomial_vec.C.

{
  return DISCONTINUOUS;
}

get_continuity() [49/82]

FEContinuity libMesh::FE< 0, NEDELEC_ONE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 408 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

get_continuity() [50/82]

FEContinuity libMesh::FE< 1, NEDELEC_ONE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 409 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

get_continuity() [51/82]

FEContinuity libMesh::FE< 2, NEDELEC_ONE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 410 of file fe_nedelec_one.C.

{ return H_CURL; }

get_continuity() [52/82]

FEContinuity libMesh::FE< 3, NEDELEC_ONE >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 411 of file fe_nedelec_one.C.

{ return H_CURL; }

get_continuity() [53/82]

FEContinuity libMesh::FE< 0, RATIONAL_BERNSTEIN >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 160 of file fe_rational.C.

{ return C_ZERO; }

get_continuity() [54/82]

FEContinuity libMesh::FE< 1, RATIONAL_BERNSTEIN >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 161 of file fe_rational.C.

{ return C_ZERO; }

get_continuity() [55/82]

FEContinuity libMesh::FE< 2, RATIONAL_BERNSTEIN >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 162 of file fe_rational.C.

{ return C_ZERO; }

get_continuity() [56/82]

FEContinuity libMesh::FE< 3, RATIONAL_BERNSTEIN >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 163 of file fe_rational.C.

{ return C_ZERO; }

get_continuity() [57/82]

FEContinuity libMesh::FE< 0, RAVIART_THOMAS >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 456 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

get_continuity() [58/82]

FEContinuity libMesh::FE< 1, RAVIART_THOMAS >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 457 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

get_continuity() [59/82]

FEContinuity libMesh::FE< 2, RAVIART_THOMAS >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 458 of file fe_raviart.C.

{ return H_DIV; }

get_continuity() [60/82]

FEContinuity libMesh::FE< 3, RAVIART_THOMAS >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 459 of file fe_raviart.C.

{ return H_DIV; }

get_continuity() [61/82]

FEContinuity libMesh::FE< 0, L2_RAVIART_THOMAS >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 462 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

get_continuity() [62/82]

FEContinuity libMesh::FE< 1, L2_RAVIART_THOMAS >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 463 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

get_continuity() [63/82]

FEContinuity libMesh::FE< 2, L2_RAVIART_THOMAS >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 464 of file fe_raviart.C.

{ return DISCONTINUOUS; }

get_continuity() [64/82]

FEContinuity libMesh::FE< 3, L2_RAVIART_THOMAS >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 465 of file fe_raviart.C.

{ return DISCONTINUOUS; }

get_continuity() [65/82]

FEContinuity libMesh::FE< 0, SCALAR >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 95 of file fe_scalar.C.

{ return DISCONTINUOUS; }

get_continuity() [66/82]

FEContinuity libMesh::FE< 1, SCALAR >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 96 of file fe_scalar.C.

{ return DISCONTINUOUS; }

get_continuity() [67/82]

FEContinuity libMesh::FE< 2, SCALAR >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 97 of file fe_scalar.C.

{ return DISCONTINUOUS; }

get_continuity() [68/82]

FEContinuity libMesh::FE< 3, SCALAR >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 98 of file fe_scalar.C.

{ return DISCONTINUOUS; }

get_continuity() [69/82]

FEContinuity libMesh::FE< 0, SIDE_HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 327 of file fe_side_hierarchic.C.

{ return SIDE_DISCONTINUOUS; }

get_continuity() [70/82]

FEContinuity libMesh::FE< 1, SIDE_HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 328 of file fe_side_hierarchic.C.

{ return SIDE_DISCONTINUOUS; }

get_continuity() [71/82]

FEContinuity libMesh::FE< 2, SIDE_HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 329 of file fe_side_hierarchic.C.

{ return SIDE_DISCONTINUOUS; }

get_continuity() [72/82]

FEContinuity libMesh::FE< 3, SIDE_HIERARCHIC >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 330 of file fe_side_hierarchic.C.

{ return SIDE_DISCONTINUOUS; }

get_continuity() [73/82]

FEContinuity libMesh::FE< 2, SUBDIVISION >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 974 of file fe_subdivision_2D.C.

{ return C_ONE; }

get_continuity() [74/82]

FEContinuity libMesh::FE< 0, SZABAB >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1325 of file fe_szabab.C.

{ return C_ZERO; }

get_continuity() [75/82]

FEContinuity libMesh::FE< 1, SZABAB >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1326 of file fe_szabab.C.

{ return C_ZERO; }

get_continuity() [76/82]

FEContinuity libMesh::FE< 2, SZABAB >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1327 of file fe_szabab.C.

{ return C_ZERO; }

get_continuity() [77/82]

FEContinuity libMesh::FE< 3, SZABAB >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 1328 of file fe_szabab.C.

{ return C_ZERO; }

get_continuity() [78/82]

FEContinuity libMesh::FE< 0, XYZ >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 406 of file fe_xyz.C.

{ return DISCONTINUOUS; }

get_continuity() [79/82]

FEContinuity libMesh::FE< 1, XYZ >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 407 of file fe_xyz.C.

{ return DISCONTINUOUS; }

get_continuity() [80/82]

FEContinuity libMesh::FE< 2, XYZ >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 408 of file fe_xyz.C.

{ return DISCONTINUOUS; }

get_continuity() [81/82]

FEContinuity libMesh::FE< 3, XYZ >::get_continuity ( ) const

virtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

Definition at line 409 of file fe_xyz.C.

{ return DISCONTINUOUS; }

get_continuity() [82/82]

virtual FEContinuity libMesh::FE< Dim, T >::get_continuity ( ) const

overridevirtualinherited

Returns

The continuity level of the finite element.

Implements libMesh::FEAbstract.

get_curl_phi()

virtual_for_inffe const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_curl_phi ( ) const

inlineinherited

Returns

The curl of the shape function at the quadrature points.

Definition at line 252 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_curl_phi);
    calculate_curl_phi = calculate_dphiref = true; return curl_phi; }

get_curvatures()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_curvatures ( ) const

inlineinherited

Returns

The curvatures for use in face integration.

Definition at line 467 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_curvatures();}

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_d2phi()

const std::vector< std::vector< OutputTensor > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phi ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points.

Definition at line 319 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phi; }

get_d2phideta2()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phideta2 ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 403 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phideta2; }

get_d2phidetadzeta()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidetadzeta ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 411 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidetadzeta; }

get_d2phidx2()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidx2 ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points.

Definition at line 331 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidx2; }

get_d2phidxdy()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidxdy ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points.

Definition at line 339 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidxdy; }

get_d2phidxdz()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidxdz ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points.

Definition at line 347 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidxdz; }

get_d2phidxi2()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidxi2 ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 379 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidxi2; }

get_d2phidxideta()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidxideta ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 387 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidxideta; }

get_d2phidxidzeta()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidxidzeta ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 395 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidxidzeta; }

get_d2phidy2()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidy2 ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points.

Definition at line 355 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi =  calculate_dphiref = true; return d2phidy2; }

get_d2phidydz()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidydz ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points.

Definition at line 363 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidydz; }

get_d2phidz2()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidz2 ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points.

Definition at line 371 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidz2; }

get_d2phidzeta2()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_d2phidzeta2 ( ) const

inlineinherited

Returns

The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 419 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dphiref = true; return d2phidzeta2; }

get_d2xyzdeta2()

virtual_for_inffe const std::vector< RealGradient > & libMesh::FEAbstract::get_d2xyzdeta2 ( ) const

inlineinherited

Returns

The second partial derivatives in eta.

Definition at line 343 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_d2xyzdeta2(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_d2xyzdetadzeta()

virtual_for_inffe const std::vector< RealGradient > & libMesh::FEAbstract::get_d2xyzdetadzeta ( ) const

inlineinherited

Returns

The second partial derivatives in eta-zeta.

Definition at line 371 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_d2xyzdetadzeta(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_d2xyzdxi2()

virtual_for_inffe const std::vector< RealGradient > & libMesh::FEAbstract::get_d2xyzdxi2 ( ) const

inlineinherited

Returns

The second partial derivatives in xi.

Definition at line 336 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_d2xyzdxi2(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_d2xyzdxideta()

virtual_for_inffe const std::vector< RealGradient > & libMesh::FEAbstract::get_d2xyzdxideta ( ) const

inlineinherited

Returns

The second partial derivatives in xi-eta.

Definition at line 357 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_d2xyzdxideta(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_d2xyzdxidzeta()

virtual_for_inffe const std::vector< RealGradient > & libMesh::FEAbstract::get_d2xyzdxidzeta ( ) const

inlineinherited

Returns

The second partial derivatives in xi-zeta.

Definition at line 364 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_d2xyzdxidzeta(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_d2xyzdzeta2()

virtual_for_inffe const std::vector< RealGradient > & libMesh::FEAbstract::get_d2xyzdzeta2 ( ) const

inlineinherited

Returns

The second partial derivatives in zeta.

Definition at line 350 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_d2xyzdzeta2(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_detadx()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_detadx ( ) const

inlineinherited

Returns

The deta/dx entry in the transformation matrix from physical to local coordinates.

Definition at line 405 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_detadx(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_detady()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_detady ( ) const

inlineinherited

Returns

The deta/dy entry in the transformation matrix from physical to local coordinates.

Definition at line 413 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_detady(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_detadz()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_detadz ( ) const

inlineinherited

Returns

The deta/dz entry in the transformation matrix from physical to local coordinates.

Definition at line 421 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_detadz(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_dim()

unsigned int libMesh::FEAbstract::get_dim ( ) const

inlineinherited

Returns

the dimension of this FE

Definition at line 258 of file fe_abstract.h.

  { return dim; }

References libMesh::FEAbstract::dim.

get_div_phi()

virtual_for_inffe const std::vector< std::vector< OutputDivergence > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_div_phi ( ) const

inlineinherited

Returns

The divergence of the shape function at the quadrature points.

Definition at line 261 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_div_phi);
    calculate_div_phi = calculate_dphiref = true; return div_phi; }

get_dphase()

const std::vector< OutputGradient > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphase ( ) const

inlineinherited

Returns

The global first derivative of the phase term which is used in infinite elements, evaluated at the quadrature points.

In case of the general finite element class FE this field is initialized to all zero, so that the variational formulation for an infinite element produces correct element matrices for a mesh using both finite and infinite elements.

Definition at line 437 of file fe_base.h.

  { return dphase; }

get_dphi()

const std::vector< std::vector< OutputGradient > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphi ( ) const

inlineinherited

Returns

The shape function derivatives at the quadrature points.

Definition at line 230 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_dphi);
    calculate_dphi = calculate_dphiref = true; return dphi; }

get_dphi_over_decay()

virtual const std::vector< std::vector< OutputGradient > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphi_over_decay ( ) const

inlinevirtualinherited

Returns

the gradient of the shape function (see get_dphi()), but in case of InfFE, weighted with 1/decay.

In contrast to the shape function, its gradient stays finite when divided by the decay function.

Definition at line 511 of file fe_base.h.

  { return get_dphi();}

get_dphi_over_decayxR()

virtual const std::vector< std::vector< OutputGradient > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphi_over_decayxR ( ) const

inlinevirtualinherited

Returns

the gradient of the shape function (see get_dphi()), but in case of InfFE, weighted with r/decay. See get_phi_over_decayxR() for details.

Definition at line 501 of file fe_base.h.

  { return get_dphi();}

get_dphideta()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphideta ( ) const

inlineinherited

Returns

The shape function eta-derivative at the quadrature points.

Definition at line 301 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_dphiref);
    calculate_dphiref = true; return dphideta; }

get_dphidx()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphidx ( ) const

inlineinherited

Returns

The shape function x-derivative at the quadrature points.

Definition at line 269 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_dphi);
    calculate_dphi = calculate_dphiref = true; return dphidx; }

get_dphidxi()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphidxi ( ) const

inlineinherited

Returns

The shape function xi-derivative at the quadrature points.

Definition at line 293 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_dphiref);
    calculate_dphiref = true; return dphidxi; }

get_dphidy()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphidy ( ) const

inlineinherited

Returns

The shape function y-derivative at the quadrature points.

Definition at line 277 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_dphi);
    calculate_dphi = calculate_dphiref = true; return dphidy; }

get_dphidz()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphidz ( ) const

inlineinherited

Returns

The shape function z-derivative at the quadrature points.

Definition at line 285 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_dphi);
    calculate_dphi = calculate_dphiref = true; return dphidz; }

get_dphidzeta()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dphidzeta ( ) const

inlineinherited

Returns

The shape function zeta-derivative at the quadrature points.

Definition at line 309 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_dphiref);
    calculate_dphiref = true; return dphidzeta; }

get_dual_coeff()

const DenseMatrix< Real > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dual_coeff ( ) const

inlineinherited

Definition at line 244 of file fe_base.h.

  { return dual_coeff; }

get_dual_d2phi()

const std::vector< std::vector< OutputTensor > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dual_d2phi ( ) const

inlineinherited

Definition at line 323 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_d2phi);
    calculate_d2phi = calculate_dual = calculate_dphiref = true; return dual_d2phi; }

get_dual_dphi()

const std::vector< std::vector< OutputGradient > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dual_dphi ( ) const

inlineinherited

Definition at line 234 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_dphi);
    calculate_dphi = calculate_dual = calculate_dphiref = true; return dual_dphi; }

get_dual_phi()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_dual_phi ( ) const

inlineinherited

Definition at line 211 of file fe_base.h.

  {
    libmesh_assert(!calculations_started || calculate_dual);
    calculate_dual = true;
    // Dual phi computation relies on primal phi computation
    this->request_phi();
    return dual_phi;
  }

get_dxidx()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_dxidx ( ) const

inlineinherited

Returns

The dxi/dx entry in the transformation matrix from physical to local coordinates.

Definition at line 381 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_dxidx(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_dxidy()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_dxidy ( ) const

inlineinherited

Returns

The dxi/dy entry in the transformation matrix from physical to local coordinates.

Definition at line 389 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_dxidy(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_dxidz()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_dxidz ( ) const

inlineinherited

Returns

The dxi/dz entry in the transformation matrix from physical to local coordinates.

Definition at line 397 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_dxidz(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_dxyzdeta()

virtual_for_inffe const std::vector< RealGradient > & libMesh::FEAbstract::get_dxyzdeta ( ) const

inlineinherited

Returns

The element tangents in eta-direction at the quadrature points.

Definition at line 319 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_dxyzdeta(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_dxyzdxi()

virtual_for_inffe const std::vector< RealGradient > & libMesh::FEAbstract::get_dxyzdxi ( ) const

inlineinherited

Returns

The element tangents in xi-direction at the quadrature points.

Definition at line 311 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_dxyzdxi(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_dxyzdzeta()

virtual_for_inffe const std::vector< RealGradient > & libMesh::FEAbstract::get_dxyzdzeta ( ) const

inlineinherited

Returns

The element tangents in zeta-direction at the quadrature points.

Definition at line 327 of file fe_abstract.h.

  { return _fe_map->get_dxyzdzeta(); }

References libMesh::FEAbstract::_fe_map.

get_dzetadx()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_dzetadx ( ) const

inlineinherited

Returns

The dzeta/dx entry in the transformation matrix from physical to local coordinates.

Definition at line 429 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_dzetadx(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_dzetady()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_dzetady ( ) const

inlineinherited

Returns

The dzeta/dy entry in the transformation matrix from physical to local coordinates.

Definition at line 437 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_dzetady(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_dzetadz()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_dzetadz ( ) const

inlineinherited

Returns

The dzeta/dz entry in the transformation matrix from physical to local coordinates.

Definition at line 445 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_dzetadz(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_elem()

const Elem * libMesh::FEAbstract::get_elem ( ) const

inlineinherited

Returns

The element that the current shape functions have been calculated for. Useful in determining when shape functions must be recomputed.

Definition at line 496 of file fe_abstract.h.

{ return _elem; }

References libMesh::FEAbstract::_elem.

get_family()

FEFamily libMesh::FEAbstract::get_family ( ) const

inlineinherited

Returns

The finite element family of this element.

Definition at line 547 of file fe_abstract.h.

{ return fe_type.family; }

References libMesh::FEType::family, and libMesh::FEAbstract::fe_type.

Referenced by libMesh::FE< Dim, T >::FE().

get_fe_map() [1/2]

FEMap & libMesh::FEAbstract::get_fe_map ( )

inlineinherited

Definition at line 555 of file fe_abstract.h.

{ return *_fe_map.get(); }

References libMesh::FEAbstract::_fe_map.

get_fe_map() [2/2]

const FEMap & libMesh::FEAbstract::get_fe_map ( ) const

inlineinherited

Returns

The mapping object

Note

for InfFE, this gives a useless object.

Definition at line 554 of file fe_abstract.h.

{ return *_fe_map.get(); }

References libMesh::FEAbstract::_fe_map.

Referenced by libMesh::VariationalSmootherSystem::init_context(), libMesh::H1FETransformation< OutputShape >::init_map_d2phi(), libMesh::HCurlFETransformation< OutputShape >::init_map_d2phi(), libMesh::HDivFETransformation< OutputShape >::init_map_d2phi(), libMesh::H1FETransformation< OutputShape >::init_map_dphi(), libMesh::HCurlFETransformation< OutputShape >::init_map_dphi(), libMesh::HDivFETransformation< OutputShape >::init_map_dphi(), libMesh::HCurlFETransformation< OutputShape >::init_map_phi(), libMesh::HDivFETransformation< OutputShape >::init_map_phi(), libMesh::HCurlFETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_d2phi(), libMesh::HDivFETransformation< OutputShape >::map_div(), libMesh::H1FETransformation< OutputShape >::map_div(), libMesh::H1FETransformation< OutputShape >::map_dphi(), libMesh::HCurlFETransformation< OutputShape >::map_phi(), and libMesh::HDivFETransformation< OutputShape >::map_phi().

get_fe_type()

FEType libMesh::FEAbstract::get_fe_type ( ) const

inlineinherited

Returns

The FE Type (approximation order and family) of the finite element.

Definition at line 520 of file fe_abstract.h.

{ return fe_type; }

References libMesh::FEAbstract::fe_type.

Referenced by libMesh::RBConstruction::add_scaled_matrix_and_vector(), assemble_func(), assemble_SchroedingerEquation(), assemble_wave(), libMesh::FEMContext::build_new_fe(), libMesh::HCurlFETransformation< OutputShape >::map_phi(), libMesh::HDivFETransformation< OutputShape >::map_phi(), libMesh::H1FETransformation< OutputShape >::map_phi(), NavierSystem::side_constraint(), and libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubFunctor::SubFunctor().

get_info()

std::string libMesh::ReferenceCounter::get_info ( )

staticinherited

Gets a string containing the reference information.

Definition at line 47 of file reference_counter.C.

{
#if defined(LIBMESH_ENABLE_REFERENCE_COUNTING) && defined(DEBUG)
 
  std::ostringstream oss;
 
  oss << '\n'
      << " ---------------------------------------------------------------------------- \n"
      << "| Reference count information                                                |\n"
      << " ---------------------------------------------------------------------------- \n";
 
  for (const auto & [name, cd] : _counts)
    oss << "| " << name << " reference count information:\n"
        << "|  Creations:    " << cd.first    << '\n'
        << "|  Destructions: " << cd.second << '\n';
 
  oss << " ---------------------------------------------------------------------------- \n";
 
  return oss.str();
 
#else
 
  return "";
 
#endif
}

References libMesh::ReferenceCounter::_counts.

Referenced by libMesh::ReferenceCounter::print_info().

get_JxW()

virtual_for_inffe const std::vector< Real > & libMesh::FEAbstract::get_JxW ( ) const

inlineinherited

Returns

The element Jacobian times the quadrature weight for each quadrature point.

For InfFE, use get_JxWxdecay_sq() instead.

Definition at line 303 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_JxW(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

Referenced by libMesh::ExactSolution::_compute_error(), assembly_with_dg_fem_context(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::KellyErrorEstimator::boundary_side_integration(), compute_enriched_soln(), libMesh::FirstOrderUnsteadySolver::compute_second_order_eqns(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubProjector::construct_projection(), CoupledSystem::element_constraint(), NavierSystem::element_constraint(), LaplaceSystem::element_postprocess(), PoissonSystem::element_postprocess(), LaplaceQoI::element_qoi(), HeatSystem::element_qoi(), HeatSystem::element_qoi_derivative(), LaplaceSystem::element_qoi_derivative(), LaplaceQoI::element_qoi_derivative(), LaplaceSystem::element_time_derivative(), CoupledSystem::element_time_derivative(), HeatSystem::element_time_derivative(), PoissonSystem::element_time_derivative(), NavierSystem::element_time_derivative(), SolidSystem::element_time_derivative(), ElasticitySystem::element_time_derivative(), CurlCurlSystem::element_time_derivative(), SigmaPhysics::element_time_derivative(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::FEAbstract::get_JxWxdecay_sq(), CoupledSystemQoI::init_context(), libMesh::FEMSystem::init_context(), LaplaceSystem::init_context(), LaplaceQoI::init_context(), CoupledSystem::init_context(), HeatSystem::init_context(), PoissonSystem::init_context(), NavierSystem::init_context(), SolidSystem::init_context(), ElasticitySystem::init_context(), CurlCurlSystem::init_context(), SigmaPhysics::init_context(), ElasticityRBConstruction::init_context(), libMesh::DiscontinuityMeasure::init_context(), HilbertSystem::init_context(), libMesh::DiscontinuityMeasure::internal_side_integration(), libMesh::LaplacianErrorEstimator::internal_side_integration(), libMesh::KellyErrorEstimator::internal_side_integration(), libMesh::FEMPhysics::mass_residual(), NavierSystem::mass_residual(), ElasticitySystem::mass_residual(), Integrate::operator()(), LaplaceSystem::side_constraint(), LaplaceSystem::side_postprocess(), CoupledSystemQoI::side_qoi(), LaplaceSystem::side_qoi_derivative(), CoupledSystemQoI::side_qoi_derivative(), SolidSystem::side_time_derivative(), ElasticitySystem::side_time_derivative(), CurlCurlSystem::side_time_derivative(), and libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubFunctor::SubFunctor().

get_JxWxdecay_sq()

virtual const std::vector< Real > & libMesh::FEAbstract::get_JxWxdecay_sq ( ) const

inlinevirtualinherited

This function is the variant of get_JxW() for InfFE.

Since J diverges there, a respectize decay-function must be applied to obtain well-defined quantities.

For FE, it is equivalent to the common get_JxW().

Reimplemented in libMesh::InfFE< Dim, T_radial, T_map >.

Definition at line 292 of file fe_abstract.h.

  { return get_JxW();}

References libMesh::FEAbstract::get_JxW().

Referenced by assemble_func(), assemble_SchroedingerEquation(), and assemble_wave().

get_normals()

virtual_for_inffe const std::vector< Point > & libMesh::FEAbstract::get_normals ( ) const

inlineinherited

Returns

The outward pointing normal vectors for face integration.

Definition at line 459 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_normals(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

Referenced by libMesh::KellyErrorEstimator::boundary_side_integration(), compute_enriched_soln(), libMesh::ParsedFEMFunction< Output >::eval_args(), libMesh::ParsedFEMFunction< Output >::init_context(), ElasticitySystem::init_context(), libMesh::KellyErrorEstimator::init_context(), libMesh::KellyErrorEstimator::internal_side_integration(), LaplaceSystem::side_postprocess(), LaplaceSystem::side_qoi_derivative(), ElasticitySystem::side_time_derivative(), and CurlCurlSystem::side_time_derivative().

get_nothing()

void libMesh::FEAbstract::get_nothing ( ) const

inlineinherited

Returns

nothing, but lets the FE know you're explicitly prerequesting calculations. This is useful when you only want the FE for n_quadrature_points, n_dofs_on_side, or other methods that don't require shape function calculations, but you don't want libMesh "backwards compatibility" mode to assume you've made no prerequests and need to calculate everything.

Definition at line 269 of file fe_abstract.h.

  { calculate_nothing = true; }

References libMesh::FEAbstract::calculate_nothing.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::ParsedFEMFunction< Output >::init_context(), libMesh::WrappedFunctor< Output >::init_context(), CoupledSystemQoI::init_context(), CoupledSystem::init_context(), HeatSystem::init_context(), NavierSystem::init_context(), ElasticitySystem::init_context(), SigmaPhysics::init_context(), HilbertSystem::init_context(), libMesh::VariationalSmootherSystem::init_context(), and Integrate::operator()().

get_order()

Order libMesh::FEAbstract::get_order ( ) const

inlineinherited

Returns

The approximation order of the finite element.

Definition at line 525 of file fe_abstract.h.

  { return fe_type.order + _p_level; }

References libMesh::FEAbstract::_p_level, libMesh::FEAbstract::fe_type, and libMesh::FEType::order.

get_p_level()

unsigned int libMesh::FEAbstract::get_p_level ( ) const

inlineinherited

Returns

The p refinement level that the current shape functions have been calculated for.

Definition at line 515 of file fe_abstract.h.

{ return _p_level; }

References libMesh::FEAbstract::_p_level.

get_phi()

const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_phi ( ) const

inlineinherited

Returns

The shape function values at the quadrature points on the element.

Definition at line 207 of file fe_base.h.

  { libmesh_assert(!calculations_started || calculate_phi);
    calculate_phi = true; return phi; }

get_phi_over_decayxR()

virtual const std::vector< std::vector< OutputShape > > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_phi_over_decayxR ( ) const

inlinevirtualinherited

Returns

The shape function phi (for FE) and phi weighted by r/decay for InfFE.

To compensate for the decay function applied to the Jacobian (see get_JxWxdecay_sq), the wave function phi should be divided by this function.

The factor r must be compensated for by the Sobolev weight. (i.e. by using get_Sobolev_weightxR_sq())

Definition at line 493 of file fe_base.h.

  { return get_phi();}

get_refspace_nodes()

void libMesh::FEAbstract::get_refspace_nodes ( const ElemType  t, std::vector< Point > &  nodes  )

staticinherited

Returns

The reference space coordinates of nodes based on the element type.

Definition at line 400 of file fe_abstract.C.

{
  const unsigned int n_nodes = Elem::type_to_n_nodes_map[itemType];
  if (n_nodes == invalid_uint)
    libmesh_error_msg("Number of nodes is not well-defined for " <<
                      Utility::enum_to_string(itemType));
 
  nodes.resize(n_nodes);
  switch(itemType)
    {
    case NODEELEM:
      {
        nodes[0] = Point (0.,0.,0.);
        return;
      }
    case EDGE3:
      {
        nodes[2] = Point (0.,0.,0.);
        libmesh_fallthrough();
      }
    case EDGE2:
      {
        nodes[0] = Point (-1.,0.,0.);
        nodes[1] = Point (1.,0.,0.);
        return;
      }
    case EDGE4: // not nested with EDGE3
      {
        nodes[0] = Point (-1.,0.,0.);
        nodes[1] = Point (1.,0.,0.);
        nodes[2] = Point (-1./3.,0.,0.);
        nodes[3] - Point (1./3.,0.,0.);
        return;
      }
    case TRI7:
      {
        nodes[6] = Point (1./3.,1./3.,0.);
        libmesh_fallthrough();
      }
    case TRI6:
      {
        nodes[3] = Point (.5,0.,0.);
        nodes[4] = Point (.5,.5,0.);
        nodes[5] = Point (0.,.5,0.);
        libmesh_fallthrough();
      }
    case TRI3:
    case TRISHELL3:
      {
        nodes[0] = Point (0.,0.,0.);
        nodes[1] = Point (1.,0.,0.);
        nodes[2] = Point (0.,1.,0.);
        return;
      }
    case QUAD9:
    case QUADSHELL9:
      {
        nodes[8] = Point (0.,0.,0.);
        libmesh_fallthrough();
      }
    case QUAD8:
    case QUADSHELL8:
      {
        nodes[4] = Point (0.,-1.,0.);
        nodes[5] = Point (1.,0.,0.);
        nodes[6] = Point (0.,1.,0.);
        nodes[7] = Point (-1.,0.,0.);
        libmesh_fallthrough();
      }
    case QUAD4:
    case QUADSHELL4:
      {
        nodes[0] = Point (-1.,-1.,0.);
        nodes[1] = Point (1.,-1.,0.);
        nodes[2] = Point (1.,1.,0.);
        nodes[3] = Point (-1.,1.,0.);
        return;
      }
    case TET14:
      {
        nodes[10] = Point (1/Real(3),1/Real(3),0.);
        nodes[11] = Point (1/Real(3),0.,1/Real(3));
        nodes[12] = Point (1/Real(3),1/Real(3),1/Real(3));
        nodes[13] = Point (0.,1/Real(3),1/Real(3));
        libmesh_fallthrough();
      }
    case TET10:
      {
        nodes[4] = Point (.5,0.,0.);
        nodes[5] = Point (.5,.5,0.);
        nodes[6] = Point (0.,.5,0.);
        nodes[7] = Point (0.,0.,.5);
        nodes[8] = Point (.5,0.,.5);
        nodes[9] = Point (0.,.5,.5);
        libmesh_fallthrough();
      }
    case TET4:
      {
        nodes[0] = Point (0.,0.,0.);
        nodes[1] = Point (1.,0.,0.);
        nodes[2] = Point (0.,1.,0.);
        nodes[3] = Point (0.,0.,1.);
        return;
      }
    case HEX27:
      {
        nodes[20] = Point (0.,0.,-1.);
        nodes[21] = Point (0.,-1.,0.);
        nodes[22] = Point (1.,0.,0.);
        nodes[23] = Point (0.,1.,0.);
        nodes[24] = Point (-1.,0.,0.);
        nodes[25] = Point (0.,0.,1.);
        nodes[26] = Point (0.,0.,0.);
        libmesh_fallthrough();
      }
    case HEX20:
      {
        nodes[8] = Point (0.,-1.,-1.);
        nodes[9] = Point (1.,0.,-1.);
        nodes[10] = Point (0.,1.,-1.);
        nodes[11] = Point (-1.,0.,-1.);
        nodes[12] = Point (-1.,-1.,0.);
        nodes[13] = Point (1.,-1.,0.);
        nodes[14] = Point (1.,1.,0.);
        nodes[15] = Point (-1.,1.,0.);
        nodes[16] = Point (0.,-1.,1.);
        nodes[17] = Point (1.,0.,1.);
        nodes[18] = Point (0.,1.,1.);
        nodes[19] = Point (-1.,0.,1.);
        libmesh_fallthrough();
      }
    case HEX8:
      {
        nodes[0] = Point (-1.,-1.,-1.);
        nodes[1] = Point (1.,-1.,-1.);
        nodes[2] = Point (1.,1.,-1.);
        nodes[3] = Point (-1.,1.,-1.);
        nodes[4] = Point (-1.,-1.,1.);
        nodes[5] = Point (1.,-1.,1.);
        nodes[6] = Point (1.,1.,1.);
        nodes[7] = Point (-1.,1.,1.);
        return;
      }
    case PRISM21:
      {
        nodes[20] = Point (1/Real(3),1/Real(3),0);
        libmesh_fallthrough();
      }
    case PRISM20:
      {
        nodes[18] = Point (1/Real(3),1/Real(3),-1);
        nodes[19] = Point (1/Real(3),1/Real(3),1);
        libmesh_fallthrough();
      }
    case PRISM18:
      {
        nodes[15] = Point (.5,0.,0.);
        nodes[16] = Point (.5,.5,0.);
        nodes[17] = Point (0.,.5,0.);
        libmesh_fallthrough();
      }
    case PRISM15:
      {
        nodes[6] = Point (.5,0.,-1.);
        nodes[7] = Point (.5,.5,-1.);
        nodes[8] = Point (0.,.5,-1.);
        nodes[9] = Point (0.,0.,0.);
        nodes[10] = Point (1.,0.,0.);
        nodes[11] = Point (0.,1.,0.);
        nodes[12] = Point (.5,0.,1.);
        nodes[13] = Point (.5,.5,1.);
        nodes[14] = Point (0.,.5,1.);
        libmesh_fallthrough();
      }
    case PRISM6:
      {
        nodes[0] = Point (0.,0.,-1.);
        nodes[1] = Point (1.,0.,-1.);
        nodes[2] = Point (0.,1.,-1.);
        nodes[3] = Point (0.,0.,1.);
        nodes[4] = Point (1.,0.,1.);
        nodes[5] = Point (0.,1.,1.);
        return;
      }
    case PYRAMID18:
      {
        // triangle centers
        nodes[14] = Point (-2/Real(3),0.,1/Real(3));
        nodes[15] = Point (0.,2/Real(3),1/Real(3));
        nodes[16] = Point (2/Real(3),0.,1/Real(3));
        nodes[17] = Point (0.,-2/Real(3),1/Real(3));
 
        libmesh_fallthrough();
      }
    case PYRAMID14:
      {
        // base center
        nodes[13] = Point (0.,0.,0.);
 
        libmesh_fallthrough();
      }
    case PYRAMID13:
      {
        // base midedge
        nodes[5] = Point (0.,-1.,0.);
        nodes[6] = Point (1.,0.,0.);
        nodes[7] = Point (0.,1.,0.);
        nodes[8] = Point (-1,0.,0.);
 
        // lateral midedge
        nodes[9] = Point (-.5,-.5,.5);
        nodes[10] = Point (.5,-.5,.5);
        nodes[11] = Point (.5,.5,.5);
        nodes[12] = Point (-.5,.5,.5);
 
        libmesh_fallthrough();
      }
    case PYRAMID5:
      {
        // base corners
        nodes[0] = Point (-1.,-1.,0.);
        nodes[1] = Point (1.,-1.,0.);
        nodes[2] = Point (1.,1.,0.);
        nodes[3] = Point (-1.,1.,0.);
        // apex
        nodes[4] = Point (0.,0.,1.);
        return;
      }
 
    default:
      libmesh_error_msg("ERROR: Unknown element type " << Utility::enum_to_string(itemType));
    }
}

References libMesh::EDGE2, libMesh::EDGE3, libMesh::EDGE4, libMesh::Utility::enum_to_string(), libMesh::HEX20, libMesh::HEX27, libMesh::HEX8, libMesh::invalid_uint, n_nodes, libMesh::NODEELEM, libMesh::PRISM15, libMesh::PRISM18, libMesh::PRISM20, libMesh::PRISM21, libMesh::PRISM6, libMesh::PYRAMID13, libMesh::PYRAMID14, libMesh::PYRAMID18, libMesh::PYRAMID5, libMesh::QUAD4, libMesh::QUAD8, libMesh::QUAD9, libMesh::QUADSHELL4, libMesh::QUADSHELL8, libMesh::QUADSHELL9, libMesh::Real, libMesh::TET10, libMesh::TET14, libMesh::TET4, libMesh::TRI3, libMesh::TRI6, libMesh::TRI7, libMesh::TRISHELL3, and libMesh::Elem::type_to_n_nodes_map.

Referenced by libMesh::LIBMESH_DEFAULT_VECTORIZED_FE(), libMesh::LIBMESH_DEFAULT_VECTORIZED_FE(), libMesh::LIBMESH_DEFAULT_VECTORIZED_FE(), and libMesh::LIBMESH_DEFAULT_VECTORIZED_FE().

get_Sobolev_dweight()

virtual const std::vector< RealGradient > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_Sobolev_dweight ( ) const

inlinevirtualinherited

Returns

The first global derivative of the multiplicative weight at each quadrature point. See get_Sobolev_weight() for details. In case of FE initialized to all zero.

Definition at line 461 of file fe_base.h.

  { return dweight; }

get_Sobolev_dweightxR_sq()

virtual const std::vector< RealGradient > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_Sobolev_dweightxR_sq ( ) const

inlinevirtualinherited

Returns

The first global derivative of the multiplicative weight (see dget_Sobolev_weight) but weighted with the square of the radial coordinate.

In finite elements, this is 0.

Definition at line 480 of file fe_base.h.

  { return dweight; }

get_Sobolev_weight()

virtual const std::vector< Real > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_Sobolev_weight ( ) const

inlinevirtualinherited

Returns

The multiplicative weight at each quadrature point. This weight is used for certain infinite element weak formulations, so that weighted Sobolev spaces are used for the trial function space. This renders the variational form easily computable.

In case of the general finite element class FE this field is initialized to all ones, so that the variational formulation for an infinite element produces correct element matrices for a mesh using both finite and infinite elements.

Definition at line 453 of file fe_base.h.

  { return weight; }

get_Sobolev_weightxR_sq()

virtual const std::vector< Real > & libMesh::FEGenericBase< FEOutputType< T >::type >::get_Sobolev_weightxR_sq ( ) const

inlinevirtualinherited

Returns

The multiplicative weight (see get_Sobolev_weight) but weighted with the radial coordinate square.

In finite elements, this gives just 1, similar to get_Sobolev_Weight()

Definition at line 470 of file fe_base.h.

  { return weight; }

get_tangents()

virtual_for_inffe const std::vector< std::vector< Point > > & libMesh::FEAbstract::get_tangents ( ) const

inlineinherited

Returns

The tangent vectors for face integration.

Definition at line 452 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_tangents(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

get_type()

ElemType libMesh::FEAbstract::get_type ( ) const

inlineinherited

Returns

The element type that the current shape functions have been calculated for, or INVALID_ELEM if no such element exists. Useful in determining when shape functions must be recomputed.

This is generally redundant with _elem->type(), but must be cached separately for cases (such as internal FE use in QComposite) where _elem might be a dangling pointer to a temporary.

Definition at line 509 of file fe_abstract.h.

{ return _elem_type; }

References libMesh::FEAbstract::_elem_type.

get_xyz()

virtual_for_inffe const std::vector< Point > & libMesh::FEAbstract::get_xyz ( ) const

inlineinherited

Returns

The xyz spatial locations of the quadrature points on the element.

It is overwritten by infinite elements since there FEMap cannot be used to compute xyz.

Definition at line 280 of file fe_abstract.h.

  { calculate_map = true; return this->_fe_map->get_xyz(); }

References libMesh::FEAbstract::_fe_map, and libMesh::FEAbstract::calculate_map.

Referenced by libMesh::ExactSolution::_compute_error(), assemble_SchroedingerEquation(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::KellyErrorEstimator::boundary_side_integration(), compute_enriched_soln(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubProjector::construct_projection(), LaplaceSystem::element_postprocess(), PoissonSystem::element_postprocess(), LaplaceQoI::element_qoi(), LaplaceSystem::element_qoi_derivative(), LaplaceQoI::element_qoi_derivative(), HeatSystem::element_time_derivative(), PoissonSystem::element_time_derivative(), NavierSystem::element_time_derivative(), CurlCurlSystem::element_time_derivative(), SigmaPhysics::element_time_derivative(), libMesh::JumpErrorEstimator::estimate_error(), libMesh::ParsedFEMFunction< Output >::eval_args(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::ParsedFEMFunction< Output >::init_context(), CoupledSystemQoI::init_context(), LaplaceSystem::init_context(), LaplaceQoI::init_context(), CoupledSystem::init_context(), HeatSystem::init_context(), PoissonSystem::init_context(), NavierSystem::init_context(), SolidSystem::init_context(), CurlCurlSystem::init_context(), SigmaPhysics::init_context(), HilbertSystem::init_context(), libMesh::DGFEMContext::neighbor_side_fe_reinit(), Integrate::operator()(), libMesh::JumpErrorEstimator::reinit_sides(), LaplaceSystem::side_constraint(), LaplaceSystem::side_postprocess(), CoupledSystemQoI::side_qoi(), LaplaceSystem::side_qoi_derivative(), CoupledSystemQoI::side_qoi_derivative(), SolidSystem::side_time_derivative(), CurlCurlSystem::side_time_derivative(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubFunctor::SubFunctor(), SlitMeshRefinedSystemTest::testRestart(), and SlitMeshRefinedSystemTest::testSystem().

increment_constructor_count()

void libMesh::ReferenceCounter::increment_constructor_count ( const std::string &  name )

inlineprotectednoexceptinherited

Increments the construction counter.

Should be called in the constructor of any derived class that will be reference counted.

Definition at line 183 of file reference_counter.h.

{
  libmesh_try
  {
    Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
    std::pair<unsigned int, unsigned int> & p = _counts[name];
    p.first++;
  }
  libmesh_catch (...)
  {
    auto stream = libMesh::err.get();
    stream->exceptions(stream->goodbit); // stream must not throw
    libMesh::err << "Encountered unrecoverable error while calling "
                 << "ReferenceCounter::increment_constructor_count() "
                 << "for a(n) " << name << " object." << std::endl;
    std::terminate();
  }
}

References libMesh::err, libMesh::BasicOStreamProxy< charT, traits >::get(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< T >::ReferenceCountedObject(), libMesh::ReferenceCountedObject< T >::ReferenceCountedObject(), and libMesh::ReferenceCountedObject< T >::ReferenceCountedObject().

increment_destructor_count()

void libMesh::ReferenceCounter::increment_destructor_count ( const std::string &  name )

inlineprotectednoexceptinherited

Increments the destruction counter.

Should be called in the destructor of any derived class that will be reference counted.

Definition at line 207 of file reference_counter.h.

{
  libmesh_try
  {
    Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
    std::pair<unsigned int, unsigned int> & p = _counts[name];
    p.second++;
  }
  libmesh_catch (...)
  {
    auto stream = libMesh::err.get();
    stream->exceptions(stream->goodbit); // stream must not throw
    libMesh::err << "Encountered unrecoverable error while calling "
                 << "ReferenceCounter::increment_destructor_count() "
                 << "for a(n) " << name << " object." << std::endl;
    std::terminate();
  }
}

References libMesh::err, libMesh::BasicOStreamProxy< charT, traits >::get(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< T >::~ReferenceCountedObject().

init_base_shape_functions()

void libMesh::FE< Dim, T >::init_base_shape_functions ( const std::vector< Point > &  qp, const Elem *  e  )

overrideprotectedvirtualinherited

Initialize the data fields for the base of an an infinite element.

Implements libMesh::FEGenericBase< FEOutputType< T >::type >.

Definition at line 730 of file fe.C.

{
  this->_elem = e;
  this->_elem_type = e->type();
  this->_fe_map->template init_reference_to_physical_map<Dim>(qp, e);
  init_shape_functions(qp, e);
}

init_dual_shape_functions()

void libMesh::FE< Dim, T >::init_dual_shape_functions ( unsigned int  n_shapes, unsigned int  n_qp  )

protectedinherited

Init dual_phi and potentially dual_dphi, dual_d2phi.

Definition at line 722 of file fe.C.

{
  if (!this->calculate_dual)
    return;
 
  libmesh_assert_msg(this->calculate_phi,
                     "dual shape function calculation relies on "
                     "primal shape functions being calculated");
 
  this->dual_phi.resize(n_shapes);
  if (this->calculate_dphi)
    this->dual_dphi.resize(n_shapes);
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
  if (this->calculate_d2phi)
    this->dual_d2phi.resize(n_shapes);
#endif
 
  for (auto i : index_range(this->dual_phi))
  {
    this->dual_phi[i].resize(n_qp);
    if (this->calculate_dphi)
      this->dual_dphi[i].resize(n_qp);
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
  if (this->calculate_d2phi)
    this->dual_d2phi[i].resize(n_qp);
#endif
  }
}

init_shape_functions()

void libMesh::FE< Dim, T >::init_shape_functions ( const std::vector< Point > &  qp, const Elem *  e  )

protectedvirtualinherited

Update the various member data fields phi, dphidxi, dphideta, dphidzeta, etc.

for the current element. These data will be computed at the points qp, which are generally (but need not be) the quadrature points.

Definition at line 706 of file fe.C.

{
  // Start logging the shape function initialization
  LOG_SCOPE("init_shape_functions()", "FE");
 
  // The number of quadrature points.
  const unsigned int n_qp = cast_int<unsigned int>(qp.size());
  this->_n_total_qp = n_qp;
 
  // Number of shape functions in the finite element approximation
  // space.
  const unsigned int n_approx_shape_functions =
    this->n_dofs(elem, this->get_order());
 
  // Maybe we already have correctly-sized data?  Check data sizes,
  // and get ready to break out of a "loop" if all these resize()
  // calls are redundant.
  unsigned int old_n_qp = 0;
  do
    {
      // resize the vectors to hold current data
      // Phi are the shape functions used for the FE approximation
      // Phi_map are the shape functions used for the FE mapping
      if (this->calculate_phi)
        {
          if (this->phi.size() == n_approx_shape_functions)
            {
              old_n_qp = n_approx_shape_functions ? this->phi[0].size() : 0;
              break;
            }
          this->phi.resize     (n_approx_shape_functions);
        }
      if (this->calculate_dphi)
        {
          if (this->dphi.size() == n_approx_shape_functions)
            {
              old_n_qp = n_approx_shape_functions ? this->dphi[0].size() : 0;
              break;
            }
          this->dphi.resize    (n_approx_shape_functions);
          this->dphidx.resize  (n_approx_shape_functions);
          this->dphidy.resize  (n_approx_shape_functions);
          this->dphidz.resize  (n_approx_shape_functions);
        }
 
      if (this->calculate_dphiref)
        {
          if (Dim > 0)
            {
              if (this->dphidxi.size() == n_approx_shape_functions)
                {
                  old_n_qp = n_approx_shape_functions ? this->dphidxi[0].size() : 0;
                  break;
                }
              this->dphidxi.resize (n_approx_shape_functions);
            }
 
          if (Dim > 1)
            this->dphideta.resize      (n_approx_shape_functions);
 
          if (Dim > 2)
            this->dphidzeta.resize     (n_approx_shape_functions);
        }
 
      if (this->calculate_curl_phi && (FEInterface::field_type(T) == TYPE_VECTOR))
        this->curl_phi.resize(n_approx_shape_functions);
 
      if (this->calculate_div_phi && (FEInterface::field_type(T) == TYPE_VECTOR))
        this->div_phi.resize(n_approx_shape_functions);
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
      if (this->calculate_d2phi)
        {
          if (this->d2phi.size() == n_approx_shape_functions)
            {
              old_n_qp = n_approx_shape_functions ? this->d2phi[0].size() : 0;
              break;
            }
 
          this->d2phi.resize     (n_approx_shape_functions);
          this->d2phidx2.resize  (n_approx_shape_functions);
          this->d2phidxdy.resize (n_approx_shape_functions);
          this->d2phidxdz.resize (n_approx_shape_functions);
          this->d2phidy2.resize  (n_approx_shape_functions);
          this->d2phidydz.resize (n_approx_shape_functions);
          this->d2phidz2.resize  (n_approx_shape_functions);
 
          if (Dim > 0)
            this->d2phidxi2.resize (n_approx_shape_functions);
 
          if (Dim > 1)
            {
              this->d2phidxideta.resize (n_approx_shape_functions);
              this->d2phideta2.resize   (n_approx_shape_functions);
            }
          if (Dim > 2)
            {
              this->d2phidxidzeta.resize  (n_approx_shape_functions);
              this->d2phidetadzeta.resize (n_approx_shape_functions);
              this->d2phidzeta2.resize    (n_approx_shape_functions);
            }
        }
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
    }
  while (false);
 
  if (old_n_qp != n_qp)
    for (unsigned int i=0; i<n_approx_shape_functions; i++)
      {
        if (this->calculate_phi)
          this->phi[i].resize         (n_qp);
 
        if (this->calculate_dphi)
          {
            this->dphi[i].resize        (n_qp);
            this->dphidx[i].resize      (n_qp);
            this->dphidy[i].resize      (n_qp);
            this->dphidz[i].resize      (n_qp);
          }
 
        if (this->calculate_dphiref)
          {
            if (Dim > 0)
              this->dphidxi[i].resize(n_qp);
 
            if (Dim > 1)
              this->dphideta[i].resize(n_qp);
 
            if (Dim > 2)
              this->dphidzeta[i].resize(n_qp);
          }
 
        if (this->calculate_curl_phi && (FEInterface::field_type(T) == TYPE_VECTOR))
          this->curl_phi[i].resize(n_qp);
 
        if (this->calculate_div_phi && (FEInterface::field_type(T) == TYPE_VECTOR))
          this->div_phi[i].resize(n_qp);
 
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
        if (this->calculate_d2phi)
          {
            this->d2phi[i].resize     (n_qp);
            this->d2phidx2[i].resize  (n_qp);
            this->d2phidxdy[i].resize (n_qp);
            this->d2phidxdz[i].resize (n_qp);
            this->d2phidy2[i].resize  (n_qp);
            this->d2phidydz[i].resize (n_qp);
            this->d2phidz2[i].resize  (n_qp);
            if (Dim > 0)
              this->d2phidxi2[i].resize (n_qp);
            if (Dim > 1)
              {
                this->d2phidxideta[i].resize (n_qp);
                this->d2phideta2[i].resize   (n_qp);
              }
            if (Dim > 2)
              {
                this->d2phidxidzeta[i].resize  (n_qp);
                this->d2phidetadzeta[i].resize (n_qp);
                this->d2phidzeta2[i].resize    (n_qp);
              }
          }
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
      }
 
 
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
  //------------------------------------------------------------
  // Initialize the data fields, which should only be used for infinite
  // elements, to some sensible values, so that using a FE with the
  // variational formulation of an InfFE, correct element matrices are
  // returned
 
  {
    if (this->calculate_phi || this->calculate_dphi)
      {
        this->weight.resize  (n_qp);
        for (unsigned int p=0; p<n_qp; p++)
          this->weight[p] = 1.;
      }
 
    if (this->calculate_dphi)
      {
        this->dweight.resize (n_qp);
        this->dphase.resize  (n_qp);
        for (unsigned int p=0; p<n_qp; p++)
          {
            this->dweight[p].zero();
            this->dphase[p].zero();
          }
      }
  }
#endif // ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
 
        // Compute the values of the shape function derivatives
  if (this->calculate_dphiref && Dim > 0)
    {
      std::vector<std::vector<OutputShape>> * comps[3]
        { &this->dphidxi, &this->dphideta, &this->dphidzeta };
      FE<Dim,T>::all_shape_derivs(elem, this->fe_type.order, qp, comps, this->_add_p_level_in_reinit);
    }
 
  switch (Dim)
    {
 
      //------------------------------------------------------------
      // 0D
    case 0:
      {
        break;
      }
 
      //------------------------------------------------------------
      // 1D
    case 1:
      {
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
        // Compute the value of shape function i Hessians at quadrature point p
        if (this->calculate_d2phi)
          for (unsigned int i=0; i<n_approx_shape_functions; i++)
            for (unsigned int p=0; p<n_qp; p++)
              this->d2phidxi2[i][p] = FE<Dim, T>::shape_second_deriv(
                  elem, this->fe_type.order, i, 0, qp[p], this->_add_p_level_in_reinit);
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
 
        break;
      }
 
 
 
      //------------------------------------------------------------
      // 2D
    case 2:
      {
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
        // Compute the value of shape function i Hessians at quadrature point p
        if (this->calculate_d2phi)
          for (unsigned int i=0; i<n_approx_shape_functions; i++)
            for (unsigned int p=0; p<n_qp; p++)
              {
                this->d2phidxi2[i][p] = FE<Dim, T>::shape_second_deriv(
                    elem, this->fe_type.order, i, 0, qp[p], this->_add_p_level_in_reinit);
                this->d2phidxideta[i][p] = FE<Dim, T>::shape_second_deriv(
                    elem, this->fe_type.order, i, 1, qp[p], this->_add_p_level_in_reinit);
                this->d2phideta2[i][p] = FE<Dim, T>::shape_second_deriv(
                    elem, this->fe_type.order, i, 2, qp[p], this->_add_p_level_in_reinit);
              }
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
 
 
        break;
      }
 
 
 
      //------------------------------------------------------------
      // 3D
    case 3:
      {
#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
        // Compute the value of shape function i Hessians at quadrature point p
        if (this->calculate_d2phi)
          for (unsigned int i=0; i<n_approx_shape_functions; i++)
            for (unsigned int p=0; p<n_qp; p++)
              {
                this->d2phidxi2[i][p] = FE<Dim, T>::shape_second_deriv(
                    elem, this->fe_type.order, i, 0, qp[p], this->_add_p_level_in_reinit);
                this->d2phidxideta[i][p] = FE<Dim, T>::shape_second_deriv(
                    elem, this->fe_type.order, i, 1, qp[p], this->_add_p_level_in_reinit);
                this->d2phideta2[i][p] = FE<Dim, T>::shape_second_deriv(
                    elem, this->fe_type.order, i, 2, qp[p], this->_add_p_level_in_reinit);
                this->d2phidxidzeta[i][p] = FE<Dim, T>::shape_second_deriv(
                    elem, this->fe_type.order, i, 3, qp[p], this->_add_p_level_in_reinit);
                this->d2phidetadzeta[i][p] = FE<Dim, T>::shape_second_deriv(
                    elem, this->fe_type.order, i, 4, qp[p], this->_add_p_level_in_reinit);
                this->d2phidzeta2[i][p] = FE<Dim, T>::shape_second_deriv(
                    elem, this->fe_type.order, i, 5, qp[p], this->_add_p_level_in_reinit);
              }
#endif // ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
 
        break;
      }
 
 
    default:
      libmesh_error_msg("Invalid dimension Dim = " << Dim);
    }
 
  if (this->calculate_dual)
    this->init_dual_shape_functions(n_approx_shape_functions, n_qp);
}

inverse_map() [1/4]

Point libMesh::FE< 2, SUBDIVISION >::inverse_map ( const Elem *  , const Point &  , const Real  , const bool    )

inherited

Definition at line 937 of file fe_subdivision_2D.C.

{
  libmesh_not_implemented();
}

inverse_map() [2/4]

void libMesh::FE< 2, SUBDIVISION >::inverse_map ( const Elem *  , const std::vector< Point > &  , std::vector< Point > &  , Real  , bool    )

inherited

Definition at line 946 of file fe_subdivision_2D.C.

{
  libmesh_not_implemented();
}

inverse_map() [3/4]

static Point libMesh::FE< Dim, T >::inverse_map ( const Elem *  elem, const Point &  p, const Real  tolerance = TOLERANCE, const bool  secure = true  )

inlinestaticinherited

Definition at line 534 of file fe.h.

  {
    // libmesh_deprecated(); // soon
    return FEMap::inverse_map(Dim, elem, p, tolerance, secure, secure);
  }

inverse_map() [4/4]

static void libMesh::FE< Dim, T >::inverse_map ( const Elem *  elem, const std::vector< Point > &  physical_points, std::vector< Point > &  reference_points, const Real  tolerance = TOLERANCE, const bool  secure = true  )

inlinestaticinherited

Definition at line 543 of file fe.h.

  {
    // libmesh_deprecated(); // soon
    FEMap::inverse_map(Dim, elem, physical_points, reference_points,
                       tolerance, secure, secure);
  }

is_hierarchic() [1/86]

bool libMesh::FE< 0, BERNSTEIN >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 428 of file fe_bernstein.C.

{ return false; }

is_hierarchic() [2/86]

bool libMesh::FE< 1, BERNSTEIN >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 429 of file fe_bernstein.C.

{ return false; }

is_hierarchic() [3/86]

bool libMesh::FE< 2, BERNSTEIN >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 430 of file fe_bernstein.C.

{ return false; }

is_hierarchic() [4/86]

bool libMesh::FE< 3, BERNSTEIN >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 431 of file fe_bernstein.C.

{ return false; }

is_hierarchic() [5/86]

bool libMesh::FE< 0, CLOUGH >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 276 of file fe_clough.C.

{ return false; } // FIXME - this will be changed

is_hierarchic() [6/86]

bool libMesh::FE< 1, CLOUGH >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 277 of file fe_clough.C.

{ return false; } // FIXME - this will be changed

is_hierarchic() [7/86]

bool libMesh::FE< 2, CLOUGH >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 278 of file fe_clough.C.

{ return false; } // FIXME - this will be changed

is_hierarchic() [8/86]

bool libMesh::FE< 3, CLOUGH >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 279 of file fe_clough.C.

{ return false; } // FIXME - this will be changed

is_hierarchic() [9/86]

bool libMesh::FE< 0, HERMITE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 318 of file fe_hermite.C.

{ return true; }

is_hierarchic() [10/86]

bool libMesh::FE< 1, HERMITE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 319 of file fe_hermite.C.

{ return true; }

is_hierarchic() [11/86]

bool libMesh::FE< 2, HERMITE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 320 of file fe_hermite.C.

{ return true; }

is_hierarchic() [12/86]

bool libMesh::FE< 3, HERMITE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 321 of file fe_hermite.C.

{ return true; }

is_hierarchic() [13/86]

bool libMesh::FE< 0, HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 482 of file fe_hierarchic.C.

{ return true; }

is_hierarchic() [14/86]

bool libMesh::FE< 1, HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 483 of file fe_hierarchic.C.

{ return true; }

is_hierarchic() [15/86]

bool libMesh::FE< 2, HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 484 of file fe_hierarchic.C.

{ return true; }

is_hierarchic() [16/86]

bool libMesh::FE< 3, HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 485 of file fe_hierarchic.C.

{ return true; }

is_hierarchic() [17/86]

bool libMesh::FE< 0, HIERARCHIC_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 785 of file fe_hierarchic_vec.C.

{ return true; }

is_hierarchic() [18/86]

bool libMesh::FE< 1, HIERARCHIC_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 786 of file fe_hierarchic_vec.C.

{ return true; }

is_hierarchic() [19/86]

bool libMesh::FE< 2, HIERARCHIC_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 787 of file fe_hierarchic_vec.C.

{ return true; }

is_hierarchic() [20/86]

bool libMesh::FE< 3, HIERARCHIC_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 788 of file fe_hierarchic_vec.C.

{ return true; }

is_hierarchic() [21/86]

bool libMesh::FE< 0, L2_HIERARCHIC_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 789 of file fe_hierarchic_vec.C.

{ return true; }

is_hierarchic() [22/86]

bool libMesh::FE< 1, L2_HIERARCHIC_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 790 of file fe_hierarchic_vec.C.

{ return true; }

is_hierarchic() [23/86]

bool libMesh::FE< 2, L2_HIERARCHIC_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 791 of file fe_hierarchic_vec.C.

{ return true; }

is_hierarchic() [24/86]

bool libMesh::FE< 3, L2_HIERARCHIC_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 792 of file fe_hierarchic_vec.C.

{ return true; }

is_hierarchic() [25/86]

bool libMesh::FE< 0, L2_HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 194 of file fe_l2_hierarchic.C.

{ return true; }

is_hierarchic() [26/86]

bool libMesh::FE< 1, L2_HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 195 of file fe_l2_hierarchic.C.

{ return true; }

is_hierarchic() [27/86]

bool libMesh::FE< 2, L2_HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 196 of file fe_l2_hierarchic.C.

{ return true; }

is_hierarchic() [28/86]

bool libMesh::FE< 3, L2_HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 197 of file fe_l2_hierarchic.C.

{ return true; }

is_hierarchic() [29/86]

bool libMesh::FE< 0, L2_LAGRANGE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 262 of file fe_l2_lagrange.C.

{ return false; }

is_hierarchic() [30/86]

bool libMesh::FE< 1, L2_LAGRANGE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 263 of file fe_l2_lagrange.C.

{ return false; }

is_hierarchic() [31/86]

bool libMesh::FE< 2, L2_LAGRANGE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 264 of file fe_l2_lagrange.C.

{ return false; }

is_hierarchic() [32/86]

bool libMesh::FE< 3, L2_LAGRANGE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 265 of file fe_l2_lagrange.C.

{ return false; }

is_hierarchic() [33/86]

bool libMesh::FE< 0, LAGRANGE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1120 of file fe_lagrange.C.

{ return false; }

is_hierarchic() [34/86]

bool libMesh::FE< 1, LAGRANGE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1121 of file fe_lagrange.C.

{ return false; }

is_hierarchic() [35/86]

bool libMesh::FE< 2, LAGRANGE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1122 of file fe_lagrange.C.

{ return false; }

is_hierarchic() [36/86]

bool libMesh::FE< 3, LAGRANGE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1123 of file fe_lagrange.C.

{ return false; }

is_hierarchic() [37/86]

bool libMesh::FE< 0, LAGRANGE_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1354 of file fe_lagrange_vec.C.

{ return false; }

is_hierarchic() [38/86]

bool libMesh::FE< 1, LAGRANGE_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1355 of file fe_lagrange_vec.C.

{ return false; }

is_hierarchic() [39/86]

bool libMesh::FE< 2, LAGRANGE_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1356 of file fe_lagrange_vec.C.

{ return false; }

is_hierarchic() [40/86]

bool libMesh::FE< 3, LAGRANGE_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1357 of file fe_lagrange_vec.C.

{ return false; }

is_hierarchic() [41/86]

bool libMesh::FE< 0, L2_LAGRANGE_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1358 of file fe_lagrange_vec.C.

{ return false; }

is_hierarchic() [42/86]

bool libMesh::FE< 1, L2_LAGRANGE_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1359 of file fe_lagrange_vec.C.

{ return false; }

is_hierarchic() [43/86]

bool libMesh::FE< 2, L2_LAGRANGE_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1360 of file fe_lagrange_vec.C.

{ return false; }

is_hierarchic() [44/86]

bool libMesh::FE< 3, L2_LAGRANGE_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1361 of file fe_lagrange_vec.C.

{ return false; }

is_hierarchic() [45/86]

bool libMesh::FE< 0, MONOMIAL >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 428 of file fe_monomial.C.

{ return true; }

is_hierarchic() [46/86]

bool libMesh::FE< 1, MONOMIAL >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 429 of file fe_monomial.C.

{ return true; }

is_hierarchic() [47/86]

bool libMesh::FE< 2, MONOMIAL >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 430 of file fe_monomial.C.

{ return true; }

is_hierarchic() [48/86]

bool libMesh::FE< 3, MONOMIAL >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 431 of file fe_monomial.C.

{ return true; }

is_hierarchic() [49/86]

bool libMesh::FE< 0, MONOMIAL_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 723 of file fe_monomial_vec.C.

{
  return true;
}

is_hierarchic() [50/86]

bool libMesh::FE< 1, MONOMIAL_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 729 of file fe_monomial_vec.C.

{
  return true;
}

is_hierarchic() [51/86]

bool libMesh::FE< 2, MONOMIAL_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 735 of file fe_monomial_vec.C.

{
  return true;
}

is_hierarchic() [52/86]

bool libMesh::FE< 3, MONOMIAL_VEC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 741 of file fe_monomial_vec.C.

{
  return true;
}

is_hierarchic() [53/86]

bool libMesh::FE< 0, NEDELEC_ONE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 414 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

is_hierarchic() [54/86]

bool libMesh::FE< 1, NEDELEC_ONE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 415 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

is_hierarchic() [55/86]

bool libMesh::FE< 2, NEDELEC_ONE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 416 of file fe_nedelec_one.C.

{ return false; }

is_hierarchic() [56/86]

bool libMesh::FE< 3, NEDELEC_ONE >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 417 of file fe_nedelec_one.C.

{ return false; }

is_hierarchic() [57/86]

bool libMesh::FE< 0, RATIONAL_BERNSTEIN >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 166 of file fe_rational.C.

{ return false; }

is_hierarchic() [58/86]

bool libMesh::FE< 1, RATIONAL_BERNSTEIN >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 167 of file fe_rational.C.

{ return false; }

is_hierarchic() [59/86]

bool libMesh::FE< 2, RATIONAL_BERNSTEIN >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 168 of file fe_rational.C.

{ return false; }

is_hierarchic() [60/86]

bool libMesh::FE< 3, RATIONAL_BERNSTEIN >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 169 of file fe_rational.C.

{ return false; }

is_hierarchic() [61/86]

bool libMesh::FE< 0, RAVIART_THOMAS >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 468 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

is_hierarchic() [62/86]

bool libMesh::FE< 1, RAVIART_THOMAS >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 469 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

is_hierarchic() [63/86]

bool libMesh::FE< 2, RAVIART_THOMAS >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 470 of file fe_raviart.C.

{ return false; }

is_hierarchic() [64/86]

bool libMesh::FE< 3, RAVIART_THOMAS >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 471 of file fe_raviart.C.

{ return false; }

is_hierarchic() [65/86]

bool libMesh::FE< 0, L2_RAVIART_THOMAS >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 472 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

is_hierarchic() [66/86]

bool libMesh::FE< 1, L2_RAVIART_THOMAS >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 473 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

is_hierarchic() [67/86]

bool libMesh::FE< 2, L2_RAVIART_THOMAS >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 474 of file fe_raviart.C.

{ return false; }

is_hierarchic() [68/86]

bool libMesh::FE< 3, L2_RAVIART_THOMAS >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 475 of file fe_raviart.C.

{ return false; }

is_hierarchic() [69/86]

bool libMesh::FE< 0, SCALAR >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 101 of file fe_scalar.C.

{ return false; }

is_hierarchic() [70/86]

bool libMesh::FE< 1, SCALAR >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 102 of file fe_scalar.C.

{ return false; }

is_hierarchic() [71/86]

bool libMesh::FE< 2, SCALAR >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 103 of file fe_scalar.C.

{ return false; }

is_hierarchic() [72/86]

bool libMesh::FE< 3, SCALAR >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 104 of file fe_scalar.C.

{ return false; }

is_hierarchic() [73/86]

bool libMesh::FE< 0, SIDE_HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 333 of file fe_side_hierarchic.C.

{ return true; }

is_hierarchic() [74/86]

bool libMesh::FE< 1, SIDE_HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 334 of file fe_side_hierarchic.C.

{ return true; }

is_hierarchic() [75/86]

bool libMesh::FE< 2, SIDE_HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 335 of file fe_side_hierarchic.C.

{ return true; }

is_hierarchic() [76/86]

bool libMesh::FE< 3, SIDE_HIERARCHIC >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 336 of file fe_side_hierarchic.C.

{ return true; }

is_hierarchic() [77/86]

bool libMesh::FE< 2, SUBDIVISION >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 977 of file fe_subdivision_2D.C.

{ return false; }

is_hierarchic() [78/86]

bool libMesh::FE< 0, SZABAB >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1331 of file fe_szabab.C.

{ return true; }

is_hierarchic() [79/86]

bool libMesh::FE< 1, SZABAB >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1332 of file fe_szabab.C.

{ return true; }

is_hierarchic() [80/86]

bool libMesh::FE< 2, SZABAB >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1333 of file fe_szabab.C.

{ return true; }

is_hierarchic() [81/86]

bool libMesh::FE< 3, SZABAB >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 1334 of file fe_szabab.C.

{ return true; }

is_hierarchic() [82/86]

bool libMesh::FE< 0, XYZ >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 413 of file fe_xyz.C.

{ return true; }

is_hierarchic() [83/86]

bool libMesh::FE< 1, XYZ >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 414 of file fe_xyz.C.

{ return true; }

is_hierarchic() [84/86]

bool libMesh::FE< 2, XYZ >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 415 of file fe_xyz.C.

{ return true; }

is_hierarchic() [85/86]

bool libMesh::FE< 3, XYZ >::is_hierarchic ( ) const

virtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

Definition at line 416 of file fe_xyz.C.

{ return true; }

is_hierarchic() [86/86]

virtual bool libMesh::FE< Dim, T >::is_hierarchic ( ) const

overridevirtualinherited

Returns

true if the finite element's higher order shape functions are hierarchic

Implements libMesh::FEAbstract.

map()

static Point libMesh::FE< Dim, T >::map ( const Elem *  elem, const Point &  reference_point  )

inlinestaticinherited

Definition at line 660 of file fe.h.

  {
    // libmesh_deprecated(); // soon
    return FEMap::map(Dim, elem, reference_point);
  }

map_eta()

static Point libMesh::FE< Dim, T >::map_eta ( const Elem *  elem, const Point &  reference_point  )

inlinestaticinherited

Definition at line 674 of file fe.h.

  {
    // libmesh_deprecated(); // soon
    return FEMap::map_deriv(Dim, elem, 1, reference_point);
  }

map_xi()

static Point libMesh::FE< Dim, T >::map_xi ( const Elem *  elem, const Point &  reference_point  )

inlinestaticinherited

Definition at line 667 of file fe.h.

  {
    // libmesh_deprecated(); // soon
    return FEMap::map_deriv(Dim, elem, 0, reference_point);
  }

map_zeta()

static Point libMesh::FE< Dim, T >::map_zeta ( const Elem *  elem, const Point &  reference_point  )

inlinestaticinherited

Definition at line 681 of file fe.h.

  {
    // libmesh_deprecated(); // soon
    return FEMap::map_deriv(Dim, elem, 2, reference_point);
  }

matches_cache()

bool libMesh::FE< Dim, T >::matches_cache ( const Elem *  elem )

protectedinherited

Check if the node locations, edge and face orientations held in the element cache match those of element elem.

Definition at line 809 of file fe.C.

{
  bool m = cached_nodes.size() == elem->n_nodes();
  for (unsigned n = 1; m && n < elem->n_nodes(); n++)
    m = (elem->point(n) - elem->point(0)).relative_fuzzy_equals(cached_nodes[n] - cached_nodes[0]);
 
  if (FEInterface::orientation_dependent(T))
    {
      m &= cached_edges.size() == elem->n_edges();
      for (unsigned n = 0; m && n < elem->n_edges(); n++)
        m = elem->positive_edge_orientation(n) == cached_edges[n];
 
      m &= cached_faces.size() == elem->n_faces();
      for (unsigned n = 0; m && n < elem->n_faces(); n++)
        m = elem->positive_face_orientation(n) == cached_faces[n];
    }
 
  return m;
}

n_dofs() [1/121]

unsigned int libMesh::FE< 0, SCALAR >::n_dofs ( const Elem *  , const Order  o  )

inherited

Definition at line 65 of file fe_scalar.C.

{ return o; }

n_dofs() [2/121]

unsigned int libMesh::FE< 1, SCALAR >::n_dofs ( const Elem *  , const Order  o  )

inherited

Definition at line 66 of file fe_scalar.C.

{ return o; }

n_dofs() [3/121]

unsigned int libMesh::FE< 2, SCALAR >::n_dofs ( const Elem *  , const Order  o  )

inherited

Definition at line 67 of file fe_scalar.C.

{ return o; }

n_dofs() [4/121]

unsigned int libMesh::FE< 3, SCALAR >::n_dofs ( const Elem *  , const Order  o  )

inherited

Definition at line 68 of file fe_scalar.C.

{ return o; }

n_dofs() [5/121]

unsigned int libMesh::FE< 0, NEDELEC_ONE >::n_dofs ( const Elem *  , const Order    )

inherited

Definition at line 382 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs() [6/121]

unsigned int libMesh::FE< 1, NEDELEC_ONE >::n_dofs ( const Elem *  , const Order    )

inherited

Definition at line 383 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs() [7/121]

unsigned int libMesh::FE< 0, RAVIART_THOMAS >::n_dofs ( const Elem *  , const Order    )

inherited

Definition at line 399 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs() [8/121]

unsigned int libMesh::FE< 1, RAVIART_THOMAS >::n_dofs ( const Elem *  , const Order    )

inherited

Definition at line 400 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs() [9/121]

unsigned int libMesh::FE< 0, L2_RAVIART_THOMAS >::n_dofs ( const Elem *  , const Order    )

inherited

Definition at line 409 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs() [10/121]

unsigned int libMesh::FE< 1, L2_RAVIART_THOMAS >::n_dofs ( const Elem *  , const Order    )

inherited

Definition at line 410 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs() [11/121]

unsigned int libMesh::FE< 2, SUBDIVISION >::n_dofs ( const Elem *  , const Order    )

inherited

Definition at line 959 of file fe_subdivision_2D.C.

{ libmesh_not_implemented(); return 0; }

n_dofs() [12/121]

static unsigned int libMesh::FE< Dim, T >::n_dofs ( const Elem *  e, const Order  o  )

staticinherited

Returns

The number of shape functions associated with this finite element.

On a p-refined element, o should be the total order of the element.

e should only be a null pointer if using a FE family like SCALAR that has degrees of freedom independent of any element.

n_dofs() [13/121]

unsigned int libMesh::FE< 0, L2_HIERARCHIC_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 747 of file fe_hierarchic_vec.C.

{ return FE<0,L2_HIERARCHIC>::n_dofs(e,o); }

n_dofs() [14/121]

unsigned int libMesh::FE< 1, L2_HIERARCHIC_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 748 of file fe_hierarchic_vec.C.

{ return FE<1,L2_HIERARCHIC>::n_dofs(e,o); }

n_dofs() [15/121]

unsigned int libMesh::FE< 2, L2_HIERARCHIC_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 749 of file fe_hierarchic_vec.C.

{ return 2*FE<2,L2_HIERARCHIC>::n_dofs(e,o); }

n_dofs() [16/121]

unsigned int libMesh::FE< 3, L2_HIERARCHIC_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 750 of file fe_hierarchic_vec.C.

{ return 3*FE<3,L2_HIERARCHIC>::n_dofs(e,o); }

n_dofs() [17/121]

unsigned int libMesh::FE< 0, L2_HIERARCHIC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 159 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(e, o); }

n_dofs() [18/121]

unsigned int libMesh::FE< 1, L2_HIERARCHIC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 160 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(e, o); }

n_dofs() [19/121]

unsigned int libMesh::FE< 2, L2_HIERARCHIC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 161 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(e, o); }

n_dofs() [20/121]

unsigned int libMesh::FE< 3, L2_HIERARCHIC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 162 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(e, o); }

n_dofs() [21/121]

unsigned int libMesh::FE< 0, L2_LAGRANGE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 228 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(e, o); }

n_dofs() [22/121]

unsigned int libMesh::FE< 1, L2_LAGRANGE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 229 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(e, o); }

n_dofs() [23/121]

unsigned int libMesh::FE< 2, L2_LAGRANGE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 230 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(e, o); }

n_dofs() [24/121]

unsigned int libMesh::FE< 3, L2_LAGRANGE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 231 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(e, o); }

n_dofs() [25/121]

unsigned int libMesh::FE< 0, LAGRANGE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1082 of file fe_lagrange.C.

{ return lagrange_n_dofs(e->type(), e, o); }

n_dofs() [26/121]

unsigned int libMesh::FE< 1, LAGRANGE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1083 of file fe_lagrange.C.

{ return lagrange_n_dofs(e->type(), e, o); }

n_dofs() [27/121]

unsigned int libMesh::FE< 2, LAGRANGE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1084 of file fe_lagrange.C.

{ return lagrange_n_dofs(e->type(), e, o); }

n_dofs() [28/121]

unsigned int libMesh::FE< 3, LAGRANGE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1085 of file fe_lagrange.C.

{ return lagrange_n_dofs(e->type(), e, o); }

n_dofs() [29/121]

unsigned int libMesh::FE< 0, LAGRANGE_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1279 of file fe_lagrange_vec.C.

{ return FE<0,LAGRANGE>::n_dofs(e,o); }

n_dofs() [30/121]

unsigned int libMesh::FE< 1, LAGRANGE_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1280 of file fe_lagrange_vec.C.

{ return FE<1,LAGRANGE>::n_dofs(e,o); }

n_dofs() [31/121]

unsigned int libMesh::FE< 2, LAGRANGE_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1281 of file fe_lagrange_vec.C.

{ return 2*FE<2,LAGRANGE>::n_dofs(e,o); }

n_dofs() [32/121]

unsigned int libMesh::FE< 3, LAGRANGE_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1282 of file fe_lagrange_vec.C.

{ return 3*FE<3,LAGRANGE>::n_dofs(e,o); }

n_dofs() [33/121]

unsigned int libMesh::FE< 0, L2_LAGRANGE_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1289 of file fe_lagrange_vec.C.

{ return FE<0,L2_LAGRANGE>::n_dofs(e,o); }

n_dofs() [34/121]

unsigned int libMesh::FE< 1, L2_LAGRANGE_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1290 of file fe_lagrange_vec.C.

{ return FE<1,L2_LAGRANGE>::n_dofs(e,o); }

n_dofs() [35/121]

unsigned int libMesh::FE< 2, L2_LAGRANGE_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1291 of file fe_lagrange_vec.C.

{ return 2*FE<2,L2_LAGRANGE>::n_dofs(e,o); }

n_dofs() [36/121]

unsigned int libMesh::FE< 3, L2_LAGRANGE_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1292 of file fe_lagrange_vec.C.

{ return 3*FE<3,L2_LAGRANGE>::n_dofs(e,o); }

n_dofs() [37/121]

unsigned int libMesh::FE< 0, MONOMIAL >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 391 of file fe_monomial.C.

{ return monomial_n_dofs(e, o); }

n_dofs() [38/121]

unsigned int libMesh::FE< 1, MONOMIAL >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 392 of file fe_monomial.C.

{ return monomial_n_dofs(e, o); }

n_dofs() [39/121]

unsigned int libMesh::FE< 2, MONOMIAL >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 393 of file fe_monomial.C.

{ return monomial_n_dofs(e, o); }

n_dofs() [40/121]

unsigned int libMesh::FE< 3, MONOMIAL >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 394 of file fe_monomial.C.

{ return monomial_n_dofs(e, o); }

n_dofs() [41/121]

unsigned int libMesh::FE< 0, MONOMIAL_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 669 of file fe_monomial_vec.C.

{ return FE<0, MONOMIAL>::n_dofs(e, o); }

n_dofs() [42/121]

unsigned int libMesh::FE< 1, MONOMIAL_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 670 of file fe_monomial_vec.C.

{ return FE<1, MONOMIAL>::n_dofs(e, o); }

n_dofs() [43/121]

unsigned int libMesh::FE< 2, MONOMIAL_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 671 of file fe_monomial_vec.C.

{ return 2 * FE<2, MONOMIAL>::n_dofs(e, o); }

n_dofs() [44/121]

unsigned int libMesh::FE< 3, MONOMIAL_VEC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 672 of file fe_monomial_vec.C.

{ return 3 * FE<3, MONOMIAL>::n_dofs(e, o); }

n_dofs() [45/121]

unsigned int libMesh::FE< 2, NEDELEC_ONE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 384 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs(e, o); }

n_dofs() [46/121]

unsigned int libMesh::FE< 3, NEDELEC_ONE >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 385 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs(e, o); }

n_dofs() [47/121]

unsigned int libMesh::FE< 0, RATIONAL_BERNSTEIN >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 132 of file fe_rational.C.

{ return FE<0,_underlying_fe_family>::n_dofs(e, o); }

n_dofs() [48/121]

unsigned int libMesh::FE< 1, RATIONAL_BERNSTEIN >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 133 of file fe_rational.C.

{ return FE<1,_underlying_fe_family>::n_dofs(e, o); }

n_dofs() [49/121]

unsigned int libMesh::FE< 2, RATIONAL_BERNSTEIN >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 134 of file fe_rational.C.

{ return FE<2,_underlying_fe_family>::n_dofs(e, o); }

n_dofs() [50/121]

unsigned int libMesh::FE< 3, RATIONAL_BERNSTEIN >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 135 of file fe_rational.C.

{ return FE<3,_underlying_fe_family>::n_dofs(e, o); }

n_dofs() [51/121]

unsigned int libMesh::FE< 2, RAVIART_THOMAS >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 401 of file fe_raviart.C.

{ return raviart_thomas_n_dofs(e, o); }

n_dofs() [52/121]

unsigned int libMesh::FE< 3, RAVIART_THOMAS >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 402 of file fe_raviart.C.

{ return raviart_thomas_n_dofs(e, o); }

n_dofs() [53/121]

unsigned int libMesh::FE< 2, L2_RAVIART_THOMAS >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 411 of file fe_raviart.C.

{ return raviart_thomas_n_dofs(e, o); }

n_dofs() [54/121]

unsigned int libMesh::FE< 3, L2_RAVIART_THOMAS >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 412 of file fe_raviart.C.

{ return raviart_thomas_n_dofs(e, o); }

n_dofs() [55/121]

unsigned int libMesh::FE< 0, SIDE_HIERARCHIC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 299 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs(e, o); }

n_dofs() [56/121]

unsigned int libMesh::FE< 1, SIDE_HIERARCHIC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 300 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs(e, o); }

n_dofs() [57/121]

unsigned int libMesh::FE< 2, SIDE_HIERARCHIC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 301 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs(e, o); }

n_dofs() [58/121]

unsigned int libMesh::FE< 3, SIDE_HIERARCHIC >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 302 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs(e, o); }

n_dofs() [59/121]

unsigned int libMesh::FE< 0, SZABAB >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1297 of file fe_szabab.C.

{ return szabab_n_dofs(e, o); }

n_dofs() [60/121]

unsigned int libMesh::FE< 1, SZABAB >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1298 of file fe_szabab.C.

{ return szabab_n_dofs(e, o); }

n_dofs() [61/121]

unsigned int libMesh::FE< 2, SZABAB >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1299 of file fe_szabab.C.

{ return szabab_n_dofs(e, o); }

n_dofs() [62/121]

unsigned int libMesh::FE< 3, SZABAB >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 1300 of file fe_szabab.C.

{ return szabab_n_dofs(e, o); }

n_dofs() [63/121]

unsigned int libMesh::FE< 0, XYZ >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 377 of file fe_xyz.C.

{ return monomial_n_dofs(e, o); }

n_dofs() [64/121]

unsigned int libMesh::FE< 1, XYZ >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 378 of file fe_xyz.C.

{ return monomial_n_dofs(e, o); }

n_dofs() [65/121]

unsigned int libMesh::FE< 2, XYZ >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 379 of file fe_xyz.C.

{ return monomial_n_dofs(e, o); }

n_dofs() [66/121]

unsigned int libMesh::FE< 3, XYZ >::n_dofs ( const Elem *  e, const Order  o  )

inherited

Definition at line 380 of file fe_xyz.C.

{ return monomial_n_dofs(e, o); }

n_dofs() [67/121]

static unsigned int libMesh::FE< Dim, T >::n_dofs ( const ElemType  t, const Order  o  )

staticinherited

Returns

The number of shape functions associated with this finite element.

On a p-refined element, o should be the total order of the element.

This method does not support all finite element types; e.g. for an arbitrary polygon or polyhedron type the number of shape functions may depend on an individual element and not just its type.

n_dofs() [68/121]

unsigned int libMesh::FE< 1, L2_HIERARCHIC_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 743 of file fe_hierarchic_vec.C.

{ return FE<1,L2_HIERARCHIC>::n_dofs(t,o); }

n_dofs() [69/121]

unsigned int libMesh::FE< 2, L2_HIERARCHIC_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 744 of file fe_hierarchic_vec.C.

{ return 2*FE<2,L2_HIERARCHIC>::n_dofs(t,o); }

n_dofs() [70/121]

unsigned int libMesh::FE< 3, L2_HIERARCHIC_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 745 of file fe_hierarchic_vec.C.

{ return 3*FE<3,L2_HIERARCHIC>::n_dofs(t,o); }

n_dofs() [71/121]

unsigned int libMesh::FE< 1, L2_HIERARCHIC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 155 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(t, o); }

n_dofs() [72/121]

unsigned int libMesh::FE< 2, L2_HIERARCHIC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 156 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(t, o); }

n_dofs() [73/121]

unsigned int libMesh::FE< 3, L2_HIERARCHIC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 157 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(t, o); }

n_dofs() [74/121]

unsigned int libMesh::FE< 1, L2_LAGRANGE >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 224 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(t, o); }

n_dofs() [75/121]

unsigned int libMesh::FE< 2, L2_LAGRANGE >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 225 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(t, o); }

n_dofs() [76/121]

unsigned int libMesh::FE< 3, L2_LAGRANGE >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 226 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(t, o); }

n_dofs() [77/121]

unsigned int libMesh::FE< 1, LAGRANGE >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1078 of file fe_lagrange.C.

{ return lagrange_n_dofs(t, nullptr, o); }

n_dofs() [78/121]

unsigned int libMesh::FE< 2, LAGRANGE >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1079 of file fe_lagrange.C.

{ return lagrange_n_dofs(t, nullptr, o); }

n_dofs() [79/121]

unsigned int libMesh::FE< 3, LAGRANGE >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1080 of file fe_lagrange.C.

{ return lagrange_n_dofs(t, nullptr, o); }

n_dofs() [80/121]

unsigned int libMesh::FE< 0, LAGRANGE_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1274 of file fe_lagrange_vec.C.

{ return FE<0,LAGRANGE>::n_dofs(t,o); }

n_dofs() [81/121]

unsigned int libMesh::FE< 1, LAGRANGE_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1275 of file fe_lagrange_vec.C.

{ return FE<1,LAGRANGE>::n_dofs(t,o); }

n_dofs() [82/121]

unsigned int libMesh::FE< 2, LAGRANGE_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1276 of file fe_lagrange_vec.C.

{ return 2*FE<2,LAGRANGE>::n_dofs(t,o); }

n_dofs() [83/121]

unsigned int libMesh::FE< 3, LAGRANGE_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1277 of file fe_lagrange_vec.C.

{ return 3*FE<3,LAGRANGE>::n_dofs(t,o); }

n_dofs() [84/121]

unsigned int libMesh::FE< 0, L2_LAGRANGE_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1284 of file fe_lagrange_vec.C.

{ return FE<0,L2_LAGRANGE>::n_dofs(t,o); }

n_dofs() [85/121]

unsigned int libMesh::FE< 1, L2_LAGRANGE_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1285 of file fe_lagrange_vec.C.

{ return FE<1,L2_LAGRANGE>::n_dofs(t,o); }

n_dofs() [86/121]

unsigned int libMesh::FE< 2, L2_LAGRANGE_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1286 of file fe_lagrange_vec.C.

{ return 2*FE<2,L2_LAGRANGE>::n_dofs(t,o); }

n_dofs() [87/121]

unsigned int libMesh::FE< 3, L2_LAGRANGE_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1287 of file fe_lagrange_vec.C.

{ return 3*FE<3,L2_LAGRANGE>::n_dofs(t,o); }

n_dofs() [88/121]

unsigned int libMesh::FE< 1, MONOMIAL >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 387 of file fe_monomial.C.

{ return monomial_n_dofs(t, o); }

n_dofs() [89/121]

unsigned int libMesh::FE< 2, MONOMIAL >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 388 of file fe_monomial.C.

{ return monomial_n_dofs(t, o); }

n_dofs() [90/121]

unsigned int libMesh::FE< 3, MONOMIAL >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 389 of file fe_monomial.C.

{ return monomial_n_dofs(t, o); }

n_dofs() [91/121]

unsigned int libMesh::FE< 0, MONOMIAL_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 664 of file fe_monomial_vec.C.

{ return FE<0, MONOMIAL>::n_dofs(t, o); }

n_dofs() [92/121]

unsigned int libMesh::FE< 1, MONOMIAL_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 665 of file fe_monomial_vec.C.

{ return FE<1, MONOMIAL>::n_dofs(t, o); }

n_dofs() [93/121]

unsigned int libMesh::FE< 2, MONOMIAL_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 666 of file fe_monomial_vec.C.

{ return 2 * FE<2, MONOMIAL>::n_dofs(t, o); }

n_dofs() [94/121]

unsigned int libMesh::FE< 3, MONOMIAL_VEC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 667 of file fe_monomial_vec.C.

{ return 3 * FE<3, MONOMIAL>::n_dofs(t, o); }

n_dofs() [95/121]

unsigned int libMesh::FE< 2, NEDELEC_ONE >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 379 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs(t, o); }

n_dofs() [96/121]

unsigned int libMesh::FE< 3, NEDELEC_ONE >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 380 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs(t, o); }

n_dofs() [97/121]

unsigned int libMesh::FE< 1, RATIONAL_BERNSTEIN >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 128 of file fe_rational.C.

{ return FE<1,_underlying_fe_family>::n_dofs(t, o); }

n_dofs() [98/121]

unsigned int libMesh::FE< 2, RATIONAL_BERNSTEIN >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 129 of file fe_rational.C.

{ return FE<2,_underlying_fe_family>::n_dofs(t, o); }

n_dofs() [99/121]

unsigned int libMesh::FE< 3, RATIONAL_BERNSTEIN >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 130 of file fe_rational.C.

{ return FE<3,_underlying_fe_family>::n_dofs(t, o); }

n_dofs() [100/121]

unsigned int libMesh::FE< 2, RAVIART_THOMAS >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 396 of file fe_raviart.C.

{ return raviart_thomas_n_dofs(t, o); }

n_dofs() [101/121]

unsigned int libMesh::FE< 3, RAVIART_THOMAS >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 397 of file fe_raviart.C.

{ return raviart_thomas_n_dofs(t, o); }

n_dofs() [102/121]

unsigned int libMesh::FE< 2, L2_RAVIART_THOMAS >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 406 of file fe_raviart.C.

{ return raviart_thomas_n_dofs(t, o); }

n_dofs() [103/121]

unsigned int libMesh::FE< 3, L2_RAVIART_THOMAS >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 407 of file fe_raviart.C.

{ return raviart_thomas_n_dofs(t, o); }

n_dofs() [104/121]

unsigned int libMesh::FE< 0, SIDE_HIERARCHIC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 294 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs(t, o); }

n_dofs() [105/121]

unsigned int libMesh::FE< 1, SIDE_HIERARCHIC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 295 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs(t, o); }

n_dofs() [106/121]

unsigned int libMesh::FE< 2, SIDE_HIERARCHIC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 296 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs(t, o); }

n_dofs() [107/121]

unsigned int libMesh::FE< 3, SIDE_HIERARCHIC >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 297 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs(t, o); }

n_dofs() [108/121]

unsigned int libMesh::FE< 1, SZABAB >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1293 of file fe_szabab.C.

{ return szabab_n_dofs(t, o); }

n_dofs() [109/121]

unsigned int libMesh::FE< 2, SZABAB >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1294 of file fe_szabab.C.

{ return szabab_n_dofs(t, o); }

n_dofs() [110/121]

unsigned int libMesh::FE< 3, SZABAB >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 1295 of file fe_szabab.C.

{ return szabab_n_dofs(t, o); }

n_dofs() [111/121]

unsigned int libMesh::FE< 1, XYZ >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 373 of file fe_xyz.C.

{ return monomial_n_dofs(t, o); }

n_dofs() [112/121]

unsigned int libMesh::FE< 2, XYZ >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 374 of file fe_xyz.C.

{ return monomial_n_dofs(t, o); }

n_dofs() [113/121]

unsigned int libMesh::FE< 3, XYZ >::n_dofs ( const ElemType  t, const Order  o  )

inherited

Definition at line 375 of file fe_xyz.C.

{ return monomial_n_dofs(t, o); }

n_dofs() [114/121]

unsigned int libMesh::FE< 1, SCALAR >::n_dofs ( const ElemType  , const Order  o  )

inherited

Definition at line 61 of file fe_scalar.C.

{ return o; }

n_dofs() [115/121]

unsigned int libMesh::FE< 2, SCALAR >::n_dofs ( const ElemType  , const Order  o  )

inherited

Definition at line 62 of file fe_scalar.C.

{ return o; }

n_dofs() [116/121]

unsigned int libMesh::FE< 3, SCALAR >::n_dofs ( const ElemType  , const Order  o  )

inherited

Definition at line 63 of file fe_scalar.C.

{ return o; }

n_dofs() [117/121]

unsigned int libMesh::FE< 1, NEDELEC_ONE >::n_dofs ( const ElemType  , const Order    )

inherited

Definition at line 378 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs() [118/121]

unsigned int libMesh::FE< 1, RAVIART_THOMAS >::n_dofs ( const ElemType  , const Order    )

inherited

Definition at line 395 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs() [119/121]

unsigned int libMesh::FE< 0, L2_RAVIART_THOMAS >::n_dofs ( const ElemType  , const Order    )

inherited

Definition at line 404 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs() [120/121]

unsigned int libMesh::FE< 1, L2_RAVIART_THOMAS >::n_dofs ( const ElemType  , const Order    )

inherited

Definition at line 405 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs() [121/121]

unsigned int libMesh::FE< 2, SUBDIVISION >::n_dofs ( const ElemType  , const Order    )

inherited

Definition at line 958 of file fe_subdivision_2D.C.

{ libmesh_not_implemented(); return 0; }

n_dofs_at_node() [1/132]

unsigned int libMesh::FE< 0, L2_HIERARCHIC_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 757 of file fe_hierarchic_vec.C.

{ return 0; }

n_dofs_at_node() [2/132]

unsigned int libMesh::FE< 1, L2_HIERARCHIC_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 758 of file fe_hierarchic_vec.C.

{ return 0; }

n_dofs_at_node() [3/132]

unsigned int libMesh::FE< 2, L2_HIERARCHIC_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 759 of file fe_hierarchic_vec.C.

{ return 0; }

n_dofs_at_node() [4/132]

unsigned int libMesh::FE< 3, L2_HIERARCHIC_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 760 of file fe_hierarchic_vec.C.

{ return 0; }

n_dofs_at_node() [5/132]

unsigned int libMesh::FE< 0, L2_HIERARCHIC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 171 of file fe_l2_hierarchic.C.

{ return 0; }

n_dofs_at_node() [6/132]

unsigned int libMesh::FE< 1, L2_HIERARCHIC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 172 of file fe_l2_hierarchic.C.

{ return 0; }

n_dofs_at_node() [7/132]

unsigned int libMesh::FE< 2, L2_HIERARCHIC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 173 of file fe_l2_hierarchic.C.

{ return 0; }

n_dofs_at_node() [8/132]

unsigned int libMesh::FE< 3, L2_HIERARCHIC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 174 of file fe_l2_hierarchic.C.

{ return 0; }

n_dofs_at_node() [9/132]

unsigned int libMesh::FE< 0, L2_LAGRANGE >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 239 of file fe_l2_lagrange.C.

{ return 0; }

n_dofs_at_node() [10/132]

unsigned int libMesh::FE< 1, L2_LAGRANGE >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 240 of file fe_l2_lagrange.C.

{ return 0; }

n_dofs_at_node() [11/132]

unsigned int libMesh::FE< 2, L2_LAGRANGE >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 241 of file fe_l2_lagrange.C.

{ return 0; }

n_dofs_at_node() [12/132]

unsigned int libMesh::FE< 3, L2_LAGRANGE >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 242 of file fe_l2_lagrange.C.

{ return 0; }

n_dofs_at_node() [13/132]

unsigned int libMesh::FE< 0, L2_LAGRANGE_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 1312 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_at_node() [14/132]

unsigned int libMesh::FE< 1, L2_LAGRANGE_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 1313 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_at_node() [15/132]

unsigned int libMesh::FE< 2, L2_LAGRANGE_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 1314 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_at_node() [16/132]

unsigned int libMesh::FE< 3, L2_LAGRANGE_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 1315 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_at_node() [17/132]

unsigned int libMesh::FE< 0, MONOMIAL >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 403 of file fe_monomial.C.

{ return 0; }

n_dofs_at_node() [18/132]

unsigned int libMesh::FE< 1, MONOMIAL >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 404 of file fe_monomial.C.

{ return 0; }

n_dofs_at_node() [19/132]

unsigned int libMesh::FE< 2, MONOMIAL >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 405 of file fe_monomial.C.

{ return 0; }

n_dofs_at_node() [20/132]

unsigned int libMesh::FE< 3, MONOMIAL >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 406 of file fe_monomial.C.

{ return 0; }

n_dofs_at_node() [21/132]

unsigned int libMesh::FE< 0, MONOMIAL_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 679 of file fe_monomial_vec.C.

{ return 0; }

n_dofs_at_node() [22/132]

unsigned int libMesh::FE< 1, MONOMIAL_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 680 of file fe_monomial_vec.C.

{ return 0; }

n_dofs_at_node() [23/132]

unsigned int libMesh::FE< 2, MONOMIAL_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 681 of file fe_monomial_vec.C.

{ return 0; }

n_dofs_at_node() [24/132]

unsigned int libMesh::FE< 3, MONOMIAL_VEC >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 682 of file fe_monomial_vec.C.

{ return 0; }

n_dofs_at_node() [25/132]

unsigned int libMesh::FE< 0, NEDELEC_ONE >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 392 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [26/132]

unsigned int libMesh::FE< 1, NEDELEC_ONE >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 393 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [27/132]

unsigned int libMesh::FE< 0, RAVIART_THOMAS >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 419 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [28/132]

unsigned int libMesh::FE< 1, RAVIART_THOMAS >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 420 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [29/132]

unsigned int libMesh::FE< 0, L2_RAVIART_THOMAS >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 429 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [30/132]

unsigned int libMesh::FE< 1, L2_RAVIART_THOMAS >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 430 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [31/132]

unsigned int libMesh::FE< 2, L2_RAVIART_THOMAS >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 431 of file fe_raviart.C.

{ return 0; }

n_dofs_at_node() [32/132]

unsigned int libMesh::FE< 3, L2_RAVIART_THOMAS >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 432 of file fe_raviart.C.

{ return 0; }

n_dofs_at_node() [33/132]

unsigned int libMesh::FE< 0, SCALAR >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 77 of file fe_scalar.C.

{ return 0; }

n_dofs_at_node() [34/132]

unsigned int libMesh::FE< 1, SCALAR >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 78 of file fe_scalar.C.

{ return 0; }

n_dofs_at_node() [35/132]

unsigned int libMesh::FE< 2, SCALAR >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 79 of file fe_scalar.C.

{ return 0; }

n_dofs_at_node() [36/132]

unsigned int libMesh::FE< 3, SCALAR >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 80 of file fe_scalar.C.

{ return 0; }

n_dofs_at_node() [37/132]

unsigned int libMesh::FE< 2, SUBDIVISION >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 963 of file fe_subdivision_2D.C.

{ return 1; }

n_dofs_at_node() [38/132]

unsigned int libMesh::FE< 0, XYZ >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 389 of file fe_xyz.C.

{ return 0; }

n_dofs_at_node() [39/132]

unsigned int libMesh::FE< 1, XYZ >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 390 of file fe_xyz.C.

{ return 0; }

n_dofs_at_node() [40/132]

unsigned int libMesh::FE< 2, XYZ >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 391 of file fe_xyz.C.

{ return 0; }

n_dofs_at_node() [41/132]

unsigned int libMesh::FE< 3, XYZ >::n_dofs_at_node ( const Elem &  , const Order  , const unsigned int    )

inherited

Definition at line 392 of file fe_xyz.C.

{ return 0; }

n_dofs_at_node() [42/132]

static unsigned int libMesh::FE< Dim, T >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

staticinherited

Returns

The number of dofs at node n for a finite element of type t and order o.

On a p-refined element, o should be the total order of the element.

n_dofs_at_node() [43/132]

unsigned int libMesh::FE< 0, LAGRANGE >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1095 of file fe_lagrange.C.

{ return lagrange_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [44/132]

unsigned int libMesh::FE< 1, LAGRANGE >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1096 of file fe_lagrange.C.

{ return lagrange_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [45/132]

unsigned int libMesh::FE< 2, LAGRANGE >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1097 of file fe_lagrange.C.

{ return lagrange_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [46/132]

unsigned int libMesh::FE< 3, LAGRANGE >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1098 of file fe_lagrange.C.

{ return lagrange_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [47/132]

unsigned int libMesh::FE< 0, LAGRANGE_VEC >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1302 of file fe_lagrange_vec.C.

{ return FE<0,LAGRANGE>::n_dofs_at_node(e,o,n); }

n_dofs_at_node() [48/132]

unsigned int libMesh::FE< 1, LAGRANGE_VEC >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1303 of file fe_lagrange_vec.C.

{ return FE<1,LAGRANGE>::n_dofs_at_node(e,o,n); }

n_dofs_at_node() [49/132]

unsigned int libMesh::FE< 2, LAGRANGE_VEC >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1304 of file fe_lagrange_vec.C.

{ return 2*FE<2,LAGRANGE>::n_dofs_at_node(e,o,n); }

n_dofs_at_node() [50/132]

unsigned int libMesh::FE< 3, LAGRANGE_VEC >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1305 of file fe_lagrange_vec.C.

{ return 3*FE<3,LAGRANGE>::n_dofs_at_node(e,o,n); }

n_dofs_at_node() [51/132]

unsigned int libMesh::FE< 2, NEDELEC_ONE >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 394 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [52/132]

unsigned int libMesh::FE< 3, NEDELEC_ONE >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 395 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [53/132]

unsigned int libMesh::FE< 0, RATIONAL_BERNSTEIN >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 143 of file fe_rational.C.

{ return FE<0,_underlying_fe_family>::n_dofs_at_node(e, o, n); }

n_dofs_at_node() [54/132]

unsigned int libMesh::FE< 1, RATIONAL_BERNSTEIN >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 144 of file fe_rational.C.

{ return FE<1,_underlying_fe_family>::n_dofs_at_node(e, o, n); }

n_dofs_at_node() [55/132]

unsigned int libMesh::FE< 2, RATIONAL_BERNSTEIN >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 145 of file fe_rational.C.

{ return FE<2,_underlying_fe_family>::n_dofs_at_node(e, o, n); }

n_dofs_at_node() [56/132]

unsigned int libMesh::FE< 3, RATIONAL_BERNSTEIN >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 146 of file fe_rational.C.

{ return FE<3,_underlying_fe_family>::n_dofs_at_node(e, o, n); }

n_dofs_at_node() [57/132]

unsigned int libMesh::FE< 2, RAVIART_THOMAS >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 421 of file fe_raviart.C.

{ return raviart_thomas_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [58/132]

unsigned int libMesh::FE< 3, RAVIART_THOMAS >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 422 of file fe_raviart.C.

{ return raviart_thomas_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [59/132]

unsigned int libMesh::FE< 0, SIDE_HIERARCHIC >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 310 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [60/132]

unsigned int libMesh::FE< 1, SIDE_HIERARCHIC >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 311 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [61/132]

unsigned int libMesh::FE< 2, SIDE_HIERARCHIC >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 312 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [62/132]

unsigned int libMesh::FE< 3, SIDE_HIERARCHIC >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 313 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [63/132]

unsigned int libMesh::FE< 0, SZABAB >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1308 of file fe_szabab.C.

{ return szabab_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [64/132]

unsigned int libMesh::FE< 1, SZABAB >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1309 of file fe_szabab.C.

{ return szabab_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [65/132]

unsigned int libMesh::FE< 2, SZABAB >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1310 of file fe_szabab.C.

{ return szabab_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [66/132]

unsigned int libMesh::FE< 3, SZABAB >::n_dofs_at_node ( const Elem &  e, const Order  o, const unsigned int  n  )

inherited

Definition at line 1311 of file fe_szabab.C.

{ return szabab_n_dofs_at_node(e, o, n); }

n_dofs_at_node() [67/132]

static unsigned int libMesh::FE< Dim, T >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

staticinherited

Returns

The number of dofs at node n for a finite element of type t and order o.

On a p-refined element, o should be the total order of the element.

This method does not support all finite element types; e.g. for an arbitrary polygon or polyhedron type the meaning of a node index n may depend on an individual element and not just its type.

n_dofs_at_node() [68/132]

unsigned int libMesh::FE< 0, LAGRANGE >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1090 of file fe_lagrange.C.

{ return lagrange_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [69/132]

unsigned int libMesh::FE< 1, LAGRANGE >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1091 of file fe_lagrange.C.

{ return lagrange_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [70/132]

unsigned int libMesh::FE< 2, LAGRANGE >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1092 of file fe_lagrange.C.

{ return lagrange_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [71/132]

unsigned int libMesh::FE< 3, LAGRANGE >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1093 of file fe_lagrange.C.

{ return lagrange_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [72/132]

unsigned int libMesh::FE< 0, LAGRANGE_VEC >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1297 of file fe_lagrange_vec.C.

{ return FE<0,LAGRANGE>::n_dofs_at_node(t,o,n); }

n_dofs_at_node() [73/132]

unsigned int libMesh::FE< 1, LAGRANGE_VEC >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1298 of file fe_lagrange_vec.C.

{ return FE<1,LAGRANGE>::n_dofs_at_node(t,o,n); }

n_dofs_at_node() [74/132]

unsigned int libMesh::FE< 2, LAGRANGE_VEC >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1299 of file fe_lagrange_vec.C.

{ return 2*FE<2,LAGRANGE>::n_dofs_at_node(t,o,n); }

n_dofs_at_node() [75/132]

unsigned int libMesh::FE< 3, LAGRANGE_VEC >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1300 of file fe_lagrange_vec.C.

{ return 3*FE<3,LAGRANGE>::n_dofs_at_node(t,o,n); }

n_dofs_at_node() [76/132]

unsigned int libMesh::FE< 2, NEDELEC_ONE >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 389 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [77/132]

unsigned int libMesh::FE< 3, NEDELEC_ONE >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 390 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [78/132]

unsigned int libMesh::FE< 0, RATIONAL_BERNSTEIN >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 138 of file fe_rational.C.

{ return FE<0,_underlying_fe_family>::n_dofs_at_node(t, o, n); }

n_dofs_at_node() [79/132]

unsigned int libMesh::FE< 1, RATIONAL_BERNSTEIN >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 139 of file fe_rational.C.

{ return FE<1,_underlying_fe_family>::n_dofs_at_node(t, o, n); }

n_dofs_at_node() [80/132]

unsigned int libMesh::FE< 2, RATIONAL_BERNSTEIN >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 140 of file fe_rational.C.

{ return FE<2,_underlying_fe_family>::n_dofs_at_node(t, o, n); }

n_dofs_at_node() [81/132]

unsigned int libMesh::FE< 3, RATIONAL_BERNSTEIN >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 141 of file fe_rational.C.

{ return FE<3,_underlying_fe_family>::n_dofs_at_node(t, o, n); }

n_dofs_at_node() [82/132]

unsigned int libMesh::FE< 2, RAVIART_THOMAS >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 416 of file fe_raviart.C.

{ return raviart_thomas_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [83/132]

unsigned int libMesh::FE< 3, RAVIART_THOMAS >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 417 of file fe_raviart.C.

{ return raviart_thomas_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [84/132]

unsigned int libMesh::FE< 0, SIDE_HIERARCHIC >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 305 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [85/132]

unsigned int libMesh::FE< 1, SIDE_HIERARCHIC >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 306 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [86/132]

unsigned int libMesh::FE< 2, SIDE_HIERARCHIC >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 307 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [87/132]

unsigned int libMesh::FE< 3, SIDE_HIERARCHIC >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 308 of file fe_side_hierarchic.C.

{ return side_hierarchic_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [88/132]

unsigned int libMesh::FE< 0, SZABAB >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1303 of file fe_szabab.C.

{ return szabab_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [89/132]

unsigned int libMesh::FE< 1, SZABAB >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1304 of file fe_szabab.C.

{ return szabab_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [90/132]

unsigned int libMesh::FE< 2, SZABAB >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1305 of file fe_szabab.C.

{ return szabab_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [91/132]

unsigned int libMesh::FE< 3, SZABAB >::n_dofs_at_node ( const ElemType  t, const Order  o, const unsigned int  n  )

inherited

Definition at line 1306 of file fe_szabab.C.

{ return szabab_n_dofs_at_node(t, o, n); }

n_dofs_at_node() [92/132]

unsigned int libMesh::FE< 0, L2_HIERARCHIC_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 752 of file fe_hierarchic_vec.C.

{ return 0; }

n_dofs_at_node() [93/132]

unsigned int libMesh::FE< 1, L2_HIERARCHIC_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 753 of file fe_hierarchic_vec.C.

{ return 0; }

n_dofs_at_node() [94/132]

unsigned int libMesh::FE< 2, L2_HIERARCHIC_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 754 of file fe_hierarchic_vec.C.

{ return 0; }

n_dofs_at_node() [95/132]

unsigned int libMesh::FE< 3, L2_HIERARCHIC_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 755 of file fe_hierarchic_vec.C.

{ return 0; }

n_dofs_at_node() [96/132]

unsigned int libMesh::FE< 0, L2_HIERARCHIC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 166 of file fe_l2_hierarchic.C.

{ return 0; }

n_dofs_at_node() [97/132]

unsigned int libMesh::FE< 1, L2_HIERARCHIC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 167 of file fe_l2_hierarchic.C.

{ return 0; }

n_dofs_at_node() [98/132]

unsigned int libMesh::FE< 2, L2_HIERARCHIC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 168 of file fe_l2_hierarchic.C.

{ return 0; }

n_dofs_at_node() [99/132]

unsigned int libMesh::FE< 3, L2_HIERARCHIC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 169 of file fe_l2_hierarchic.C.

{ return 0; }

n_dofs_at_node() [100/132]

unsigned int libMesh::FE< 0, L2_LAGRANGE >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 234 of file fe_l2_lagrange.C.

{ return 0; }

n_dofs_at_node() [101/132]

unsigned int libMesh::FE< 1, L2_LAGRANGE >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 235 of file fe_l2_lagrange.C.

{ return 0; }

n_dofs_at_node() [102/132]

unsigned int libMesh::FE< 2, L2_LAGRANGE >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 236 of file fe_l2_lagrange.C.

{ return 0; }

n_dofs_at_node() [103/132]

unsigned int libMesh::FE< 3, L2_LAGRANGE >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 237 of file fe_l2_lagrange.C.

{ return 0; }

n_dofs_at_node() [104/132]

unsigned int libMesh::FE< 0, L2_LAGRANGE_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 1307 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_at_node() [105/132]

unsigned int libMesh::FE< 1, L2_LAGRANGE_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 1308 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_at_node() [106/132]

unsigned int libMesh::FE< 2, L2_LAGRANGE_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 1309 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_at_node() [107/132]

unsigned int libMesh::FE< 3, L2_LAGRANGE_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 1310 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_at_node() [108/132]

unsigned int libMesh::FE< 0, MONOMIAL >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 398 of file fe_monomial.C.

{ return 0; }

n_dofs_at_node() [109/132]

unsigned int libMesh::FE< 1, MONOMIAL >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 399 of file fe_monomial.C.

{ return 0; }

n_dofs_at_node() [110/132]

unsigned int libMesh::FE< 2, MONOMIAL >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 400 of file fe_monomial.C.

{ return 0; }

n_dofs_at_node() [111/132]

unsigned int libMesh::FE< 3, MONOMIAL >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 401 of file fe_monomial.C.

{ return 0; }

n_dofs_at_node() [112/132]

unsigned int libMesh::FE< 0, MONOMIAL_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 674 of file fe_monomial_vec.C.

{ return 0; }

n_dofs_at_node() [113/132]

unsigned int libMesh::FE< 1, MONOMIAL_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 675 of file fe_monomial_vec.C.

{ return 0; }

n_dofs_at_node() [114/132]

unsigned int libMesh::FE< 2, MONOMIAL_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 676 of file fe_monomial_vec.C.

{ return 0; }

n_dofs_at_node() [115/132]

unsigned int libMesh::FE< 3, MONOMIAL_VEC >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 677 of file fe_monomial_vec.C.

{ return 0; }

n_dofs_at_node() [116/132]

unsigned int libMesh::FE< 0, NEDELEC_ONE >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 387 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [117/132]

unsigned int libMesh::FE< 1, NEDELEC_ONE >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 388 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [118/132]

unsigned int libMesh::FE< 0, RAVIART_THOMAS >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 414 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [119/132]

unsigned int libMesh::FE< 1, RAVIART_THOMAS >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 415 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [120/132]

unsigned int libMesh::FE< 0, L2_RAVIART_THOMAS >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 424 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [121/132]

unsigned int libMesh::FE< 1, L2_RAVIART_THOMAS >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 425 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_at_node() [122/132]

unsigned int libMesh::FE< 2, L2_RAVIART_THOMAS >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 426 of file fe_raviart.C.

{ return 0; }

n_dofs_at_node() [123/132]

unsigned int libMesh::FE< 3, L2_RAVIART_THOMAS >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 427 of file fe_raviart.C.

{ return 0; }

n_dofs_at_node() [124/132]

unsigned int libMesh::FE< 0, SCALAR >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 72 of file fe_scalar.C.

{ return 0; }

n_dofs_at_node() [125/132]

unsigned int libMesh::FE< 1, SCALAR >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 73 of file fe_scalar.C.

{ return 0; }

n_dofs_at_node() [126/132]

unsigned int libMesh::FE< 2, SCALAR >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 74 of file fe_scalar.C.

{ return 0; }

n_dofs_at_node() [127/132]

unsigned int libMesh::FE< 3, SCALAR >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 75 of file fe_scalar.C.

{ return 0; }

n_dofs_at_node() [128/132]

unsigned int libMesh::FE< 2, SUBDIVISION >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 962 of file fe_subdivision_2D.C.

{ return 1; }

n_dofs_at_node() [129/132]

unsigned int libMesh::FE< 0, XYZ >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 384 of file fe_xyz.C.

{ return 0; }

n_dofs_at_node() [130/132]

unsigned int libMesh::FE< 1, XYZ >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 385 of file fe_xyz.C.

{ return 0; }

n_dofs_at_node() [131/132]

unsigned int libMesh::FE< 2, XYZ >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 386 of file fe_xyz.C.

{ return 0; }

n_dofs_at_node() [132/132]

unsigned int libMesh::FE< 3, XYZ >::n_dofs_at_node ( const ElemType  , const Order  , const unsigned int    )

inherited

Definition at line 387 of file fe_xyz.C.

{ return 0; }

n_dofs_per_elem() [1/132]

unsigned int libMesh::FE< 0, LAGRANGE >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 1108 of file fe_lagrange.C.

{ return 0; }

n_dofs_per_elem() [2/132]

unsigned int libMesh::FE< 1, LAGRANGE >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 1109 of file fe_lagrange.C.

{ return 0; }

n_dofs_per_elem() [3/132]

unsigned int libMesh::FE< 2, LAGRANGE >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 1110 of file fe_lagrange.C.

{ return 0; }

n_dofs_per_elem() [4/132]

unsigned int libMesh::FE< 3, LAGRANGE >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 1111 of file fe_lagrange.C.

{ return 0; }

n_dofs_per_elem() [5/132]

unsigned int libMesh::FE< 0, LAGRANGE_VEC >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 1325 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_per_elem() [6/132]

unsigned int libMesh::FE< 1, LAGRANGE_VEC >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 1326 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_per_elem() [7/132]

unsigned int libMesh::FE< 2, LAGRANGE_VEC >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 1327 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_per_elem() [8/132]

unsigned int libMesh::FE< 3, LAGRANGE_VEC >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 1328 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_per_elem() [9/132]

unsigned int libMesh::FE< 0, NEDELEC_ONE >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 402 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [10/132]

unsigned int libMesh::FE< 1, NEDELEC_ONE >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 403 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [11/132]

unsigned int libMesh::FE< 0, RAVIART_THOMAS >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 439 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [12/132]

unsigned int libMesh::FE< 1, RAVIART_THOMAS >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 440 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [13/132]

unsigned int libMesh::FE< 0, L2_RAVIART_THOMAS >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 450 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [14/132]

unsigned int libMesh::FE< 1, L2_RAVIART_THOMAS >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 451 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [15/132]

unsigned int libMesh::FE< 0, SCALAR >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 89 of file fe_scalar.C.

{ return 0; }

n_dofs_per_elem() [16/132]

unsigned int libMesh::FE< 1, SCALAR >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 90 of file fe_scalar.C.

{ return 0; }

n_dofs_per_elem() [17/132]

unsigned int libMesh::FE< 2, SCALAR >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 91 of file fe_scalar.C.

{ return 0; }

n_dofs_per_elem() [18/132]

unsigned int libMesh::FE< 3, SCALAR >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 92 of file fe_scalar.C.

{ return 0; }

n_dofs_per_elem() [19/132]

unsigned int libMesh::FE< 0, SIDE_HIERARCHIC >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 321 of file fe_side_hierarchic.C.

{ return 0; }

n_dofs_per_elem() [20/132]

unsigned int libMesh::FE< 1, SIDE_HIERARCHIC >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 322 of file fe_side_hierarchic.C.

{ return 0; }

n_dofs_per_elem() [21/132]

unsigned int libMesh::FE< 2, SIDE_HIERARCHIC >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 323 of file fe_side_hierarchic.C.

{ return 0; }

n_dofs_per_elem() [22/132]

unsigned int libMesh::FE< 3, SIDE_HIERARCHIC >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 324 of file fe_side_hierarchic.C.

{ return 0; }

n_dofs_per_elem() [23/132]

unsigned int libMesh::FE< 2, SUBDIVISION >::n_dofs_per_elem ( const Elem &  , const Order    )

inherited

Definition at line 967 of file fe_subdivision_2D.C.

{ return 0; }

n_dofs_per_elem() [24/132]

static unsigned int libMesh::FE< Dim, T >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

staticinherited

Returns

The number of dofs interior to the element, not associated with any interior nodes.

On a p-refined element, o should be the total order of the element.

n_dofs_per_elem() [25/132]

unsigned int libMesh::FE< 0, L2_HIERARCHIC_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 767 of file fe_hierarchic_vec.C.

{ return FE<0,L2_HIERARCHIC_VEC>::n_dofs(&e, o); }

n_dofs_per_elem() [26/132]

unsigned int libMesh::FE< 1, L2_HIERARCHIC_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 768 of file fe_hierarchic_vec.C.

{ return FE<1,L2_HIERARCHIC_VEC>::n_dofs(&e, o); }

n_dofs_per_elem() [27/132]

unsigned int libMesh::FE< 2, L2_HIERARCHIC_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 769 of file fe_hierarchic_vec.C.

{ return FE<2,L2_HIERARCHIC_VEC>::n_dofs(&e, o); }

n_dofs_per_elem() [28/132]

unsigned int libMesh::FE< 3, L2_HIERARCHIC_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 770 of file fe_hierarchic_vec.C.

{ return FE<3,L2_HIERARCHIC_VEC>::n_dofs(&e, o); }

n_dofs_per_elem() [29/132]

unsigned int libMesh::FE< 0, L2_HIERARCHIC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 182 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(&e, o); }

n_dofs_per_elem() [30/132]

unsigned int libMesh::FE< 1, L2_HIERARCHIC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 183 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(&e, o); }

n_dofs_per_elem() [31/132]

unsigned int libMesh::FE< 2, L2_HIERARCHIC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 184 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(&e, o); }

n_dofs_per_elem() [32/132]

unsigned int libMesh::FE< 3, L2_HIERARCHIC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 185 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(&e, o); }

n_dofs_per_elem() [33/132]

unsigned int libMesh::FE< 0, L2_LAGRANGE >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 250 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(&e, o); }

n_dofs_per_elem() [34/132]

unsigned int libMesh::FE< 1, L2_LAGRANGE >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 251 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(&e, o); }

n_dofs_per_elem() [35/132]

unsigned int libMesh::FE< 2, L2_LAGRANGE >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 252 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(&e, o); }

n_dofs_per_elem() [36/132]

unsigned int libMesh::FE< 3, L2_LAGRANGE >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 253 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(&e, o); }

n_dofs_per_elem() [37/132]

unsigned int libMesh::FE< 0, L2_LAGRANGE_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 1336 of file fe_lagrange_vec.C.

{ return FE<0,L2_LAGRANGE_VEC>::n_dofs(&e, o); }

n_dofs_per_elem() [38/132]

unsigned int libMesh::FE< 1, L2_LAGRANGE_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 1337 of file fe_lagrange_vec.C.

{ return FE<1,L2_LAGRANGE_VEC>::n_dofs(&e, o); }

n_dofs_per_elem() [39/132]

unsigned int libMesh::FE< 2, L2_LAGRANGE_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 1338 of file fe_lagrange_vec.C.

{ return FE<2,L2_LAGRANGE_VEC>::n_dofs(&e, o); }

n_dofs_per_elem() [40/132]

unsigned int libMesh::FE< 3, L2_LAGRANGE_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 1339 of file fe_lagrange_vec.C.

{ return FE<3,L2_LAGRANGE_VEC>::n_dofs(&e, o); }

n_dofs_per_elem() [41/132]

unsigned int libMesh::FE< 0, MONOMIAL >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 414 of file fe_monomial.C.

{ return monomial_n_dofs(&e, o); }

n_dofs_per_elem() [42/132]

unsigned int libMesh::FE< 1, MONOMIAL >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 415 of file fe_monomial.C.

{ return monomial_n_dofs(&e, o); }

n_dofs_per_elem() [43/132]

unsigned int libMesh::FE< 2, MONOMIAL >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 416 of file fe_monomial.C.

{ return monomial_n_dofs(&e, o); }

n_dofs_per_elem() [44/132]

unsigned int libMesh::FE< 3, MONOMIAL >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 417 of file fe_monomial.C.

{ return monomial_n_dofs(&e, o); }

n_dofs_per_elem() [45/132]

unsigned int libMesh::FE< 0, MONOMIAL_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 689 of file fe_monomial_vec.C.

{ return FE<0, MONOMIAL>::n_dofs_per_elem(e, o); }

n_dofs_per_elem() [46/132]

unsigned int libMesh::FE< 1, MONOMIAL_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 690 of file fe_monomial_vec.C.

{ return FE<1, MONOMIAL>::n_dofs_per_elem(e, o); }

n_dofs_per_elem() [47/132]

unsigned int libMesh::FE< 2, MONOMIAL_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 691 of file fe_monomial_vec.C.

{ return 2 * FE<2, MONOMIAL>::n_dofs_per_elem(e, o); }

n_dofs_per_elem() [48/132]

unsigned int libMesh::FE< 3, MONOMIAL_VEC >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 692 of file fe_monomial_vec.C.

{ return 3 * FE<3, MONOMIAL>::n_dofs_per_elem(e, o); }

n_dofs_per_elem() [49/132]

unsigned int libMesh::FE< 2, NEDELEC_ONE >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 404 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs_per_elem(e, o); }

n_dofs_per_elem() [50/132]

unsigned int libMesh::FE< 3, NEDELEC_ONE >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 405 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs_per_elem(e, o); }

n_dofs_per_elem() [51/132]

unsigned int libMesh::FE< 0, RATIONAL_BERNSTEIN >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 154 of file fe_rational.C.

{ return FE<0,_underlying_fe_family>::n_dofs_per_elem(e, o); }

n_dofs_per_elem() [52/132]

unsigned int libMesh::FE< 1, RATIONAL_BERNSTEIN >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 155 of file fe_rational.C.

{ return FE<1,_underlying_fe_family>::n_dofs_per_elem(e, o); }

n_dofs_per_elem() [53/132]

unsigned int libMesh::FE< 2, RATIONAL_BERNSTEIN >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 156 of file fe_rational.C.

{ return FE<2,_underlying_fe_family>::n_dofs_per_elem(e, o); }

n_dofs_per_elem() [54/132]

unsigned int libMesh::FE< 3, RATIONAL_BERNSTEIN >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 157 of file fe_rational.C.

{ return FE<3,_underlying_fe_family>::n_dofs_per_elem(e, o); }

n_dofs_per_elem() [55/132]

unsigned int libMesh::FE< 2, RAVIART_THOMAS >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 441 of file fe_raviart.C.

{ return raviart_thomas_n_dofs_per_elem(e, o); }

n_dofs_per_elem() [56/132]

unsigned int libMesh::FE< 3, RAVIART_THOMAS >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 442 of file fe_raviart.C.

{ return raviart_thomas_n_dofs_per_elem(e, o); }

n_dofs_per_elem() [57/132]

unsigned int libMesh::FE< 2, L2_RAVIART_THOMAS >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 452 of file fe_raviart.C.

{ return n_dofs(&e, o); }

n_dofs_per_elem() [58/132]

unsigned int libMesh::FE< 3, L2_RAVIART_THOMAS >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 453 of file fe_raviart.C.

{ return n_dofs(&e, o); }

n_dofs_per_elem() [59/132]

unsigned int libMesh::FE< 0, SZABAB >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 1319 of file fe_szabab.C.

{ return szabab_n_dofs_per_elem(e, o); }

n_dofs_per_elem() [60/132]

unsigned int libMesh::FE< 1, SZABAB >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 1320 of file fe_szabab.C.

{ return szabab_n_dofs_per_elem(e, o); }

n_dofs_per_elem() [61/132]

unsigned int libMesh::FE< 2, SZABAB >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 1321 of file fe_szabab.C.

{ return szabab_n_dofs_per_elem(e, o); }

n_dofs_per_elem() [62/132]

unsigned int libMesh::FE< 3, SZABAB >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 1322 of file fe_szabab.C.

{ return szabab_n_dofs_per_elem(e, o); }

n_dofs_per_elem() [63/132]

unsigned int libMesh::FE< 0, XYZ >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 400 of file fe_xyz.C.

{ return monomial_n_dofs(&e, o); }

n_dofs_per_elem() [64/132]

unsigned int libMesh::FE< 1, XYZ >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 401 of file fe_xyz.C.

{ return monomial_n_dofs(&e, o); }

n_dofs_per_elem() [65/132]

unsigned int libMesh::FE< 2, XYZ >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 402 of file fe_xyz.C.

{ return monomial_n_dofs(&e, o); }

n_dofs_per_elem() [66/132]

unsigned int libMesh::FE< 3, XYZ >::n_dofs_per_elem ( const Elem &  e, const Order  o  )

inherited

Definition at line 403 of file fe_xyz.C.

{ return monomial_n_dofs(&e, o); }

n_dofs_per_elem() [67/132]

static unsigned int libMesh::FE< Dim, T >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

staticinherited

Returns

The number of dofs interior to the element, not associated with any interior nodes.

On a p-refined element, o should be the total order of the element.

This method may not support all finite element types, e.g. higher order polygons or polyhedra may differ from element to element.

n_dofs_per_elem() [68/132]

unsigned int libMesh::FE< 0, L2_HIERARCHIC_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 762 of file fe_hierarchic_vec.C.

{ return FE<0,L2_HIERARCHIC_VEC>::n_dofs(t, o); }

n_dofs_per_elem() [69/132]

unsigned int libMesh::FE< 1, L2_HIERARCHIC_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 763 of file fe_hierarchic_vec.C.

{ return FE<1,L2_HIERARCHIC_VEC>::n_dofs(t, o); }

n_dofs_per_elem() [70/132]

unsigned int libMesh::FE< 2, L2_HIERARCHIC_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 764 of file fe_hierarchic_vec.C.

{ return FE<2,L2_HIERARCHIC_VEC>::n_dofs(t, o); }

n_dofs_per_elem() [71/132]

unsigned int libMesh::FE< 3, L2_HIERARCHIC_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 765 of file fe_hierarchic_vec.C.

{ return FE<3,L2_HIERARCHIC_VEC>::n_dofs(t, o); }

n_dofs_per_elem() [72/132]

unsigned int libMesh::FE< 0, L2_HIERARCHIC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 177 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(t, o); }

n_dofs_per_elem() [73/132]

unsigned int libMesh::FE< 1, L2_HIERARCHIC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 178 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(t, o); }

n_dofs_per_elem() [74/132]

unsigned int libMesh::FE< 2, L2_HIERARCHIC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 179 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(t, o); }

n_dofs_per_elem() [75/132]

unsigned int libMesh::FE< 3, L2_HIERARCHIC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 180 of file fe_l2_hierarchic.C.

{ return l2_hierarchic_n_dofs(t, o); }

n_dofs_per_elem() [76/132]

unsigned int libMesh::FE< 0, L2_LAGRANGE >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 245 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(t, o); }

n_dofs_per_elem() [77/132]

unsigned int libMesh::FE< 1, L2_LAGRANGE >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 246 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(t, o); }

n_dofs_per_elem() [78/132]

unsigned int libMesh::FE< 2, L2_LAGRANGE >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 247 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(t, o); }

n_dofs_per_elem() [79/132]

unsigned int libMesh::FE< 3, L2_LAGRANGE >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 248 of file fe_l2_lagrange.C.

{ return l2_lagrange_n_dofs(t, o); }

n_dofs_per_elem() [80/132]

unsigned int libMesh::FE< 0, L2_LAGRANGE_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 1331 of file fe_lagrange_vec.C.

{ return FE<0,L2_LAGRANGE_VEC>::n_dofs(t, o); }

n_dofs_per_elem() [81/132]

unsigned int libMesh::FE< 1, L2_LAGRANGE_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 1332 of file fe_lagrange_vec.C.

{ return FE<1,L2_LAGRANGE_VEC>::n_dofs(t, o); }

n_dofs_per_elem() [82/132]

unsigned int libMesh::FE< 2, L2_LAGRANGE_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 1333 of file fe_lagrange_vec.C.

{ return FE<2,L2_LAGRANGE_VEC>::n_dofs(t, o); }

n_dofs_per_elem() [83/132]

unsigned int libMesh::FE< 3, L2_LAGRANGE_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 1334 of file fe_lagrange_vec.C.

{ return FE<3,L2_LAGRANGE_VEC>::n_dofs(t, o); }

n_dofs_per_elem() [84/132]

unsigned int libMesh::FE< 0, MONOMIAL >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 409 of file fe_monomial.C.

{ return monomial_n_dofs(t, o); }

n_dofs_per_elem() [85/132]

unsigned int libMesh::FE< 1, MONOMIAL >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 410 of file fe_monomial.C.

{ return monomial_n_dofs(t, o); }

n_dofs_per_elem() [86/132]

unsigned int libMesh::FE< 2, MONOMIAL >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 411 of file fe_monomial.C.

{ return monomial_n_dofs(t, o); }

n_dofs_per_elem() [87/132]

unsigned int libMesh::FE< 3, MONOMIAL >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 412 of file fe_monomial.C.

{ return monomial_n_dofs(t, o); }

n_dofs_per_elem() [88/132]

unsigned int libMesh::FE< 0, MONOMIAL_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 684 of file fe_monomial_vec.C.

{ return FE<0, MONOMIAL>::n_dofs_per_elem(t, o); }

n_dofs_per_elem() [89/132]

unsigned int libMesh::FE< 1, MONOMIAL_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 685 of file fe_monomial_vec.C.

{ return FE<1, MONOMIAL>::n_dofs_per_elem(t, o); }

n_dofs_per_elem() [90/132]

unsigned int libMesh::FE< 2, MONOMIAL_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 686 of file fe_monomial_vec.C.

{ return 2 * FE<2, MONOMIAL>::n_dofs_per_elem(t, o); }

n_dofs_per_elem() [91/132]

unsigned int libMesh::FE< 3, MONOMIAL_VEC >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 687 of file fe_monomial_vec.C.

{ return 3 * FE<3, MONOMIAL>::n_dofs_per_elem(t, o); }

n_dofs_per_elem() [92/132]

unsigned int libMesh::FE< 2, NEDELEC_ONE >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 399 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs_per_elem(t, o); }

n_dofs_per_elem() [93/132]

unsigned int libMesh::FE< 3, NEDELEC_ONE >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 400 of file fe_nedelec_one.C.

{ return nedelec_one_n_dofs_per_elem(t, o); }

n_dofs_per_elem() [94/132]

unsigned int libMesh::FE< 0, RATIONAL_BERNSTEIN >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 149 of file fe_rational.C.

{ return FE<0,_underlying_fe_family>::n_dofs_per_elem(t, o); }

n_dofs_per_elem() [95/132]

unsigned int libMesh::FE< 1, RATIONAL_BERNSTEIN >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 150 of file fe_rational.C.

{ return FE<1,_underlying_fe_family>::n_dofs_per_elem(t, o); }

n_dofs_per_elem() [96/132]

unsigned int libMesh::FE< 2, RATIONAL_BERNSTEIN >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 151 of file fe_rational.C.

{ return FE<2,_underlying_fe_family>::n_dofs_per_elem(t, o); }

n_dofs_per_elem() [97/132]

unsigned int libMesh::FE< 3, RATIONAL_BERNSTEIN >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 152 of file fe_rational.C.

{ return FE<3,_underlying_fe_family>::n_dofs_per_elem(t, o); }

n_dofs_per_elem() [98/132]

unsigned int libMesh::FE< 2, RAVIART_THOMAS >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 436 of file fe_raviart.C.

{ return raviart_thomas_n_dofs_per_elem(t, o); }

n_dofs_per_elem() [99/132]

unsigned int libMesh::FE< 3, RAVIART_THOMAS >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 437 of file fe_raviart.C.

{ return raviart_thomas_n_dofs_per_elem(t, o); }

n_dofs_per_elem() [100/132]

unsigned int libMesh::FE< 2, L2_RAVIART_THOMAS >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 447 of file fe_raviart.C.

{ return n_dofs(t, o); }

n_dofs_per_elem() [101/132]

unsigned int libMesh::FE< 3, L2_RAVIART_THOMAS >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 448 of file fe_raviart.C.

{ return n_dofs(t, o); }

n_dofs_per_elem() [102/132]

unsigned int libMesh::FE< 0, SZABAB >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 1314 of file fe_szabab.C.

{ return szabab_n_dofs_per_elem(t, o); }

n_dofs_per_elem() [103/132]

unsigned int libMesh::FE< 1, SZABAB >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 1315 of file fe_szabab.C.

{ return szabab_n_dofs_per_elem(t, o); }

n_dofs_per_elem() [104/132]

unsigned int libMesh::FE< 2, SZABAB >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 1316 of file fe_szabab.C.

{ return szabab_n_dofs_per_elem(t, o); }

n_dofs_per_elem() [105/132]

unsigned int libMesh::FE< 3, SZABAB >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 1317 of file fe_szabab.C.

{ return szabab_n_dofs_per_elem(t, o); }

n_dofs_per_elem() [106/132]

unsigned int libMesh::FE< 0, XYZ >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 395 of file fe_xyz.C.

{ return monomial_n_dofs(t, o); }

n_dofs_per_elem() [107/132]

unsigned int libMesh::FE< 1, XYZ >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 396 of file fe_xyz.C.

{ return monomial_n_dofs(t, o); }

n_dofs_per_elem() [108/132]

unsigned int libMesh::FE< 2, XYZ >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 397 of file fe_xyz.C.

{ return monomial_n_dofs(t, o); }

n_dofs_per_elem() [109/132]

unsigned int libMesh::FE< 3, XYZ >::n_dofs_per_elem ( const ElemType  t, const Order  o  )

inherited

Definition at line 398 of file fe_xyz.C.

{ return monomial_n_dofs(t, o); }

n_dofs_per_elem() [110/132]

unsigned int libMesh::FE< 0, LAGRANGE >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 1103 of file fe_lagrange.C.

{ return 0; }

n_dofs_per_elem() [111/132]

unsigned int libMesh::FE< 1, LAGRANGE >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 1104 of file fe_lagrange.C.

{ return 0; }

n_dofs_per_elem() [112/132]

unsigned int libMesh::FE< 2, LAGRANGE >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 1105 of file fe_lagrange.C.

{ return 0; }

n_dofs_per_elem() [113/132]

unsigned int libMesh::FE< 3, LAGRANGE >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 1106 of file fe_lagrange.C.

{ return 0; }

n_dofs_per_elem() [114/132]

unsigned int libMesh::FE< 0, LAGRANGE_VEC >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 1320 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_per_elem() [115/132]

unsigned int libMesh::FE< 1, LAGRANGE_VEC >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 1321 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_per_elem() [116/132]

unsigned int libMesh::FE< 2, LAGRANGE_VEC >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 1322 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_per_elem() [117/132]

unsigned int libMesh::FE< 3, LAGRANGE_VEC >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 1323 of file fe_lagrange_vec.C.

{ return 0; }

n_dofs_per_elem() [118/132]

unsigned int libMesh::FE< 0, NEDELEC_ONE >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 397 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [119/132]

unsigned int libMesh::FE< 1, NEDELEC_ONE >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 398 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [120/132]

unsigned int libMesh::FE< 0, RAVIART_THOMAS >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 434 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [121/132]

unsigned int libMesh::FE< 1, RAVIART_THOMAS >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 435 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [122/132]

unsigned int libMesh::FE< 0, L2_RAVIART_THOMAS >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 445 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [123/132]

unsigned int libMesh::FE< 1, L2_RAVIART_THOMAS >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 446 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

n_dofs_per_elem() [124/132]

unsigned int libMesh::FE< 0, SCALAR >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 84 of file fe_scalar.C.

{ return 0; }

n_dofs_per_elem() [125/132]

unsigned int libMesh::FE< 1, SCALAR >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 85 of file fe_scalar.C.

{ return 0; }

n_dofs_per_elem() [126/132]

unsigned int libMesh::FE< 2, SCALAR >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 86 of file fe_scalar.C.

{ return 0; }

n_dofs_per_elem() [127/132]

unsigned int libMesh::FE< 3, SCALAR >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 87 of file fe_scalar.C.

{ return 0; }

n_dofs_per_elem() [128/132]

unsigned int libMesh::FE< 0, SIDE_HIERARCHIC >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 316 of file fe_side_hierarchic.C.

{ return 0; }

n_dofs_per_elem() [129/132]

unsigned int libMesh::FE< 1, SIDE_HIERARCHIC >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 317 of file fe_side_hierarchic.C.

{ return 0; }

n_dofs_per_elem() [130/132]

unsigned int libMesh::FE< 2, SIDE_HIERARCHIC >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 318 of file fe_side_hierarchic.C.

{ return 0; }

n_dofs_per_elem() [131/132]

unsigned int libMesh::FE< 3, SIDE_HIERARCHIC >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 319 of file fe_side_hierarchic.C.

{ return 0; }

n_dofs_per_elem() [132/132]

unsigned int libMesh::FE< 2, SUBDIVISION >::n_dofs_per_elem ( const ElemType  , const Order    )

inherited

Definition at line 966 of file fe_subdivision_2D.C.

{ return 0; }

n_objects()

static unsigned int libMesh::ReferenceCounter::n_objects ( )

inlinestaticinherited

Prints the number of outstanding (created, but not yet destroyed) objects.

Definition at line 85 of file reference_counter.h.

  { return _n_objects; }

References libMesh::ReferenceCounter::_n_objects.

Referenced by libMesh::LibMeshInit::~LibMeshInit().

n_quadrature_points()

unsigned int libMesh::FEAbstract::n_quadrature_points ( ) const

virtualinherited

Returns

The total number of quadrature points with which this was last reinitialized. Useful during matrix assembly.

Reimplemented in libMesh::InfFE< Dim, T_radial, T_map >.

Definition at line 1279 of file fe_abstract.C.

{
  if (this->shapes_on_quadrature)
    {
      libmesh_assert(this->qrule);
      libmesh_assert_equal_to(this->qrule->n_points(),
                              this->_n_total_qp);
    }
  return this->_n_total_qp;
}

References libMesh::FEAbstract::_n_total_qp, libMesh::libmesh_assert(), libMesh::QBase::n_points(), libMesh::FEAbstract::qrule, and libMesh::FEAbstract::shapes_on_quadrature.

Referenced by assemble_func(), assemble_SchroedingerEquation(), assemble_wave(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::KellyErrorEstimator::boundary_side_integration(), libMesh::DiscontinuityMeasure::internal_side_integration(), libMesh::LaplacianErrorEstimator::internal_side_integration(), and libMesh::KellyErrorEstimator::internal_side_integration().

n_shape_functions() [1/2]

unsigned int libMesh::FE< Dim, T >::n_shape_functions ( ) const

overridevirtualinherited

Returns

The number of shape functions associated with this finite element.

Implements libMesh::FEAbstract.

Definition at line 412 of file fe.C.

{
  if (this->_elem)
    return this->n_dofs (this->_elem,
                         this->fe_type.order + this->_p_level);
 
  return this->n_dofs (this->get_type(),
                       this->fe_type.order + this->_p_level);
}

n_shape_functions() [2/2]

static unsigned int libMesh::FE< Dim, T >::n_shape_functions ( const ElemType  t, const Order  o  )

inlinestaticinherited

Returns

The number of shape functions associated with a finite element of type t and approximation order o.

On a p-refined element, o should be the total order of the element.

This method does not support all finite element types; e.g. for an arbitrary polygon or polyhedron type the number of shape functions may depend on an individual element and not just its type.

Definition at line 425 of file fe.h.

  { return FE<Dim,T>::n_dofs (t,o); }

nodal_soln() [1/17]

void libMesh::FE< 0, NEDELEC_ONE >::nodal_soln ( const Elem *  , const Order  , const std::vector< Number > &  , std::vector< Number > &  , bool  , const unsigned    )

inherited

Definition at line 337 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

nodal_soln() [2/17]

void libMesh::FE< 1, NEDELEC_ONE >::nodal_soln ( const Elem *  , const Order  , const std::vector< Number > &  , std::vector< Number > &  , bool  , const unsigned    )

inherited

Definition at line 346 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

nodal_soln() [3/17]

void libMesh::FE< 0, RAVIART_THOMAS >::nodal_soln ( const Elem *  , const Order  , const std::vector< Number > &  , std::vector< Number > &  , bool  , const unsigned    )

inherited

Definition at line 316 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

nodal_soln() [4/17]

void libMesh::FE< 1, RAVIART_THOMAS >::nodal_soln ( const Elem *  , const Order  , const std::vector< Number > &  , std::vector< Number > &  , bool  , const unsigned    )

inherited

Definition at line 325 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

nodal_soln() [5/17]

void libMesh::FE< 0, L2_RAVIART_THOMAS >::nodal_soln ( const Elem *  , const Order  , const std::vector< Number > &  , std::vector< Number > &  , bool  , const unsigned    )

inherited

Definition at line 352 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

nodal_soln() [6/17]

void libMesh::FE< 1, L2_RAVIART_THOMAS >::nodal_soln ( const Elem *  , const Order  , const std::vector< Number > &  , std::vector< Number > &  , bool  , const unsigned    )

inherited

Definition at line 361 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

nodal_soln() [7/17]

static void libMesh::FE< Dim, T >::nodal_soln ( const Elem *  elem, const Order  o, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, bool  add_p_level = true, const unsigned  vdim = 1  )

staticinherited

Build the nodal soln from the element soln.

This is the solution that will be plotted.

On a p-refined element, o should be the base order of the element.

nodal_soln() [8/17]

void libMesh::FE< 2, NEDELEC_ONE >::nodal_soln ( const Elem *  elem, const Order  order, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  add_p_level, const unsigned  vdim  )

inherited

Definition at line 355 of file fe_nedelec_one.C.

{ nedelec_one_nodal_soln(elem, order, elem_soln, 2 /*dim*/, vdim, nodal_soln, add_p_level); }

nodal_soln() [9/17]

void libMesh::FE< 2, RAVIART_THOMAS >::nodal_soln ( const Elem *  elem, const Order  order, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  add_p_level, const unsigned  vdim  )

inherited

Definition at line 334 of file fe_raviart.C.

{ raviart_thomas_nodal_soln(elem, order, elem_soln, 2 /*dim*/, vdim, nodal_soln, add_p_level); }

nodal_soln() [10/17]

void libMesh::FE< 2, L2_RAVIART_THOMAS >::nodal_soln ( const Elem *  elem, const Order  order, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  add_p_level, const unsigned  vdim  )

inherited

Definition at line 370 of file fe_raviart.C.

{ raviart_thomas_nodal_soln(elem, order, elem_soln, 2 /*dim*/, vdim, nodal_soln, add_p_level); }

nodal_soln() [11/17]

void libMesh::FE< 3, HIERARCHIC_VEC >::nodal_soln ( const Elem *  elem, const Order  order, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  add_p_level, const unsigned    )

inherited

Definition at line 109 of file fe_hierarchic_vec.C.

{ hierarchic_vec_nodal_soln(elem, order, elem_soln, 3 /*dim*/, nodal_soln, add_p_level); }

nodal_soln() [12/17]

void libMesh::FE< 3, LAGRANGE_VEC >::nodal_soln ( const Elem *  elem, const Order  order, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  add_p_level, const unsigned    )

inherited

Definition at line 649 of file fe_lagrange_vec.C.

{ lagrange_vec_nodal_soln(elem, order, elem_soln, 3 /*dim*/, nodal_soln, add_p_level); }

nodal_soln() [13/17]

void libMesh::FE< 3, MONOMIAL_VEC >::nodal_soln ( const Elem *  elem, const Order  order, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  add_p_level, const unsigned    )

inherited

Definition at line 130 of file fe_monomial_vec.C.

{
  monomial_vec_nodal_soln(elem, order, elem_soln, 3 /*dim*/, nodal_soln, add_p_level);
}

nodal_soln() [14/17]

void libMesh::FE< 3, NEDELEC_ONE >::nodal_soln ( const Elem *  elem, const Order  order, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  add_p_level, const unsigned    )

inherited

Definition at line 364 of file fe_nedelec_one.C.

{ nedelec_one_nodal_soln(elem, order, elem_soln, 3 /*dim*/, 3 /*vdim*/, nodal_soln, add_p_level); }

nodal_soln() [15/17]

void libMesh::FE< 3, RAVIART_THOMAS >::nodal_soln ( const Elem *  elem, const Order  order, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  add_p_level, const unsigned    )

inherited

Definition at line 343 of file fe_raviart.C.

{ raviart_thomas_nodal_soln(elem, order, elem_soln, 3 /*dim*/, 3 /*vdim*/, nodal_soln, add_p_level); }

nodal_soln() [16/17]

void libMesh::FE< 3, L2_RAVIART_THOMAS >::nodal_soln ( const Elem *  elem, const Order  order, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  add_p_level, const unsigned    )

inherited

Definition at line 379 of file fe_raviart.C.

{ raviart_thomas_nodal_soln(elem, order, elem_soln, 3 /*dim*/, 3 /*vdim*/, nodal_soln, add_p_level); }

nodal_soln() [17/17]

void libMesh::FE< 2, SUBDIVISION >::nodal_soln ( const Elem *  elem, const Order  , const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln, const bool  , const unsigned    )

inherited

Definition at line 877 of file fe_subdivision_2D.C.

{
  libmesh_assert(elem);
  libmesh_assert_equal_to(elem->type(), TRI3SUBDIVISION);
  const Tri3Subdivision * sd_elem = static_cast<const Tri3Subdivision *>(elem);
 
  nodal_soln.resize(3); // three nodes per element
 
  // Ghost nodes are auxiliary.
  if (sd_elem->is_ghost())
    {
      nodal_soln[0] = 0;
      nodal_soln[1] = 0;
      nodal_soln[2] = 0;
      return;
    }
 
  // First node (node 0 in the element patch):
  unsigned int j = sd_elem->local_node_number(sd_elem->get_ordered_node(0)->id());
  nodal_soln[j] = elem_soln[0];
 
  // Second node (node 1 in the element patch):
  j = sd_elem->local_node_number(sd_elem->get_ordered_node(1)->id());
  nodal_soln[j] = elem_soln[1];
 
  // Third node (node 'valence' in the element patch):
  j = sd_elem->local_node_number(sd_elem->get_ordered_node(2)->id());
  nodal_soln[j] = elem_soln[sd_elem->get_ordered_valence(0)];
}

on_reference_element()

bool libMesh::FEAbstract::on_reference_element ( const Point &  p, const ElemType  t, const Real  eps = TOLERANCE  )

staticinherited

Returns

true if the point p is located on the reference element for element type t, false otherwise. Since we are doing floating point comparisons here the parameter eps can be specified to indicate a tolerance. For example, \( x \le 1 \) becomes \( x \le 1 + \epsilon \).

Deprecated:

This method overload does not support all finite element types; e.g. the reference element for an arbitrary polygon or polyhedron type may differ from element to element. Use Elem::on_reference_element() instead.

Definition at line 637 of file fe_abstract.C.

{
  // Use Elem::on_reference_element() instead
  libmesh_deprecated();
 
  libmesh_assert_greater_equal (eps, 0.);
 
  const Real xi   = p(0);
#if LIBMESH_DIM > 1
  const Real eta  = p(1);
#else
  const Real eta  = 0.;
#endif
#if LIBMESH_DIM > 2
  const Real zeta = p(2);
#else
  const Real zeta  = 0.;
#endif
 
  switch (t)
    {
    case NODEELEM:
      {
        return (!xi && !eta && !zeta);
      }
    case EDGE2:
    case EDGE3:
    case EDGE4:
      {
        // The reference 1D element is [-1,1].
        if ((xi >= -1.-eps) &&
            (xi <=  1.+eps))
          return true;
 
        return false;
      }
 
 
    case TRI3:
    case TRISHELL3:
    case TRI6:
    case TRI7:
      {
        // The reference triangle is isosceles
        // and is bound by xi=0, eta=0, and xi+eta=1.
        if ((xi  >= 0.-eps) &&
            (eta >= 0.-eps) &&
            ((xi + eta) <= 1.+eps))
          return true;
 
        return false;
      }
 
 
    case QUAD4:
    case QUADSHELL4:
    case QUAD8:
    case QUADSHELL8:
    case QUAD9:
    case QUADSHELL9:
      {
        // The reference quadrilateral element is [-1,1]^2.
        if ((xi  >= -1.-eps) &&
            (xi  <=  1.+eps) &&
            (eta >= -1.-eps) &&
            (eta <=  1.+eps))
          return true;
 
        return false;
      }
 
 
    case TET4:
    case TET10:
    case TET14:
      {
        // The reference tetrahedral is isosceles
        // and is bound by xi=0, eta=0, zeta=0,
        // and xi+eta+zeta=1.
        if ((xi   >= 0.-eps) &&
            (eta  >= 0.-eps) &&
            (zeta >= 0.-eps) &&
            ((xi + eta + zeta) <= 1.+eps))
          return true;
 
        return false;
      }
 
 
    case HEX8:
    case HEX20:
    case HEX27:
      {
        /*
          if ((xi   >= -1.) &&
          (xi   <=  1.) &&
          (eta  >= -1.) &&
          (eta  <=  1.) &&
          (zeta >= -1.) &&
          (zeta <=  1.))
          return true;
        */
 
        // The reference hexahedral element is [-1,1]^3.
        if ((xi   >= -1.-eps) &&
            (xi   <=  1.+eps) &&
            (eta  >= -1.-eps) &&
            (eta  <=  1.+eps) &&
            (zeta >= -1.-eps) &&
            (zeta <=  1.+eps))
          {
            //    libMesh::out << "Strange Point:\n";
            //    p.print();
            return true;
          }
 
        return false;
      }
 
    case PRISM6:
    case PRISM15:
    case PRISM18:
    case PRISM20:
    case PRISM21:
      {
        // Figure this one out...
        // inside the reference triangle with zeta in [-1,1]
        if ((xi   >=  0.-eps) &&
            (eta  >=  0.-eps) &&
            (zeta >= -1.-eps) &&
            (zeta <=  1.+eps) &&
            ((xi + eta) <= 1.+eps))
          return true;
 
        return false;
      }
 
 
    case PYRAMID5:
    case PYRAMID13:
    case PYRAMID14:
    case PYRAMID18:
      {
        // Check that the point is on the same side of all the faces
        // by testing whether:
        //
        // n_i.(x - x_i) <= 0
        //
        // for each i, where:
        //   n_i is the outward normal of face i,
        //   x_i is a point on face i.
        if ((-eta - 1. + zeta <= 0.+eps) &&
            (  xi - 1. + zeta <= 0.+eps) &&
            ( eta - 1. + zeta <= 0.+eps) &&
            ( -xi - 1. + zeta <= 0.+eps) &&
            (            zeta >= 0.-eps))
          return true;
 
        return false;
      }
 
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
    case INFHEX8:
    case INFHEX16:
    case INFHEX18:
      {
        // The reference infhex8 is a [-1,1]^3.
        if ((xi   >= -1.-eps) &&
            (xi   <=  1.+eps) &&
            (eta  >= -1.-eps) &&
            (eta  <=  1.+eps) &&
            (zeta >= -1.-eps) &&
            (zeta <=  1.+eps))
          {
            return true;
          }
        return false;
      }
 
    case INFPRISM6:
    case INFPRISM12:
      {
        // inside the reference triangle with zeta in [-1,1]
        if ((xi   >=  0.-eps) &&
            (eta  >=  0.-eps) &&
            (zeta >= -1.-eps) &&
            (zeta <=  1.+eps) &&
            ((xi + eta) <= 1.+eps))
          {
            return true;
          }
 
        return false;
      }
#endif
 
    default:
      libmesh_error_msg("ERROR: Unknown element type " << Utility::enum_to_string(t));
    }
 
  // If we get here then the point is _not_ in the
  // reference element.   Better return false.
 
  return false;
}

References libMesh::EDGE2, libMesh::EDGE3, libMesh::EDGE4, libMesh::Utility::enum_to_string(), libMesh::HEX20, libMesh::HEX27, libMesh::HEX8, libMesh::INFHEX16, libMesh::INFHEX18, libMesh::INFHEX8, libMesh::INFPRISM12, libMesh::INFPRISM6, libMesh::NODEELEM, libMesh::PRISM15, libMesh::PRISM18, libMesh::PRISM20, libMesh::PRISM21, libMesh::PRISM6, libMesh::PYRAMID13, libMesh::PYRAMID14, libMesh::PYRAMID18, libMesh::PYRAMID5, libMesh::QUAD4, libMesh::QUAD8, libMesh::QUAD9, libMesh::QUADSHELL4, libMesh::QUADSHELL8, libMesh::QUADSHELL9, libMesh::Real, libMesh::TET10, libMesh::TET14, libMesh::TET4, libMesh::TRI3, libMesh::TRI6, libMesh::TRI7, and libMesh::TRISHELL3.

Referenced by libMesh::FEInterface::ifem_on_reference_element(), and libMesh::FEInterface::on_reference_element().

print_d2phi()

void libMesh::FEGenericBase< FEOutputType< T >::type >::print_d2phi ( std::ostream &  os ) const

overridevirtualinherited

Prints the value of each shape function's second derivatives at each quadrature point.

Implements libMesh::FEAbstract.

Definition at line 535 of file fe_base.C.

{
  for (auto i : index_range(dphi))
    for (auto j : index_range(dphi[i]))
      os << " d2phi[" << i << "][" << j << "]=" << d2phi[i][j];
}

print_dphi()

void libMesh::FEGenericBase< FEOutputType< T >::type >::print_dphi ( std::ostream &  os ) const

overridevirtualinherited

Prints the value of each shape function's derivative at each quadrature point.

Implements libMesh::FEAbstract.

Definition at line 526 of file fe_base.C.

{
  for (auto i : index_range(dphi))
    for (auto j : index_range(dphi[i]))
      os << " dphi[" << i << "][" << j << "]=" << dphi[i][j];
}

print_dual_d2phi()

void libMesh::FEGenericBase< FEOutputType< T >::type >::print_dual_d2phi ( std::ostream &  os ) const

overridevirtualinherited

Implements libMesh::FEAbstract.

Definition at line 536 of file fe_base.C.

{
  for (auto i : index_range(dual_d2phi))
    for (auto j : index_range(dual_d2phi[i]))
      os << " dual_d2phi[" << i << "][" << j << "]=" << dual_d2phi[i][j];
}

print_dual_dphi()

void libMesh::FEGenericBase< FEOutputType< T >::type >::print_dual_dphi ( std::ostream &  os ) const

overridevirtualinherited

Implements libMesh::FEAbstract.

Definition at line 527 of file fe_base.C.

{
  for (auto i : index_range(dphi))
    for (auto j : index_range(dphi[i]))
      os << " dual_dphi[" << i << "][" << j << "]=" << dual_dphi[i][j];
}

print_dual_phi()

void libMesh::FEGenericBase< FEOutputType< T >::type >::print_dual_phi ( std::ostream &  os ) const

overridevirtualinherited

Implements libMesh::FEAbstract.

Definition at line 520 of file fe_base.C.

{
  for (auto i : index_range(dual_phi))
    for (auto j : index_range(dual_phi[i]))
      os << " dual_phi[" << i << "][" << j << "]=" << dual_phi[i][j] << std::endl;
}

print_info() [1/2]

void libMesh::FEAbstract::print_info ( std::ostream &  os ) const

inherited

Prints all the relevant information about the current element.

Definition at line 859 of file fe_abstract.C.

{
  os << "phi[i][j]: Shape function i at quadrature pt. j" << std::endl;
  this->print_phi(os);
 
  os << "dphi[i][j]: Shape function i's gradient at quadrature pt. j" << std::endl;
  this->print_dphi(os);
 
  os << "XYZ locations of the quadrature pts." << std::endl;
  this->print_xyz(os);
 
  os << "Values of JxW at the quadrature pts." << std::endl;
  this->print_JxW(os);
}

References libMesh::FEAbstract::print_dphi(), libMesh::FEAbstract::print_JxW(), libMesh::FEAbstract::print_phi(), and libMesh::FEAbstract::print_xyz().

print_info() [2/2]

void libMesh::ReferenceCounter::print_info ( std::ostream &  out_stream = libMesh::out )

staticinherited

Prints the reference information, by default to libMesh::out.

Definition at line 81 of file reference_counter.C.

{
  if (_enable_print_counter)
    out_stream << ReferenceCounter::get_info();
}

References libMesh::ReferenceCounter::_enable_print_counter, and libMesh::ReferenceCounter::get_info().

Referenced by libMesh::LibMeshInit::~LibMeshInit().

print_JxW()

void libMesh::FEAbstract::print_JxW ( std::ostream &  os ) const

inherited

Prints the Jacobian times the weight for each quadrature point.

Definition at line 846 of file fe_abstract.C.

{
  this->_fe_map->print_JxW(os);
}

References libMesh::FEAbstract::_fe_map.

Referenced by libMesh::FEAbstract::print_info().

print_phi()

void libMesh::FEGenericBase< FEOutputType< T >::type >::print_phi ( std::ostream &  os ) const

overridevirtualinherited

Prints the value of each shape function at each quadrature point.

Implements libMesh::FEAbstract.

Definition at line 519 of file fe_base.C.

{
  for (auto i : index_range(phi))
    for (auto j : index_range(phi[i]))
      os << " phi[" << i << "][" << j << "]=" << phi[i][j] << std::endl;
}

print_xyz()

void libMesh::FEAbstract::print_xyz ( std::ostream &  os ) const

inherited

Prints the spatial location of each quadrature point (on the physical element).

Definition at line 853 of file fe_abstract.C.

{
  this->_fe_map->print_xyz(os);
}

References libMesh::FEAbstract::_fe_map.

Referenced by libMesh::FEAbstract::print_info().

reinit() [1/2]

void libMesh::FE< Dim, T >::reinit ( const Elem *  elem, const std::vector< Point > *const  pts = nullptr, const std::vector< Real > *const  weights = nullptr  )

overridevirtualinherited

This is at the core of this class.

Use this for each new element in the mesh. Reinitializes all the physical element-dependent data based on the current element elem. By default the shape functions and associated data are computed at the quadrature points specified by the quadrature rule qrule, but may be any points specified on the reference element specified in the optional argument pts.

Implements libMesh::FEAbstract.

Definition at line 564 of file fe.C.

{
  // We can be called with no element.  If we're evaluating SCALAR
  // dofs we'll still have work to do.
  // libmesh_assert(elem);
 
  // We're calculating now!  Time to determine what.
  this->determine_calculations();
 
  // Try to avoid calling init_shape_functions
  // even when shapes_need_reinit
  bool cached_elem_still_fits = false;
 
  // Most of the hard work happens when we have an actual element
  if (elem)
    {
      // Initialize the shape functions at the user-specified
      // points
      if (pts != nullptr)
        {
          // Set the type and p level for this element
          this->_elem = elem;
          this->_elem_type = elem->type();
          this->_elem_p_level = elem->p_level();
          this->_p_level = this->_add_p_level_in_reinit * elem->p_level();
 
          // Initialize the shape functions
          this->_fe_map->template init_reference_to_physical_map<Dim>
            (*pts, elem);
          this->init_shape_functions (*pts, elem);
 
          // The shape functions do not correspond to the qrule
          this->shapes_on_quadrature = false;
        }
 
      // If there are no user specified points, we use the
      // quadrature rule
 
      // update the type in accordance to the current cell
      // and reinit if the cell type has changed or (as in
      // the case of the hierarchics) the shape functions need
      // reinit, since they depend on the particular element shape
      else
        {
          libmesh_assert(this->qrule);
          this->qrule->init(*elem);
 
          if (this->qrule->shapes_need_reinit())
            this->shapes_on_quadrature = false;
 
          // We're not going to bother trying to cache nodal
          // points *and* weights for fancier mapping types.
          if (this->get_type() != elem->type()       ||
              (elem->runtime_topology() &&
               this->_elem != elem)                  ||
              this->_elem_p_level != elem->p_level() ||
              !this->shapes_on_quadrature            ||
              elem->mapping_type() != LAGRANGE_MAP)
            {
              // Set the type and p level for this element
              this->_elem = elem;
              this->_elem_type = elem->type();
              this->_elem_p_level = elem->p_level();
              this->_p_level = this->_add_p_level_in_reinit * elem->p_level();
 
              // Initialize the shape functions
              this->_fe_map->template init_reference_to_physical_map<Dim>
                (this->qrule->get_points(), elem);
              this->init_shape_functions (this->qrule->get_points(), elem);
            }
          else
            {
              this->_elem = elem;
 
              // Check if cached element's nodes, edge and face orientations still fit
              cached_elem_still_fits = this->matches_cache(elem);
 
              // Initialize the shape functions if needed
              if (this->shapes_need_reinit() && !cached_elem_still_fits)
                {
                  this->_fe_map->template init_reference_to_physical_map<Dim>
                    (this->qrule->get_points(), elem);
                  this->init_shape_functions (this->qrule->get_points(), elem);
                }
            }
 
          // Replace cached nodes, edge and face orientations if no longer fitting
          if (this->shapes_need_reinit() && !cached_elem_still_fits && *caching)
            this->cache(elem);
 
          // The shape functions correspond to the qrule
          this->shapes_on_quadrature = true;
        }
    }
  else // With no defined elem, so mapping or caching to
       // be done, and our "quadrature rule" is one point for nonlocal
       // (SCALAR) variables and zero points for local variables.
    {
      this->_elem = nullptr;
      this->_elem_type = INVALID_ELEM;
      this->_elem_p_level = 0;
      this->_p_level = 0;
 
      if (!pts)
        {
          if (T == SCALAR)
            {
              this->qrule->get_points() =
                std::vector<Point>(1,Point(0));
 
              this->qrule->get_weights() =
                std::vector<Real>(1,1);
            }
          else
            {
              this->qrule->get_points().clear();
              this->qrule->get_weights().clear();
            }
 
          this->init_shape_functions (this->qrule->get_points(), elem);
        }
      else
        this->init_shape_functions (*pts, elem);
    }
 
  // Compute the map for this element.
  if (pts != nullptr)
    {
      if (weights != nullptr)
        {
          this->_fe_map->compute_map (this->dim, *weights, elem, this->calculate_d2phi);
        }
      else
        {
          std::vector<Real> dummy_weights (pts->size(), 1.);
          this->_fe_map->compute_map (this->dim, dummy_weights, elem, this->calculate_d2phi);
        }
    }
  else
    {
      this->_fe_map->compute_map (this->dim, this->qrule->get_weights(), elem, this->calculate_d2phi);
    }
 
  // Compute the shape functions and the derivatives at all of the
  // quadrature points.
  if (!cached_elem_still_fits)
    {
      if (pts != nullptr)
        this->compute_shape_functions (elem,*pts);
      else
        this->compute_shape_functions(elem,this->qrule->get_points());
      if (this->calculate_dual)
      {
        if (T != LAGRANGE)
          nonlagrange_dual_warning();
        // Check if we need to calculate the dual coefficients based on the default QRule
        // We keep the default dual coeff calculation for the initial stage of the simulation
        // and in the middel of the simulation when a customized QRule is not provided.
        // This is used in MOOSE mortar-based contact. Currently, we re-compute dual_coeff
        // for all the elements on the mortar segment mesh by setting `calculate_default_dual_coeff' = false
        // in MOOSE (in `Assembly::reinitDual`) and use the customized QRule for calculating the dual shape coefficients
        // This is to be improved in the future
        if (elem && this->calculate_default_dual_coeff)
          this->reinit_default_dual_shape_coeffs(elem);
        // The dual shape functions relies on the customized shape functions
        // and the coefficient matrix, \p dual_coeff
        this->compute_dual_shape_functions();
      }
    }
}

reinit() [2/2]

void libMesh::FE< Dim, T >::reinit ( const Elem *  elem, const unsigned int  side, const Real  tolerance = TOLERANCE, const std::vector< Point > *const  pts = nullptr, const std::vector< Real > *const  weights = nullptr  )

overridevirtualinherited

Reinitializes all the physical element-dependent data based on the side of face.

The tolerance parameter is passed to the involved call to inverse_map(). By default the shape functions and associated data are computed at the quadrature points specified by the quadrature rule qrule, but may be any points specified on the reference side element specified in the optional argument pts.

Implements libMesh::FEAbstract.

Definition at line 591 of file fe_boundary.C.

{
  libmesh_assert(elem);
  libmesh_assert (this->qrule != nullptr || pts != nullptr);
  // We now do this for 1D elements!
  // libmesh_assert_not_equal_to (Dim, 1);
 
  // If we called this function redundantly (e.g. in an FEMContext
  // that is asked not to do any side calculations) then let's skip the
  // whole inverse_map process that calculates side points
  if (this->calculating_nothing())
    {
      this->calculations_started = true; // Ironic
      return;
    }
 
  // We're (possibly re-) calculating now!  FIXME - we currently
  // expect to be able to use side_map and JxW later, but we could
  // optimize further here.
  this->_fe_map->add_calculations();
  this->_fe_map->get_JxW();
  this->_fe_map->get_xyz();
  this->determine_calculations();
 
  // Build the side of interest
  const std::unique_ptr<const Elem> side(elem->build_side_ptr(s));
 
  // Find the max p_level to select
  // the right quadrature rule for side integration
  unsigned int side_p_level = elem->p_level();
  if (elem->neighbor_ptr(s) != nullptr)
    side_p_level = std::max(side_p_level, elem->neighbor_ptr(s)->p_level());
 
  // Initialize the shape functions at the user-specified
  // points
  if (pts != nullptr)
    {
      // The shape functions do not correspond to the qrule
      this->shapes_on_quadrature = false;
 
      // Initialize the face shape functions
      this->_fe_map->template init_face_shape_functions<Dim>(*pts, side.get());
 
      // Compute the Jacobian*Weight on the face for integration
      if (weights != nullptr)
        {
          this->_fe_map->compute_face_map (Dim, *weights, side.get());
        }
      else
        {
          std::vector<Real> dummy_weights (pts->size(), 1.);
          this->_fe_map->compute_face_map (Dim, dummy_weights, side.get());
        }
    }
  // If there are no user specified points, we use the
  // quadrature rule
  else
    {
      // initialize quadrature rule
      this->qrule->init(*side, side_p_level);
 
      if (this->qrule->shapes_need_reinit())
        this->shapes_on_quadrature = false;
 
      // FIXME - could this break if the same FE object was used
      // for both volume and face integrals? - RHS
      // We might not need to reinitialize the shape functions
      if ((this->get_type() != elem->type())      ||
          (elem->runtime_topology() &&
           this->_elem != elem)                   ||
          (side->type() != last_side)             ||
          (this->_elem_p_level != side_p_level)   ||
          this->shapes_need_reinit()              ||
          !this->shapes_on_quadrature)
        {
          // Set the element
          this->_elem = elem;
          this->_elem_type = elem->type();
 
          // Set the last_side
          last_side = side->type();
 
          // Set the last p level
          this->_p_level = this->_add_p_level_in_reinit * side_p_level;
 
          // Initialize the face shape functions
          this->_fe_map->template init_face_shape_functions<Dim>(this->qrule->get_points(),  side.get());
        }
      else
        this->_elem = elem;
 
      // Compute the Jacobian*Weight on the face for integration
      this->_fe_map->compute_face_map (Dim, this->qrule->get_weights(), side.get());
 
      // The shape functions correspond to the qrule
      this->shapes_on_quadrature = true;
    }
 
  // make a copy of the Jacobian for integration
  const std::vector<Real> JxW_int(this->_fe_map->get_JxW());
 
  // make a copy of shape on quadrature info
  bool shapes_on_quadrature_side = this->shapes_on_quadrature;
 
  // Find where the integration points are located on the
  // full element.
  const std::vector<Point> * ref_qp;
  if (pts != nullptr)
    ref_qp = pts;
  else
    ref_qp = &this->qrule->get_points();
 
  std::vector<Point> qp;
  this->side_map(elem, side.get(), s, *ref_qp, qp);
 
  // compute the shape function and derivative values
  // at the points qp
  this->reinit  (elem, &qp);
 
  this->shapes_on_quadrature = shapes_on_quadrature_side;
 
  this->_elem_p_level = side_p_level;
 
  // copy back old data
  this->_fe_map->get_JxW() = JxW_int;
}

reinit_default_dual_shape_coeffs()

void libMesh::FE< Dim, T >::reinit_default_dual_shape_coeffs ( const Elem *  elem )

overridevirtualinherited

This computes the default dual shape function coefficients.

The dual shape coefficients are utilized when calculating dual shape functions.

Reimplemented from libMesh::FEAbstract.

Definition at line 580 of file fe.C.

{
  libmesh_assert(elem);
 
  FEType default_fe_type(this->get_order(), T);
  QGauss default_qrule(elem->dim(), default_fe_type.default_quadrature_order());
  default_qrule.init(*elem);
  // In preparation of computing dual_coeff, we compute the default shape
  // function values and use these to compute the dual shape coefficients.
  // The TRUE dual_phi values are computed in compute_dual_shape_functions()
  this->reinit_dual_shape_coeffs(elem, default_qrule.get_points(), default_qrule.get_weights());
  // we do not compute default dual coeff many times as this can be expensive
  this->set_calculate_default_dual_coeff(false);
}

reinit_dual_shape_coeffs()

void libMesh::FE< Dim, T >::reinit_dual_shape_coeffs ( const Elem *  elem, const std::vector< Point > &  pts, const std::vector< Real > &  JxW  )

overridevirtualinherited

This re-computes the dual shape function coefficients.

The dual shape coefficients are utilized when calculating dual shape functions.

Reimplemented from libMesh::FEAbstract.

Definition at line 572 of file fe.C.

{
  // Set the type and p level for this element
  this->_elem = elem;
  this->_elem_type = elem->type();
  this->_elem_p_level = elem->p_level();
  this->_p_level = this->_add_p_level_in_reinit * elem->p_level();
 
  const unsigned int n_shapes =
    this->n_dofs(elem, this->get_order());
 
  std::vector<std::vector<OutputShape>> phi_vals;
  phi_vals.resize(n_shapes);
  for (const auto i : make_range(phi_vals.size()))
    phi_vals[i].resize(pts.size());
 
  all_shapes(elem, this->get_order(), pts, phi_vals);
  this->compute_dual_shape_coeffs(JxW, phi_vals);
}

request_dphi()

virtual void libMesh::FEGenericBase< FEOutputType< T >::type >::request_dphi ( ) const

inlineoverridevirtualinherited

request dphi calculations

Implements libMesh::FEAbstract.

Definition at line 238 of file fe_base.h.

  { get_dphi(); }

request_dual_dphi()

virtual void libMesh::FEGenericBase< FEOutputType< T >::type >::request_dual_dphi ( ) const

inlineoverridevirtualinherited

Implements libMesh::FEAbstract.

Definition at line 241 of file fe_base.h.

  { get_dual_dphi(); }

request_dual_phi()

virtual void libMesh::FEGenericBase< FEOutputType< T >::type >::request_dual_phi ( ) const

inlineoverridevirtualinherited

Implements libMesh::FEAbstract.

Definition at line 223 of file fe_base.h.

  { get_dual_phi(); }

request_phi()

virtual void libMesh::FEGenericBase< FEOutputType< T >::type >::request_phi ( ) const

inlineoverridevirtualinherited

request phi calculations

Implements libMesh::FEAbstract.

Definition at line 220 of file fe_base.h.

  { get_phi(); }

set_calculate_default_dual_coeff()

void libMesh::FEAbstract::set_calculate_default_dual_coeff ( const bool  val )

inlineinherited

set calculate_default_dual_coeff as needed

Definition at line 626 of file fe_abstract.h.

{calculate_default_dual_coeff = val; }

References libMesh::FEAbstract::calculate_default_dual_coeff.

set_calculate_dual()

void libMesh::FEAbstract::set_calculate_dual ( const bool  val )

inlineinherited

set calculate_dual as needed

Definition at line 621 of file fe_abstract.h.

{calculate_dual = val; }

References libMesh::FEAbstract::calculate_dual.

set_fe_order()

void libMesh::FEAbstract::set_fe_order ( int  new_order )

inlineinherited

Sets the base FE order of the finite element.

Definition at line 531 of file fe_abstract.h.

{ fe_type.order = new_order; }

References libMesh::FEAbstract::fe_type, and libMesh::FEType::order.

shape() [1/195]

Real libMesh::FE< 1, SIDE_HIERARCHIC >::shape ( const Elem *  , const Order  , const unsigned int  i, const Point &  p, const bool    )

inherited

Definition at line 155 of file fe_hierarchic_shape_1D.C.

{
  unsigned int right_side = p(0) > 0; // 0 false, 1 true
  return (right_side == i);
}

shape() [2/195]

Real libMesh::FE< 0, BERNSTEIN >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 46 of file fe_bernstein_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [3/195]

Real libMesh::FE< 0, CLOUGH >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 46 of file fe_clough_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [4/195]

Real libMesh::FE< 0, HERMITE >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 46 of file fe_hermite_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [5/195]

Real libMesh::FE< 0, HIERARCHIC >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 71 of file fe_hierarchic_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [6/195]

Real libMesh::FE< 0, L2_HIERARCHIC >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 84 of file fe_hierarchic_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [7/195]

Real libMesh::FE< 0, L2_LAGRANGE >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 56 of file fe_lagrange_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [8/195]

Real libMesh::FE< 0, LAGRANGE >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 68 of file fe_lagrange_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [9/195]

Real libMesh::FE< 0, MONOMIAL >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 46 of file fe_monomial_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [10/195]

Real libMesh::FE< 0, RATIONAL_BERNSTEIN >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 46 of file fe_rational_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [11/195]

Real libMesh::FE< 0, SZABAB >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 46 of file fe_szabab_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [12/195]

Real libMesh::FE< 0, XYZ >::shape ( const Elem *  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 46 of file fe_xyz_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [13/195]

Real libMesh::FE< 0, SIDE_HIERARCHIC >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 97 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No side variables in 0D!");
  return 1.;
}

shape() [14/195]

RealGradient libMesh::FE< 0, NEDELEC_ONE >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 460 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape() [15/195]

RealGradient libMesh::FE< 1, NEDELEC_ONE >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 487 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape() [16/195]

RealGradient libMesh::FE< 0, RAVIART_THOMAS >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 552 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape() [17/195]

RealGradient libMesh::FE< 0, L2_RAVIART_THOMAS >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 558 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape() [18/195]

RealGradient libMesh::FE< 1, RAVIART_THOMAS >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 601 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape() [19/195]

RealGradient libMesh::FE< 1, L2_RAVIART_THOMAS >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 607 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape() [20/195]

Real libMesh::FE< 0, SCALAR >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 43 of file fe_scalar_shape_0D.C.

{
  return 1.;
}

shape() [21/195]

Real libMesh::FE< 1, SCALAR >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 43 of file fe_scalar_shape_1D.C.

{
  return 1.;
}

shape() [22/195]

Real libMesh::FE< 2, SCALAR >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 43 of file fe_scalar_shape_2D.C.

{
  return 1.;
}

shape() [23/195]

Real libMesh::FE< 3, SCALAR >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 43 of file fe_scalar_shape_3D.C.

{
  return 1.;
}

shape() [24/195]

Real libMesh::FE< 3, SZABAB >::shape ( const Elem *  , const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 48 of file fe_szabab_shape_3D.C.

{
  libmesh_error_msg("Szabo-Babuska polynomials are not defined in 3D");
  return 0.;
}

shape() [25/195]

Real libMesh::FE< 1, HERMITE >::shape ( const Elem *  elem, const Order  libmesh_dbg_varorder, const unsigned int  i, const Point &  p, const bool  libmesh_dbg_varadd_p_level  )

inherited

Definition at line 182 of file fe_hermite_shape_1D.C.

{
  libmesh_assert(elem);
 
  // Coefficient naming: d(1)d(2n) is the coefficient of the
  // global shape function corresponding to value 1 in terms of the
  // local shape function corresponding to normal derivative 2
  Real d1xd1x, d2xd2x;
 
  hermite_compute_coefs(elem, d1xd1x, d2xd2x);
 
  const ElemType type = elem->type();
 
#ifndef NDEBUG
  const unsigned int totalorder =
    order + add_p_level * elem->p_level();
#endif
 
  switch (type)
    {
      // C1 functions on the C1 cubic edge
    case EDGE2:
    case EDGE3:
      {
        libmesh_assert_less (i, totalorder+1);
 
        switch (i)
          {
          case 0:
            return FEHermite<1>::hermite_raw_shape(0, p(0));
          case 1:
            return d1xd1x * FEHermite<1>::hermite_raw_shape(2, p(0));
          case 2:
            return FEHermite<1>::hermite_raw_shape(1, p(0));
          case 3:
            return d2xd2x * FEHermite<1>::hermite_raw_shape(3, p(0));
          default:
            return FEHermite<1>::hermite_raw_shape(i, p(0));
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
    }
}

shape() [26/195]

static OutputShape libMesh::FE< Dim, T >::shape ( const Elem *  elem, const Order  o, const unsigned int  i, const Point &  p, const bool  add_p_level = true  )

staticinherited

Returns

The value of the \( i^{th} \) shape function at point p. This method allows you to specify the dimension, element type, and order directly. This allows the method to be static.

On a p-refined element, o should be the base order of the element if add_p_level is left true, or can be the base order of the element if add_p_level is set to false.

shape() [27/195]

Real libMesh::FE< 2, SUBDIVISION >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Subdivision finite elements.

Template specialization prototypes are needed for calling from inside FESubdivision::init_shape_functions

shape() [28/195]

Real libMesh::FE< 1, BERNSTEIN >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 193 of file fe_bernstein_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,BERNSTEIN>::shape
    (elem->type(),
     order + add_p_level*elem->p_level(), i, p);
}

shape() [29/195]

Real libMesh::FE< 1, HIERARCHIC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 101 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_hierarchic_1D_shape(elem->type(), order + add_p_level*elem->p_level(), i, p);
}

shape() [30/195]

Real libMesh::FE< 1, L2_HIERARCHIC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 130 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_hierarchic_1D_shape(elem->type(), order + add_p_level*elem->p_level(), i, p);
}

shape() [31/195]

Real libMesh::FE< 2, HIERARCHIC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 173 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape<HIERARCHIC>(elem, order, i, p, add_p_level);
}

shape() [32/195]

Real libMesh::FE< 2, L2_HIERARCHIC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 196 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape<L2_HIERARCHIC>(elem, order, i, p, add_p_level);
}

shape() [33/195]

Real libMesh::FE< 2, SIDE_HIERARCHIC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 218 of file fe_hierarchic_shape_2D.C.

{
  libmesh_assert(elem);
  const ElemType type = elem->type();
 
  const Order totalorder = order + add_p_level*elem->p_level();
 
  const unsigned int dofs_per_side = totalorder+1u;
 
  switch (type)
    {
    case TRI6:
    case TRI7:
      {
        libmesh_assert_less(i, 3*dofs_per_side);
 
        // Flip odd degree of freedom values if necessary
        // to keep continuity on sides.  We'll flip xi/eta rather than
        // flipping phi, so that we can use this to handle the "nodal"
        // degrees of freedom too.
        Real f = 1.;
 
        const Real zeta1 = p(0);
        const Real zeta2 = p(1);
        const Real zeta0 = 1. - zeta1 - zeta2;
 
        if (zeta1 > zeta2 && zeta0 > zeta2) // side 0
          {
            if (i >= dofs_per_side)
              return 0;
 
            if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
              return 1;
 
            if ((i < 2 || i % 2) &&
                elem->positive_edge_orientation(0))
              f = -1;
 
            return FE<1,HIERARCHIC>::shape(EDGE3, totalorder, i, f*(zeta1-zeta0));
          }
        else if (zeta1 > zeta0 && zeta2 > zeta0) // side 1
          {
            if (i < dofs_per_side ||
                i >= 2*dofs_per_side)
              return 0;
 
            if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
              return 1;
 
            const unsigned int side_i = i - dofs_per_side;
 
            if ((side_i < 2 || side_i % 2) &&
                elem->positive_edge_orientation(1))
              f = -1;
 
            return FE<1,HIERARCHIC>::shape(EDGE3, totalorder, side_i, f*(zeta2-zeta1));
          }
        else // side 2
          {
            libmesh_assert (zeta2 >= zeta1 && zeta0 >= zeta1); // On a corner???
 
            if (i < 2*dofs_per_side)
              return 0;
 
            if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
              return 1;
 
            const unsigned int side_i = i - 2*dofs_per_side;
 
            if ((side_i < 2 || side_i % 2) &&
                elem->positive_edge_orientation(2))
              f = -1;
 
            return FE<1,HIERARCHIC>::shape(EDGE3, totalorder, side_i, f*(zeta0-zeta2));
          }
      }
    case QUAD8:
    case QUADSHELL8:
    case QUAD9:
    case QUADSHELL9:
      {
        libmesh_assert_less(i, 4*dofs_per_side);
 
        // Flip odd degree of freedom values if necessary
        // to keep continuity on sides.  We'll flip xi/eta rather than
        // flipping phi, so that we can use this to handle the "nodal"
        // degrees of freedom too.
        Real f = 1.;
 
        const Real xi = p(0), eta = p(1);
        if (eta < xi)
          {
            if (eta < -xi) // side 0
              {
                if (i >= dofs_per_side)
                  return 0;
 
                if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
                  return 1;
 
                if ((i < 2 || i % 2) &&
                    elem->positive_edge_orientation(0))
                  f = -1;
 
                return FE<1,HIERARCHIC>::shape(EDGE3, totalorder, i, f*xi);
              }
            else           // side 1
              {
                if (i < dofs_per_side ||
                    i >= 2*dofs_per_side)
                  return 0;
 
                if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
                  return 1;
 
                const unsigned int side_i = i - dofs_per_side;
 
                if ((side_i < 2 || side_i % 2) &&
                    elem->positive_edge_orientation(1))
                  f = -1;
 
                return FE<1,HIERARCHIC>::shape(EDGE3, totalorder, side_i, f*eta);
              }
          }
        else // xi < eta
          {
            if (eta > -xi)    // side 2
              {
                if (i < 2*dofs_per_side ||
                    i >= 3*dofs_per_side)
                  return 0;
 
                if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
                  return 1;
 
                const unsigned int side_i = i - 2*dofs_per_side;
 
                if ((side_i < 2 || side_i % 2) &&
                    !elem->positive_edge_orientation(2))
                  f = -1;
 
                return FE<1,HIERARCHIC>::shape(EDGE3, totalorder, side_i, f*xi);
              }
            else           // side 3
              {
                if (i < 3*dofs_per_side)
                  return 0;
 
                if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
                  return 1;
 
                const unsigned int side_i = i - 3*dofs_per_side;
 
                if ((side_i < 2 || side_i % 2) &&
                    !elem->positive_edge_orientation(3))
                  f = -1;
 
                return FE<1,HIERARCHIC>::shape(EDGE3, totalorder, side_i, f*eta);
              }
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(elem->type()));
    }
  return 0;
}

shape() [34/195]

Real libMesh::FE< 3, HIERARCHIC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1201 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape<HIERARCHIC>(elem, order, i, p, add_p_level);
}

shape() [35/195]

Real libMesh::FE< 3, L2_HIERARCHIC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1225 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape<L2_HIERARCHIC>(elem, order, i, p, add_p_level);
}

shape() [36/195]

Real libMesh::FE< 3, SIDE_HIERARCHIC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1248 of file fe_hierarchic_shape_3D.C.

{
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
  const ElemType type = elem->type();
 
  const Order totalorder = order + add_p_level*elem->p_level();
 
  switch (type)
    {
    case HEX27:
      {
        const unsigned int dofs_per_side = (totalorder+1u)*(totalorder+1u);
        libmesh_assert_less(i, 6*dofs_per_side);
 
        const unsigned int sidenum = cube_side(p);
        if (sidenum > 5)
          return std::numeric_limits<Real>::quiet_NaN();
 
        const unsigned int dof_offset = sidenum * dofs_per_side;
 
        if (i < dof_offset) // i is on a previous side
          return 0;
 
        if (i >= dof_offset + dofs_per_side) // i is on a later side
          return 0;
 
        if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
          return 1;
 
        unsigned int side_i = i - dof_offset;
 
        std::unique_ptr<const Elem> side = elem->build_side_ptr(sidenum);
 
        Point sidep = cube_side_point(sidenum, p);
 
        cube_remap(side_i, *side, totalorder, sidep);
 
        return FE<2,HIERARCHIC>::shape(side.get(), order, side_i, sidep, add_p_level);
      }
 
    case TET14:
      {
        const unsigned int dofs_per_side = (totalorder+1u)*(totalorder+2u)/2u;
        libmesh_assert_less(i, 4*dofs_per_side);
 
        const Real zeta[4] = { Real(1.) - p(0) - p(1) - p(2), p(0), p(1), p(2) };
 
        unsigned int face_num = 0;
        if (zeta[0] > zeta[3] &&
            zeta[1] > zeta[3] &&
            zeta[2] > zeta[3])
          {
            face_num = 0;
          }
        else if (zeta[0] > zeta[2] &&
                 zeta[1] > zeta[2] &&
                 zeta[3] > zeta[2])
          {
            face_num = 1;
          }
        else if (zeta[1] > zeta[0] &&
                 zeta[2] > zeta[0] &&
                 zeta[3] > zeta[0])
          {
            face_num = 2;
          }
        else
          {
            // We'd better not be right between two faces
            libmesh_assert (zeta[0] > zeta[1] &&
                            zeta[2] > zeta[1] &&
                            zeta[3] > zeta[1]);
            face_num = 3;
          }
 
        if (i < face_num * dofs_per_side ||
            i >= (face_num+1) * dofs_per_side)
          return 0;
 
        if (totalorder == 0)
          return 1;
 
        const std::array<unsigned int, 3> face_vertex =
          oriented_tet_nodes(*elem, face_num);
 
        // We only need a Tri3 to evaluate L2_HIERARCHIC on the affine
        // master element
        Tri3 side;
 
        // We pinky swear not to modify these nodes
        Elem & e = const_cast<Elem &>(*elem);
        side.set_node(0, e.node_ptr(face_vertex[0]));
        side.set_node(1, e.node_ptr(face_vertex[1]));
        side.set_node(2, e.node_ptr(face_vertex[2]));
 
        const unsigned int basisnum = i - face_num*dofs_per_side;
 
        Point sidep {zeta[face_vertex[1]], zeta[face_vertex[2]]};
 
        return FE<2,L2_HIERARCHIC>::shape(&side, totalorder,
                                          basisnum, sidep, false);
      }
 
    case PRISM20:
    case PRISM21:
      {
        const unsigned int dofs_per_quad = (totalorder+1u)*(totalorder+1u);
        const unsigned int dofs_per_tri = (totalorder+1u)*(totalorder+2u)/2u;
        libmesh_assert_less(i, 3*dofs_per_quad + 2*dofs_per_tri);
 
        // We only need a Tri3 or Quad4 to evaluate L2_HIERARCHIC on
        // the affine master element
        Tri3 tri;
        Quad4 quad;
        Elem * side = &quad;
        unsigned int dofs_on_side = dofs_per_quad;
 
        // We pinky swear not to modify the nodes we'll point to
        Elem & e = const_cast<Elem &>(*elem);
 
        Point sidep;
 
        // Face number calculation is tricky - the ordering of side
        // nodes on Prisms does *not* match the ordering of sides!
        // (the mid-triangle side nodes were added "later")
        // Here face_num will be the numbering that matches the side
        // number, but i_offset will have to consider the nodal
        // ordering.
        unsigned int face_num = 0;
        unsigned int i_offset = 0;
 
        // Triangular coordinates
        const Real zeta[3] = { Real(1.) - p(0) - p(1), p(0), p(1) };
 
        // Closeness to midplane
        const Real zmid = 1 - std::abs(p(2));
 
        if (zeta[1] > zeta[2] && zeta[0] > zeta[2] &&
            zmid > 3*zeta[2]) // face 1, quad
          {
            face_num = 1;
            i_offset = 0;
          }
        else if (zeta[1] > zeta[0] && zeta[2] > zeta[0] &&
                 zmid > 3*zeta[0]) // face 2, quad
          {
            face_num = 2;
            i_offset = dofs_per_quad;
          }
        else if (zeta[0] > zeta[1] && zeta[2] > zeta[1] &&
                 zmid > 3*zeta[1]) // face 3, quad
          {
            face_num = 3;
            i_offset = 2*dofs_per_quad;
          }
        else if (p(2) + 1 < 3*zeta[0] &&
                 p(2) + 1 < 3*zeta[1] &&
                 p(2) + 1 < 3*zeta[2]) // face 0, tri
          {
            face_num = 0;
            i_offset = 3*dofs_per_quad;
            dofs_on_side = dofs_per_tri;
            side = &tri;
          }
        else if (1 - p(2) < 3*zeta[0] &&
                 1 - p(2) < 3*zeta[1] &&
                 1 - p(2) < 3*zeta[2]) // face 4, tri
          {
            face_num = 4;
            i_offset = dofs_per_tri + 3*dofs_per_quad;
            dofs_on_side = dofs_per_tri;
            side = &tri;
          }
        else
          {
            libmesh_error_msg("Evaluating SIDE_HIERARCHIC right between two Prism faces?");
          }
 
        if (i < i_offset ||
            i >= i_offset + dofs_on_side)
          return 0;
 
        if (totalorder == 0)
          return 1;
 
        const std::array<unsigned int, 4> face_vertex =
          oriented_prism_nodes(*elem, face_num);
 
        side->set_node(0, e.node_ptr(face_vertex[0]));
        side->set_node(1, e.node_ptr(face_vertex[1]));
        side->set_node(2, e.node_ptr(face_vertex[2]));
        if (face_vertex[3] < 21)
          side->set_node(3, e.node_ptr(face_vertex[3]));
 
        if (face_num == 0 || face_num == 4)
          sidep = {zeta[face_vertex[1]%3], zeta[face_vertex[2]%3]};
        else
          {
            // Transform a coordinate from the master prism to the
            // master quad, based on two vertex indices defining the
            // coordinate's direction
            auto coord_val = [p](int v1, int v2){
              if (v2-v1 == 3)
                return p(2);
              else if (v2-v1 == -3)
                return -p(2);
              else if (v1%3 == 0 && v2%3 == 1)
                return 2*p(0)-1;
              else if (v2%3 == 0 && v1%3 == 1)
                return 1-2*p(0);
              else if (v1%3 == 1 && v2%3 == 2)
                return p(1)-p(0);
              else if (v2%3 == 1 && v1%3 == 2)
                return p(0)-p(1);
              else if (v1%3 == 2 && v2%3 == 0)
                return 1-2*p(1);
              else if (v2%3 == 2 && v1%3 == 0)
                return 2*p(1)-1;
              else
                libmesh_error();
            };
 
            sidep = {coord_val(face_vertex[0], face_vertex[1]),
                     coord_val(face_vertex[0], face_vertex[3])};
          }
 
        const unsigned int basisnum = i - i_offset;
 
        return FE<2,L2_HIERARCHIC>::shape(side, totalorder,
                                          basisnum, sidep, false);
      }
 
 
    default:
      libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, p, add_p_level);
  libmesh_not_implemented();
#endif
}

shape() [37/195]

RealGradient libMesh::FE< 0, HIERARCHIC_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 418 of file fe_hierarchic_vec.C.

{
  const Real value = FE<0,HIERARCHIC>::shape(elem, order, i, p, add_p_level);
  return libMesh::RealGradient( value );
}

shape() [38/195]

RealGradient libMesh::FE< 0, L2_HIERARCHIC_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 447 of file fe_hierarchic_vec.C.

{
  return FE<0,HIERARCHIC_VEC>::shape(elem, order, i, p, add_p_level);
}

shape() [39/195]

RealGradient libMesh::FE< 1, HIERARCHIC_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 475 of file fe_hierarchic_vec.C.

{
  Real value = FE<1,HIERARCHIC>::shape(elem, order, i, p, add_p_level);
  return libMesh::RealGradient( value );
}

shape() [40/195]

RealGradient libMesh::FE< 1, L2_HIERARCHIC_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 503 of file fe_hierarchic_vec.C.

{
  return FE<1,HIERARCHIC_VEC>::shape(elem, order, i, p, add_p_level);
}

shape() [41/195]

RealGradient libMesh::FE< 2, HIERARCHIC_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 531 of file fe_hierarchic_vec.C.

{
  const Real value = FE<2,HIERARCHIC>::shape(elem, order, i/2, p, add_p_level);
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape() [42/195]

RealGradient libMesh::FE< 2, L2_HIERARCHIC_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 601 of file fe_hierarchic_vec.C.

{
  return FE<2,HIERARCHIC_VEC>::shape(elem, order, i, p, add_p_level);
}

shape() [43/195]

RealGradient libMesh::FE< 3, HIERARCHIC_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 628 of file fe_hierarchic_vec.C.

{
  const Real value = FE<3,HIERARCHIC>::shape(elem, order, i/3, p, add_p_level);
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape() [44/195]

RealGradient libMesh::FE< 3, L2_HIERARCHIC_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 709 of file fe_hierarchic_vec.C.

{
  return FE<3,HIERARCHIC_VEC>::shape(elem, order, i, p, add_p_level);
}

shape() [45/195]

Real libMesh::FE< 1, LAGRANGE >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 53 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_lagrange_1D_shape(order + add_p_level*elem->p_level(), i, p(0));
}

shape() [46/195]

Real libMesh::FE< 1, L2_LAGRANGE >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 78 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_lagrange_1D_shape(order + add_p_level*elem->p_level(), i, p(0));
}

shape() [47/195]

Real libMesh::FE< 2, LAGRANGE >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 94 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape functions
  return fe_lagrange_2D_shape<LAGRANGE>(elem->type(), elem, order + add_p_level*elem->p_level(), i, p);
}

shape() [48/195]

Real libMesh::FE< 2, L2_LAGRANGE >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 109 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape functions
  return fe_lagrange_2D_shape<L2_LAGRANGE>(elem->type(), elem, order + add_p_level*elem->p_level(), i, p);
}

shape() [49/195]

Real libMesh::FE< 3, LAGRANGE >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 441 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape functions
  return fe_lagrange_3D_shape<LAGRANGE>(elem->type(), order + add_p_level*elem->p_level(), elem, i, p);
}

shape() [50/195]

Real libMesh::FE< 3, L2_LAGRANGE >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 456 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape functions
  return fe_lagrange_3D_shape<L2_LAGRANGE>(elem->type(), order + add_p_level*elem->p_level(), elem, i, p);
}

shape() [51/195]

RealGradient libMesh::FE< 0, LAGRANGE_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 958 of file fe_lagrange_vec.C.

{
  Real value = FE<0,LAGRANGE>::shape( elem->type(), order + add_p_level*elem->p_level(), i, p);
  return libMesh::RealGradient( value );
}

shape() [52/195]

RealGradient libMesh::FE< 0, L2_LAGRANGE_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 987 of file fe_lagrange_vec.C.

{
  return FE<0,LAGRANGE_VEC>::shape(elem, order, i, p, add_p_level);
}

shape() [53/195]

RealGradient libMesh::FE< 1, LAGRANGE_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1014 of file fe_lagrange_vec.C.

{
  Real value = FE<1,LAGRANGE>::shape( elem->type(), order + add_p_level*elem->p_level(), i, p);
  return libMesh::RealGradient( value );
}

shape() [54/195]

RealGradient libMesh::FE< 1, L2_LAGRANGE_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1042 of file fe_lagrange_vec.C.

{
  return FE<1,LAGRANGE_VEC>::shape(elem, order, i, p, add_p_level);
}

shape() [55/195]

RealGradient libMesh::FE< 2, LAGRANGE_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1069 of file fe_lagrange_vec.C.

{
  Real value = FE<2,LAGRANGE>::shape( elem->type(), order + add_p_level*elem->p_level(), i/2, p );
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape() [56/195]

RealGradient libMesh::FE< 2, L2_LAGRANGE_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1139 of file fe_lagrange_vec.C.

{
  return FE<2,LAGRANGE_VEC>::shape(elem, order, i, p, add_p_level);
}

shape() [57/195]

RealGradient libMesh::FE< 3, LAGRANGE_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1166 of file fe_lagrange_vec.C.

{
  Real value = FE<3,LAGRANGE>::shape( elem->type(), order + add_p_level*elem->p_level(), i/3, p );
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape() [58/195]

RealGradient libMesh::FE< 3, L2_LAGRANGE_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1246 of file fe_lagrange_vec.C.

{
  return FE<3,LAGRANGE_VEC>::shape(elem, order, i, p, add_p_level);
}

shape() [59/195]

Real libMesh::FE< 1, MONOMIAL >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 72 of file fe_monomial_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,MONOMIAL>::shape(elem->type(), order + add_p_level*elem->p_level(), i, p);
}

shape() [60/195]

Real libMesh::FE< 2, MONOMIAL >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 122 of file fe_monomial_shape_2D.C.

{
  libmesh_assert(elem);
 
  // by default call the orientation-independent shape functions
  return FE<2,MONOMIAL>::shape(elem->type(), order + add_p_level*elem->p_level(), i, p);
}

shape() [61/195]

Real libMesh::FE< 3, MONOMIAL >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 190 of file fe_monomial_shape_3D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape functions
  return FE<3,MONOMIAL>::shape(elem->type(), order + add_p_level*elem->p_level(), i, p);
}

shape() [62/195]

RealVectorValue libMesh::FE< 0, MONOMIAL_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 393 of file fe_monomial_vec.C.

{
  Real value =
      FE<0, MONOMIAL>::shape(elem->type(), order + add_p_level*elem->p_level(), i, p);
  return libMesh::RealVectorValue(value);
}

shape() [63/195]

RealVectorValue libMesh::FE< 1, MONOMIAL_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 438 of file fe_monomial_vec.C.

{
  Real value =
      FE<1, MONOMIAL>::shape(elem->type(), order + add_p_level*elem->p_level(), i, p);
  return libMesh::RealVectorValue(value);
}

shape() [64/195]

RealVectorValue libMesh::FE< 2, MONOMIAL_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 482 of file fe_monomial_vec.C.

{
  Real value =
      FE<2, MONOMIAL>::shape(elem->type(), order + add_p_level*elem->p_level(), i / 2, p);
 
  switch (i % 2)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape() [65/195]

RealVectorValue libMesh::FE< 3, MONOMIAL_VEC >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 568 of file fe_monomial_vec.C.

{
  Real value =
      FE<3, MONOMIAL>::shape(elem->type(), order + add_p_level*elem->p_level(), i / 3, p);
 
  switch (i % 3)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    case 2:
      return libMesh::RealVectorValue(Real(0), Real(0), value);
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape() [66/195]

RealGradient libMesh::FE< 2, NEDELEC_ONE >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 32 of file fe_nedelec_one_shape_2D.C.

{
#if LIBMESH_DIM > 1
  libmesh_assert(elem);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = i >= totalorder * elem->n_edges() || elem->positive_edge_orientation(i / totalorder) ? 1 : -1;
  const unsigned int ii = sign > 0 ? i : (i / totalorder * 2 + 1) * totalorder - 1 - i;
 
  const Real xi  = p(0);
  const Real eta = p(1);
 
  switch (totalorder)
    {
      // linear Nedelec (first kind) shape functions
    case FIRST:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              // Even with a loose inverse_map tolerance we ought to
              // be nearly on the element interior in master
              // coordinates
              libmesh_assert_less_equal ( std::fabs(xi), 1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(eta), 1.0+10*TOLERANCE );
 
              switch(ii)
                {
                case 0:
                  return sign * RealGradient( -0.25*(1.0-eta), 0.0 );
                case 1:
                  return sign * RealGradient( 0.0, -0.25*(1.0+xi) );
                case 2:
                  return sign * RealGradient( 0.25*(1.0+eta), 0.0 );
                case 3:
                  return sign * RealGradient( 0.0, -0.25*(xi-1.0) );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch(ii)
                {
                case 0:
                  return sign * RealGradient( -1.0+eta, -xi );
                case 1:
                  return sign * RealGradient( eta, -xi );
                case 2:
                  return sign * RealGradient( eta, -xi+1.0 );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
 
      // quadratic Nedelec (first kind) shape functions
    case SECOND:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              // Even with a loose inverse_map tolerance we ought to
              // be nearly on the element interior in master
              // coordinates
              libmesh_assert_less_equal ( std::fabs(xi), 1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(eta), 1.0+10*TOLERANCE );
 
              const Real x = 0.5 * (xi + 1.0);
              const Real y = 0.5 * (eta + 1.0);
 
              switch(ii)
                {
                case 0:
                  return sign * RealGradient( 0.5*(-18.0*x*y*y+24.0*x*y-6.0*x+12.0*y*y-16.0*y+4.0), 0.0 );
                case 1:
                  return sign * RealGradient( 0.5*( 18.0*x*y*y-24.0*x*y+6.0*x-6.0*y*y+8.0*y-2.0), 0.0 );
                case 2:
                  return sign * RealGradient( 0.0, x*(-9.0*x*y+6.0*x+6.0*y-4.0) );
                case 3:
                  return sign * RealGradient( 0.0, x*( 9.0*x*y-3.0*x-6.0*y+2.0) );
                case 4:
                  return sign * RealGradient( y*(-9.0*x*y+6.0*x+3.0*y-2.0), 0.0 );
                case 5:
                  return sign * RealGradient( y*( 9.0*x*y-6.0*x-6.0*y+4.0), 0.0 );
                case 6:
                  return sign * RealGradient( 0.0, 0.5*(-18.0*x*x*y+6.0*x*x+24.0*x*y-8.0*x-6.0*y+2.0) );
                case 7:
                  return sign * RealGradient( 0.0, 0.5*( 18.0*x*x*y-12.0*x*x-24.0*x*y+16.0*x+6.0*y-4.0) );
                case 8:
                  return RealGradient( 0.0, 3.0*x*(3*x*y-2.0*x-3.0*y+2.0) );
                case 9:
                  return RealGradient( 3.0*y*(-3.0*x*y+3.0*x+2.0*y-2.0), 0.0 );
                case 10:
                  return RealGradient( 3.0*y*(3.0*x*y-3.0*x-y+1.0), 0.0 );
                case 11:
                  return RealGradient( 0.0, 3.0*x*(-3.0*x*y+x+3.0*y-1.0) );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch(ii)
                {
                case 0:
                  return sign * RealGradient( 8.0*xi*eta-6.0*xi+8.0*eta*eta-12.0*eta+4.0, 2.0*xi*(-4.0*xi-4.0*eta+3.0) );
                case 1:
                  return sign * RealGradient( -8.0*xi*eta+6.0*xi+2.0*eta-2.0, 4.0*xi*(2.0*xi-1.0) );
                case 2:
                  return sign * RealGradient( 2.0*eta*(1.0-4.0*xi), 4.0*xi*(2.0*xi-1.0) );
                case 3:
                  return sign * RealGradient( 4.0*eta*(1.0-2.0*eta), 2.0*xi*(4.0*eta-1.0) );
                case 4:
                  return sign * RealGradient( 4.0*eta*(1.0-2.0*eta), 8.0*xi*eta-2.0*xi-6.0*eta+2.0 );
                case 5:
                  return sign * RealGradient( 2.0*eta*(4.0*xi+4*eta-3.0), -8.0*xi*xi-8.0*xi*eta+12.0*xi+6.0*eta-4.0 );
                case 6:
                  return RealGradient( 8.0*eta*(-xi-2.0*eta+2.0), 8.0*xi*(xi+2.0*eta-1.0) );
                case 7:
                  return RealGradient( 8.0*eta*(2.0*xi+eta-1.0), 8.0*xi*(-2.0*xi-eta+2.0) );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
 
      // cubic Nedelec (first kind) shape functions
    case THIRD:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch(ii)
                {
                case 0:
                  return sign * RealGradient(-81.*eta/4. - 9.*xi + 162.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 135.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 324.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 99./4. + 81.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 270.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 15.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 45.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                case 1:
                  return sign * RealGradient(27.*eta/8. + 15.*xi/4. - 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 135.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. + 135.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 75.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 51./8. - 27.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 15.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 75.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 15.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2., 0.);
                case 2:
                  return sign * RealGradient(-27.*eta/4. - 6.*xi + 108.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 135.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 216.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 45./4. + 27.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 270.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 15.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 15.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                case 3:
                  return sign * RealGradient(0., 27.*xi/4. - 54.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 216.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 45.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 27./4. - 180.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 54.*(xi + 1.)*(xi + 1.)/(2.*2.) + 45.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 4:
                  return sign * RealGradient(0., -9.*xi/8. + 45.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 90.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 75.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 45.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 9./8. + 90.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 75.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 9.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 15.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2.);
                case 5:
                  return sign * RealGradient(0., 9.*xi/4. - 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 144.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 45.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 9./4. - 180.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 18.*(xi + 1.)*(xi + 1.)/(2.*2.) + 15.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 6:
                  return sign * RealGradient(-9.*eta/4. + 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 45.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 144.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 9./4. + 18.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 180.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 15.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                case 7:
                  return sign * RealGradient(9.*eta/8. - 45.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 45.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. + 90.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 75.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 9./8. - 9.*(eta + 1.)*(eta + 1.)/(2.*2.) - 90.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 75.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 15.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2., 0.);
                case 8:
                  return sign * RealGradient(-27.*eta/4. + 54.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 45.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 216.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 27./4. + 54.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 180.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 45.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                case 9:
                  return sign * RealGradient(0., 6.*eta + 27.*xi/4. - 108.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 216.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 135.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 45./4. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.) - 270.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 27.*(xi + 1.)*(xi + 1.)/(2.*2.) + 15.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 10:
                  return sign * RealGradient(0., -15.*eta/4. - 27.*xi/8. + 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 135.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 75.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 135.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 51./8. + 15.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 75.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 27.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 15.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2.);
                case 11:
                  return sign * RealGradient(0., 9.*eta + 81.*xi/4. - 162.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 324.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 135.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 99./4. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.) - 270.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 81.*(xi + 1.)*(xi + 1.)/(2.*2.) + 45.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 12:
                  return RealGradient(0., 18.*xi - 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 324.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 18. - 270.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 81.*(xi + 1.)*(xi + 1.)/(2.*2.) + 45.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 13:
                  return RealGradient(0., -9.*xi/2. + 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 216.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 30.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 9./2. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 54.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 45.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                case 14:
                  return RealGradient(-18.*eta + 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 324.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 18. + 81.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 270.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 45.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                case 15:
                  return RealGradient(9.*eta/2. - 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 30.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 216.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 9./2. - 54.*(eta + 1.)*(eta + 1.)/(2.*2.) - 180.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 45.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                case 16:
                  return RealGradient(-6.*eta + 96.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 216.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 6. + 27.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 270.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 15.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                case 17:
                  return RealGradient(3.*eta/2. - 24.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 30.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 144.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 120.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3./2. - 18.*(eta + 1.)*(eta + 1.)/(2.*2.) - 180.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 15.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                case 18:
                  return RealGradient(0., 6.*xi - 96.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 216.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 6. - 270.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 27.*(xi + 1.)*(xi + 1.)/(2.*2.) + 15.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 19:
                  return RealGradient(0., -3.*xi/2. + 24.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 144.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 120.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 30.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 3./2. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 18.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 15.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                case 20:
                  return RealGradient(2.*eta + 2. - 9.*(eta + 1.)*(eta + 1.)/(2.*2.) + 5.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                case 21:
                  return RealGradient(0., 2.*xi + 2. - 9.*(xi + 1.)*(xi + 1.)/(2.*2.) + 5.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 22:
                  return RealGradient(0., -xi/2. - 1./2. + 6.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 5.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                case 23:
                  return RealGradient(-eta/2. - 1./2. + 6.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 5.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch(ii)
                {
                case 0:
                  return sign * RealGradient(120.*eta*xi - 54.*eta - 45.*eta*xi*xi - 36.*xi - 90.*xi*eta*eta + 9. + 90.*(eta*eta) + 30.*(xi*xi) - 45.*eta*eta*eta, -60.*eta*xi + 90.*eta*(xi*xi) + 18.*xi + 45.*xi*(eta*eta) - 60.*xi*xi + 45.*(xi*xi*xi));
                case 1:
                  return sign * RealGradient(-75.*eta*xi/2. - 9.*eta/4. + 45.*eta*(xi*xi)/2. + 15.*xi + 45.*xi*(eta*eta)/2. - 3./2. + 15.*(eta*eta) - 15.*xi*xi - 45.*eta*eta*eta/4., -45.*eta*xi*xi/2. - 21.*xi/4. + 45.*xi*(eta*eta)/4. + 105.*(xi*xi)/4. - 45.*xi*xi*xi/2.);
                case 2:
                  return sign * RealGradient(30.*eta*xi - 3.*eta - 45.*eta*xi*xi - 24.*xi + 3. + 30.*(xi*xi), 9.*xi - 45.*xi*xi + 45.*(xi*xi*xi));
                case 3:
                  return sign * RealGradient(30.*eta*xi - 3.*eta - 45.*eta*xi*xi, 9.*xi - 45.*xi*xi + 45.*(xi*xi*xi));
                case 4:
                  return sign * RealGradient(45.*eta*xi/2. - 6.*eta - 45.*eta*xi*xi/4. - 45.*xi*eta*eta + 75.*(eta*eta)/4. - 45.*eta*eta*eta/4., -45.*eta*xi/2. + 45.*eta*(xi*xi) + 6.*xi + 45.*xi*(eta*eta)/4. - 75.*xi*xi/4. + 45.*(xi*xi*xi)/4.);
                case 5:
                  return sign * RealGradient(-9.*eta + 45.*(eta*eta) - 45.*eta*eta*eta, -30.*eta*xi + 3.*xi + 45.*xi*(eta*eta));
                case 6:
                  return sign * RealGradient(-9.*eta + 45.*(eta*eta) - 45.*eta*eta*eta, -30.*eta*xi + 24.*eta + 3.*xi + 45.*xi*(eta*eta) - 3. - 30.*eta*eta);
                case 7:
                  return sign * RealGradient(21.*eta/4. - 45.*eta*xi*xi/4. + 45.*xi*(eta*eta)/2. - 105.*eta*eta/4. + 45.*(eta*eta*eta)/2., 75.*eta*xi/2. - 15.*eta - 45.*eta*xi*xi/2. + 9.*xi/4. - 45.*xi*eta*eta/2. + 3./2. + 15.*(eta*eta) - 15.*xi*xi + 45.*(xi*xi*xi)/4.);
                case 8:
                  return sign * RealGradient(60.*eta*xi - 18.*eta - 45.*eta*xi*xi - 90.*xi*eta*eta + 60.*(eta*eta) - 45.*eta*eta*eta, -120.*eta*xi + 36.*eta + 90.*eta*(xi*xi) + 54.*xi + 45.*xi*(eta*eta) - 9. - 30.*eta*eta - 90.*xi*xi + 45.*(xi*xi*xi));
                case 9:
                  return RealGradient(-300.*eta*xi + 180.*eta + 90.*eta*(xi*xi) + 360.*xi*(eta*eta) - 450.*eta*eta + 270.*(eta*eta*eta), 300.*eta*xi - 360.*eta*xi*xi - 60.*xi - 270.*xi*eta*eta + 150.*(xi*xi) - 90.*xi*xi*xi);
                case 10:
                  return RealGradient(300.*eta*xi - 60.*eta - 270.*eta*xi*xi - 360.*xi*eta*eta + 150.*(eta*eta) - 90.*eta*eta*eta, -300.*eta*xi + 360.*eta*(xi*xi) + 180.*xi + 90.*xi*(eta*eta) - 450.*xi*xi + 270.*(xi*xi*xi));
                case 11:
                  return RealGradient(360.*eta*xi - 60.*eta - 180.*eta*xi*xi - 360.*xi*eta*eta + 60.*(eta*eta), -120.*eta*xi + 360.*eta*(xi*xi) + 60.*xi - 240.*xi*xi + 180.*(xi*xi*xi));
                case 12:
                  return RealGradient(-240.*eta*xi + 30.*eta + 270.*eta*(xi*xi) + 180.*xi*(eta*eta) - 30.*eta*eta, 60.*eta*xi - 180.*eta*xi*xi - 90.*xi + 360.*(xi*xi) - 270.*xi*xi*xi);
                case 13:
                  return RealGradient(60.*eta*xi - 90.*eta - 180.*xi*eta*eta + 360.*(eta*eta) - 270.*eta*eta*eta, -240.*eta*xi + 180.*eta*(xi*xi) + 30.*xi + 270.*xi*(eta*eta) - 30.*xi*xi);
                case 14:
                  return RealGradient(-120.*eta*xi + 60.*eta + 360.*xi*(eta*eta) - 240.*eta*eta + 180.*(eta*eta*eta), 360.*eta*xi - 360.*eta*xi*xi - 60.*xi - 180.*xi*eta*eta + 60.*(xi*xi));
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          } // end switch (type)
      } // end case THIRD
 
      // quartic Nedelec (first kind) shape functions
    case FOURTH:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch(ii)
                {
                case 0:
                  return sign * RealGradient(-64.*eta - 30.*xi + 960.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1920.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 1120.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 4800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2100.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 86. + 480.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 7200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 120.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 9600.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 640.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 5600.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 70.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 2450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 280.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                case 1:
                  return sign * RealGradient(272.*eta/27. + 95.*xi/9. - 3040.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. + 6880.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 12320.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. + 3800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. - 15200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 6650.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9. + 523./27. - 680.*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 8600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 15400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 430.*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 34400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 15050.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9. + 2720.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/27. - 61600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. + 770.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. + 26950.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/27. - 1190.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/27., 0.);
                case 2:
                  return sign * RealGradient(-128.*eta/27. - 50.*xi/9. + 1600.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. - 5440.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 12320.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. - 2000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. + 8000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 3500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9. - 262./27. + 320.*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 6800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 15400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 340.*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 27200.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 11900.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9. - 1280.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/27. + 61600.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. - 770.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. - 26950.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/27. + 560.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/27., 0.);
                case 3:
                  return sign * RealGradient(16.*eta + 15.*xi - 480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1440.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 1050.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 29. - 120.*(eta + 1.)*(eta + 1.)/(2.*2.) - 5400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 4200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 90.*(xi + 1.)*(xi + 1.)/(2.*2.) + 7200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 160.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 70.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 2450.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 70.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                case 4:
                  return sign * RealGradient(0., -16.*xi + 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 3600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2100.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 480.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 280.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 16. + 3600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 240.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2100.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2450.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 480.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 280.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                case 5:
                  return sign * RealGradient(0., 68.*xi/27. - 760.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. + 1900.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 3800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/3. + 6650.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9. + 1720.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/9. - 3080.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/27. + 68./27. - 4300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 8600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/3. - 15050.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9. - 340.*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 7700.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 15400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 26950.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/27. + 680.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 1190.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/27.);
                case 6:
                  return sign * RealGradient(0., -32.*xi/27. + 400.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. - 1000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 2000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/3. - 3500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9. - 1360.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/9. + 3080.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/27. - 32./27. + 3400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 6800.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/3. + 11900.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9. + 160.*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 7700.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 15400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 26950.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/27. - 320.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 560.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/27.);
                case 7:
                  return sign * RealGradient(0., 4.*xi - 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 900.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1050.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 360.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 280.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4. - 2700.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3150.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 60.*(xi + 1.)*(xi + 1.)/(2.*2.) + 2100.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4200.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 120.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 70.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                case 8:
                  return sign * RealGradient(-4.*eta + 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 360.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 280.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 900.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 1800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1050.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 4. + 60.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 2700.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2100.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 5400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3150.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 120.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 70.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                case 9:
                  return sign * RealGradient(32.*eta/27. - 400.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. + 1360.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 3080.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. + 1000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. - 2000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/3. + 3500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9. + 32./27. - 160.*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 3400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 7700.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. + 6800.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/3. - 11900.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9. + 320.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 15400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 26950.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/27. - 560.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/27., 0.);
                case 10:
                  return sign * RealGradient(-68.*eta/27. + 760.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. - 1720.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 3080.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. - 1900.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. + 3800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/3. - 6650.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9. - 68./27. + 340.*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 4300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 7700.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. - 8600.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/3. + 15050.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9. - 680.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 15400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 26950.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/27. + 1190.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/27., 0.);
                case 11:
                  return sign * RealGradient(16.*eta - 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 480.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 280.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 3600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 16. - 240.*(eta + 1.)*(eta + 1.)/(2.*2.) - 3600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2100.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 7200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4200.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 480.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4200.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2450.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 280.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                case 12:
                  return sign * RealGradient(0., -15.*eta - 16.*xi + 480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1050.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1440.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 1120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 29. + 90.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 5400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 120.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4200.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 70.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 5600.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2450.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 160.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 70.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                case 13:
                  return sign * RealGradient(0., 50.*eta/9. + 128.*xi/27. - 1600.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. + 2000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 8000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 3500.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9. + 5440.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/9. - 12320.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/27. + 262./27. - 340.*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 6800.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 27200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 11900.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9. - 320.*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 15400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. + 770.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/27. - 61600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. + 26950.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/27. + 1280.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. - 560.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/27.);
                case 14:
                  return sign * RealGradient(0., -95.*eta/9. - 272.*xi/27. + 3040.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. - 3800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 15200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 6650.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9. - 6880.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/9. + 12320.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/27. - 523./27. + 430.*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 8600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 34400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 15050.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9. + 680.*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 15400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. - 770.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/27. + 61600.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. - 26950.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/27. - 2720.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. + 1190.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/27.);
                case 15:
                  return sign * RealGradient(0., 30.*eta + 64.*xi - 960.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1920.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 1120.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 86. - 120.*(eta + 1.)*(eta + 1.)/(2.*2.) - 7200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 9600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 480.*(xi + 1.)*(xi + 1.)/(2.*2.) + 4200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 70.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 640.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 280.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                case 16:
                  return RealGradient(0., 52.*xi - 780.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3480.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1560.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 910.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 52. - 6960.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 9600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 464.*(xi + 1.)*(xi + 1.)/(2.*2.) + 4060.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 640.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 280.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                case 17:
                  return RealGradient(0., 12.*xi - 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1680.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3600.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 360.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 210.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 12. - 3360.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 7200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 224.*(xi + 1.)*(xi + 1.)/(2.*2.) + 1960.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4200.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 480.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 280.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                case 18:
                  return RealGradient(0., 16.*xi - 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 240.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 480.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 280.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 16. - 480.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 32.*(xi + 1.)*(xi + 1.)/(2.*2.) + 280.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)));
                case 19:
                  return RealGradient(-52.*eta + 780.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1560.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 910.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3480.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 4800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2100.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 52. + 464.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 6960.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4060.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 9600.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 640.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 5600.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 280.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                case 20:
                  return RealGradient(-12.*eta + 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 360.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 210.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1680.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 3600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2100.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 12. + 224.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 3360.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1960.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 7200.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 480.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 280.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                case 21:
                  return RealGradient(-16.*eta + 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 480.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 280.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 240.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 16. + 32.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 480.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 280.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                case 22:
                  return RealGradient(13.*eta - 390.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1170.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 910.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1740.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 1050.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 13. - 116.*(eta + 1.)*(eta + 1.)/(2.*2.) - 5220.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 4060.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 7200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 160.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2450.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 70.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                case 23:
                  return RealGradient(3.*eta - 90.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 210.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 840.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 1800.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 1050.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 3. - 56.*(eta + 1.)*(eta + 1.)/(2.*2.) - 2520.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 1960.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 5400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 120.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4200.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2450.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 70.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                case 24:
                  return RealGradient(4.*eta - 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 360.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 280.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 4. - 8.*(eta + 1.)*(eta + 1.)/(2.*2.) - 360.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 280.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)), 0.);
                case 25:
                  return RealGradient(0., -13.*xi + 390.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1740.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1050.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1170.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 910.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 13. + 5220.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 116.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4060.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 5600.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2450.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 160.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 70.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                case 26:
                  return RealGradient(0., -3.*xi + 90.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 840.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 1800.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1050.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 210.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3. + 2520.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 5400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 56.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1960.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2450.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 120.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 70.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                case 27:
                  return RealGradient(0., -4.*xi + 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 360.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 280.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4. + 360.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 8.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 280.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.));
                case 28:
                  return RealGradient(12.*eta - 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 171.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 240.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 105.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 12. - 114.*(eta + 1.)*(eta + 1.)/(2.*2.) + 160.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 70.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                case 29:
                  return RealGradient(-6.*eta + 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 171.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 240.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 105.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 6. + 57.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 80.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 35.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                case 30:
                  return RealGradient(0., 12.*xi - 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 171.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 240.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 105.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 12. - 114.*(xi + 1.)*(xi + 1.)/(2.*2.) + 160.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 70.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                case 31:
                  return RealGradient(0., -6.*xi + 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 171.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 240.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 105.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 6. + 57.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 80.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 35.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                case 32:
                  return RealGradient(0., 2.*xi - 6.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 81.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 105.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 2. - 54.*(xi + 1.)*(xi + 1.)/(2.*2.) + 120.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 70.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                case 33:
                  return RealGradient(0., -xi + 6.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 81.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 105.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1. + 27.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 60.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 35.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                case 34:
                  return RealGradient(2.*eta - 6.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 81.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 105.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 2. - 54.*(eta + 1.)*(eta + 1.)/(2.*2.) + 120.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 70.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                case 35:
                  return RealGradient(-eta + 6.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 81.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 105.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 1. + 27.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 60.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 35.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                case 36:
                  return RealGradient(0., 6.*xi - 18.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 18.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 6. - 12.*(xi + 1.)*(xi + 1.)/(2.*2.));
                case 37:
                  return RealGradient(-6.*eta + 18.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 18.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 6. + 12.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                case 38:
                  return RealGradient(3.*eta - 18.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 18.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 3. - 6.*(eta + 1.)*(eta + 1.)/(2.*2.), 0.);
                case 39:
                  return RealGradient(0., -3.*xi + 18.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 18.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 3. + 6.*((xi + 1.)*(xi + 1.)/(2.*2.)));
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch(ii)
                {
                case 0:
                  return sign * RealGradient(720.*eta*xi - 160.*eta - 840.*eta*xi*xi + 224.*eta*(xi*xi*xi) - 120.*xi - 1260.*xi*eta*eta + 672.*xi*(eta*eta*eta) + 16. + 480.*(eta*eta) + 672.*(eta*eta)*(xi*xi) + 240.*(xi*xi) - 560.*eta*eta*eta - 140.*xi*xi*xi + 224.*(eta*eta*eta*eta), -240.*eta*xi + 840.*eta*(xi*xi) - 672.*eta*xi*xi*xi + 40.*xi + 420.*xi*(eta*eta) - 224.*xi*eta*eta*eta - 672.*eta*eta*xi*xi - 240.*xi*xi + 420.*(xi*xi*xi) - 224.*xi*xi*xi*xi);
                case 1:
                  return sign * RealGradient(-200.*eta*xi - 76.*eta/27. + 2884.*eta*(xi*xi)/9. - 2464.*eta*xi*xi*xi/27. + 380.*xi/9. + 784.*xi*(eta*eta)/3. - 896.*xi*eta*eta*eta/9. - 68./27. + 608.*(eta*eta)/9. - 2240.*eta*eta*xi*xi/9. - 860.*xi*xi/9. - 3472.*eta*eta*eta/27. + 1540.*(xi*xi*xi)/27. + 1792.*(eta*eta*eta*eta)/27., 176.*eta*xi/9. - 2128.*eta*xi*xi/9. + 2240.*eta*(xi*xi*xi)/9. - 296.*xi/27. + 448.*xi*(eta*eta)/9. - 1792.*xi*eta*eta*eta/27. + 896.*(eta*eta)*(xi*xi)/9. + 800.*(xi*xi)/9. - 168.*xi*xi*xi + 2464.*(xi*xi*xi*xi)/27.);
                case 2:
                  return sign * RealGradient(-16.*eta*xi + 112.*eta/27. - 1120.*eta*xi*xi/9. + 2464.*eta*(xi*xi*xi)/27. - 200.*xi/9. + 476.*xi*(eta*eta)/3. - 1120.*xi*eta*eta*eta/9. + 32./27. - 104.*eta*eta/9. + 224.*(eta*eta)*(xi*xi)/9. + 680.*(xi*xi)/9. - 56.*eta*eta*eta/27. - 1540.*xi*xi*xi/27. + 224.*(eta*eta*eta*eta)/27., 112.*eta*xi/9. - 392.*eta*xi*xi/9. - 224.*eta*xi*xi*xi/9. + 152.*xi/27. - 196.*xi*eta*eta/9. - 224.*xi*eta*eta*eta/27. + 1120.*(eta*eta)*(xi*xi)/9. - 512.*xi*xi/9. + 140.*(xi*xi*xi) - 2464.*xi*xi*xi*xi/27.);
                case 3:
                  return sign * RealGradient(-72.*eta*xi + 4.*eta + 252.*eta*(xi*xi) - 224.*eta*xi*xi*xi + 60.*xi - 4. - 180.*xi*xi + 140.*(xi*xi*xi), -16.*xi + 144.*(xi*xi) - 336.*xi*xi*xi + 224.*(xi*xi*xi*xi));
                case 4:
                  return sign * RealGradient(-72.*eta*xi + 4.*eta + 252.*eta*(xi*xi) - 224.*eta*xi*xi*xi, -16.*xi + 144.*(xi*xi) - 336.*xi*xi*xi + 224.*(xi*xi*xi*xi));
                case 5:
                  return sign * RealGradient(-80.*eta*xi + 8.*eta + 448.*eta*(xi*xi)/3. - 1792.*eta*xi*xi*xi/27. + 784.*xi*(eta*eta)/3. - 448.*xi*eta*eta*eta/3. - 32.*eta*eta - 896.*eta*eta*xi*xi/3. + 280.*(eta*eta*eta)/9. - 224.*eta*eta*eta*eta/27., 56.*eta*xi - 896.*eta*xi*xi/3. + 896.*eta*(xi*xi*xi)/3. - 12.*xi - 140.*xi*eta*eta/3. + 224.*xi*(eta*eta*eta)/27. + 448.*(eta*eta)*(xi*xi)/3. + 80.*(xi*xi) - 1232.*xi*xi*xi/9. + 1792.*(xi*xi*xi*xi)/27.);
                case 6:
                  return sign * RealGradient(-56.*eta*xi + 12.*eta + 140.*eta*(xi*xi)/3. - 224.*eta*xi*xi*xi/27. + 896.*xi*(eta*eta)/3. - 896.*xi*eta*eta*eta/3. - 80.*eta*eta - 448.*eta*eta*xi*xi/3. + 1232.*(eta*eta*eta)/9. - 1792.*eta*eta*eta*eta/27., 80.*eta*xi - 784.*eta*xi*xi/3. + 448.*eta*(xi*xi*xi)/3. - 8.*xi - 448.*xi*eta*eta/3. + 1792.*xi*(eta*eta*eta)/27. + 896.*(eta*eta)*(xi*xi)/3. + 32.*(xi*xi) - 280.*xi*xi*xi/9. + 224.*(xi*xi*xi*xi)/27.);
                case 7:
                  return sign * RealGradient(16.*eta - 144.*eta*eta + 336.*(eta*eta*eta) - 224.*eta*eta*eta*eta, 72.*eta*xi - 4.*xi - 252.*xi*eta*eta + 224.*xi*(eta*eta*eta));
                case 8:
                  return sign * RealGradient(16.*eta - 144.*eta*eta + 336.*(eta*eta*eta) - 224.*eta*eta*eta*eta, 72.*eta*xi - 60.*eta - 4.*xi - 252.*xi*eta*eta + 224.*xi*(eta*eta*eta) + 4. + 180.*(eta*eta) - 140.*eta*eta*eta);
                case 9:
                  return sign * RealGradient(-112.*eta*xi/9. - 152.*eta/27. + 196.*eta*(xi*xi)/9. + 224.*eta*(xi*xi*xi)/27. + 392.*xi*(eta*eta)/9. + 224.*xi*(eta*eta*eta)/9. + 512.*(eta*eta)/9. - 1120.*eta*eta*xi*xi/9. - 140.*eta*eta*eta + 2464.*(eta*eta*eta*eta)/27., 16.*eta*xi + 200.*eta/9. - 476.*eta*xi*xi/3. + 1120.*eta*(xi*xi*xi)/9. - 112.*xi/27. + 1120.*xi*(eta*eta)/9. - 2464.*xi*eta*eta*eta/27. - 32./27. - 680.*eta*eta/9. - 224.*eta*eta*xi*xi/9. + 104.*(xi*xi)/9. + 1540.*(eta*eta*eta)/27. + 56.*(xi*xi*xi)/27. - 224.*xi*xi*xi*xi/27.);
                case 10:
                  return sign * RealGradient(-176.*eta*xi/9. + 296.*eta/27. - 448.*eta*xi*xi/9. + 1792.*eta*(xi*xi*xi)/27. + 2128.*xi*(eta*eta)/9. - 2240.*xi*eta*eta*eta/9. - 800.*eta*eta/9. - 896.*eta*eta*xi*xi/9. + 168.*(eta*eta*eta) - 2464.*eta*eta*eta*eta/27., 200.*eta*xi - 380.*eta/9. - 784.*eta*xi*xi/3. + 896.*eta*(xi*xi*xi)/9. + 76.*xi/27. - 2884.*xi*eta*eta/9. + 2464.*xi*(eta*eta*eta)/27. + 68./27. + 860.*(eta*eta)/9. + 2240.*(eta*eta)*(xi*xi)/9. - 608.*xi*xi/9. - 1540.*eta*eta*eta/27. + 3472.*(xi*xi*xi)/27. - 1792.*xi*xi*xi*xi/27.);
                case 11:
                  return sign * RealGradient(240.*eta*xi - 40.*eta - 420.*eta*xi*xi + 224.*eta*(xi*xi*xi) - 840.*xi*eta*eta + 672.*xi*(eta*eta*eta) + 240.*(eta*eta) + 672.*(eta*eta)*(xi*xi) - 420.*eta*eta*eta + 224.*(eta*eta*eta*eta), -720.*eta*xi + 120.*eta + 1260.*eta*(xi*xi) - 672.*eta*xi*xi*xi + 160.*xi + 840.*xi*(eta*eta) - 224.*xi*eta*eta*eta - 16. - 240.*eta*eta - 672.*eta*eta*xi*xi - 480.*xi*xi + 140.*(eta*eta*eta) + 560.*(xi*xi*xi) - 224.*xi*xi*xi*xi);
                case 12:
                  return RealGradient(-3240.*eta*xi + 960.*eta + 3024.*eta*(xi*xi) - 672.*eta*xi*xi*xi + 9072.*xi*(eta*eta) - 6048.*xi*eta*eta*eta - 4320.*eta*eta - 4032.*eta*eta*xi*xi + 6048.*(eta*eta*eta) - 2688.*eta*eta*eta*eta, 2160.*eta*xi - 6048.*eta*xi*xi + 4032.*eta*(xi*xi*xi) - 240.*xi - 4536.*xi*eta*eta + 2688.*xi*(eta*eta*eta) + 6048.*(eta*eta)*(xi*xi) + 1080.*(xi*xi) - 1512.*xi*xi*xi + 672.*(xi*xi*xi*xi));
                case 13:
                  return RealGradient(2160.*eta*xi - 240.*eta - 4536.*eta*xi*xi + 2688.*eta*(xi*xi*xi) - 6048.*xi*eta*eta + 4032.*xi*(eta*eta*eta) + 1080.*(eta*eta) + 6048.*(eta*eta)*(xi*xi) - 1512.*eta*eta*eta + 672.*(eta*eta*eta*eta), -3240.*eta*xi + 9072.*eta*(xi*xi) - 6048.*eta*xi*xi*xi + 960.*xi + 3024.*xi*(eta*eta) - 672.*xi*eta*eta*eta - 4032.*eta*eta*xi*xi - 4320.*xi*xi + 6048.*(xi*xi*xi) - 2688.*xi*xi*xi*xi);
                case 14:
                  return RealGradient(-1944.*eta*xi + 144.*eta + 4536.*eta*(xi*xi) - 2016.*eta*xi*xi*xi + 2016.*xi*(eta*eta) - 144.*eta*eta - 4032.*eta*eta*xi*xi, 432.*eta*xi - 3024.*eta*xi*xi + 4032.*eta*(xi*xi*xi) - 216.*xi + 1728.*(xi*xi) - 3528.*xi*xi*xi + 2016.*(xi*xi*xi*xi));
                case 15:
                  return RealGradient(1152.*eta*xi - 72.*eta - 3528.*eta*xi*xi + 2688.*eta*(xi*xi*xi) - 1008.*xi*eta*eta + 72.*(eta*eta) + 2016.*(eta*eta)*(xi*xi), -216.*eta*xi + 1512.*eta*(xi*xi) - 2016.*eta*xi*xi*xi + 288.*xi - 2304.*xi*xi + 4704.*(xi*xi*xi) - 2688.*xi*xi*xi*xi);
                case 16:
                  return RealGradient(-216.*eta*xi + 288.*eta + 1512.*xi*(eta*eta) - 2016.*xi*eta*eta*eta - 2304.*eta*eta + 4704.*(eta*eta*eta) - 2688.*eta*eta*eta*eta, 1152.*eta*xi - 1008.*eta*xi*xi - 72.*xi - 3528.*xi*eta*eta + 2688.*xi*(eta*eta*eta) + 2016.*(eta*eta)*(xi*xi) + 72.*(xi*xi));
                case 17:
                  return RealGradient(432.*eta*xi - 216.*eta - 3024.*xi*eta*eta + 4032.*xi*(eta*eta*eta) + 1728.*(eta*eta) - 3528.*eta*eta*eta + 2016.*(eta*eta*eta*eta), -1944.*eta*xi + 2016.*eta*(xi*xi) + 144.*xi + 4536.*xi*(eta*eta) - 2016.*xi*eta*eta*eta - 4032.*eta*eta*xi*xi - 144.*xi*xi);
                case 18:
                  return RealGradient(-1332.*eta*xi + 216.*eta + 1638.*eta*(xi*xi) - 504.*eta*xi*xi*xi + 4788.*xi*(eta*eta) - 3528.*xi*eta*eta*eta - 1098.*eta*eta - 3024.*eta*eta*xi*xi + 1554.*(eta*eta*eta) - 672.*eta*eta*eta*eta, 1044.*eta*xi - 4032.*eta*xi*xi + 3024.*eta*(xi*xi*xi) - 144.*xi - 1638.*xi*eta*eta + 672.*xi*(eta*eta*eta) + 3528.*(eta*eta)*(xi*xi) + 774.*(xi*xi) - 1134.*xi*xi*xi + 504.*(xi*xi*xi*xi));
                case 19:
                  return RealGradient(1044.*eta*xi - 144.*eta - 1638.*eta*xi*xi + 672.*eta*(xi*xi*xi) - 4032.*xi*eta*eta + 3024.*xi*(eta*eta*eta) + 774.*(eta*eta) + 3528.*(eta*eta)*(xi*xi) - 1134.*eta*eta*eta + 504.*(eta*eta*eta*eta), -1332.*eta*xi + 4788.*eta*(xi*xi) - 3528.*eta*xi*xi*xi + 216.*xi + 1638.*xi*(eta*eta) - 504.*xi*eta*eta*eta - 3024.*eta*eta*xi*xi - 1098.*xi*xi + 1554.*(xi*xi*xi) - 672.*xi*xi*xi*xi);
                case 20:
                  return RealGradient(-216.*eta*xi - 48.*eta + 504.*eta*(xi*xi) - 168.*eta*xi*xi*xi - 756.*xi*eta*eta + 1008.*xi*(eta*eta*eta) + 720.*(eta*eta) - 1344.*eta*eta*eta + 672.*(eta*eta*eta*eta), -360.*eta*xi + 504.*eta*(xi*xi) + 12.*xi + 1008.*xi*(eta*eta) - 672.*xi*eta*eta*eta - 1008.*eta*eta*xi*xi + 72.*(xi*xi) - 252.*xi*xi*xi + 168.*(xi*xi*xi*xi));
                case 21:
                  return RealGradient(-216.*eta*xi + 66.*eta - 378.*eta*xi*xi + 672.*eta*(xi*xi*xi) + 2268.*xi*(eta*eta) - 2016.*xi*eta*eta*eta - 486.*eta*eta - 1512.*eta*eta*xi*xi + 756.*(eta*eta*eta) - 336.*eta*eta*eta*eta, 1188.*eta*xi - 2772.*eta*xi*xi + 1512.*eta*(xi*xi*xi) + 6.*xi - 1512.*xi*eta*eta + 336.*xi*(eta*eta*eta) + 2016.*(eta*eta)*(xi*xi) - 468.*xi*xi + 1134.*(xi*xi*xi) - 672.*xi*xi*xi*xi);
                case 22:
                  return RealGradient(1188.*eta*xi + 6.*eta - 1512.*eta*xi*xi + 336.*eta*(xi*xi*xi) - 2772.*xi*eta*eta + 1512.*xi*(eta*eta*eta) - 468.*eta*eta + 2016.*(eta*eta)*(xi*xi) + 1134.*(eta*eta*eta) - 672.*eta*eta*eta*eta, -216.*eta*xi + 2268.*eta*(xi*xi) - 2016.*eta*xi*xi*xi + 66.*xi - 378.*xi*eta*eta + 672.*xi*(eta*eta*eta) - 1512.*eta*eta*xi*xi - 486.*xi*xi + 756.*(xi*xi*xi) - 336.*xi*xi*xi*xi);
                case 23:
                  return RealGradient(-360.*eta*xi + 12.*eta + 1008.*eta*(xi*xi) - 672.*eta*xi*xi*xi + 504.*xi*(eta*eta) + 72.*(eta*eta) - 1008.*eta*eta*xi*xi - 252.*eta*eta*eta + 168.*(eta*eta*eta*eta), -216.*eta*xi - 756.*eta*xi*xi + 1008.*eta*(xi*xi*xi) - 48.*xi + 504.*xi*(eta*eta) - 168.*xi*eta*eta*eta + 720.*(xi*xi) - 1344.*xi*xi*xi + 672.*(xi*xi*xi*xi));
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          } // end switch (type)
      } // end case FOURTH
 
      // quintic Nedelec (first kind) shape functions
    case FIFTH:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch(ii)
                {
                case 0:
                  return sign * RealGradient(-625.*eta/4. - 75.*xi + 3750.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 13125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 17500.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 7875.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 22500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 52500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 52500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 18900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 875./4. + 1875.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 78750.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 105000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 47250.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 525.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 183750.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 183750.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 66150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 4375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 245000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 110250.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 700.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 245000.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 88200.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 4375.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 110250.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 315.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 39690.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                case 1:
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                case 2:
                  return sign * RealGradient(-375.*eta/32. - 105.*xi/8. + 2625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/4. - 28875.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 23625.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 23625.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. - 7875.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 18375.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 18375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. + 6615.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/2. - 765./32. + 1125.*((eta + 1.)*(eta + 1.)/(2.*2.))/8. + 86625.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 70875.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 70875.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. + 1155.*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 202125.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 202125.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 72765.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/4. - 2625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/8. + 165375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 165375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. - 945.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. - 165375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. + 59535.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/2. + 2625.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8. + 165375.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/8. - 59535.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/4. - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/8., 0.);
                case 3:
                  return sign * RealGradient(2125.*eta/512. + 705.*xi/128. - 17625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/64. + 233625.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 242375.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 291375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 52875.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/32. - 123375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/32. + 123375.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/32. - 44415.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/32. + 4775./512. - 6375.*(eta + 1.)*(eta + 1.)/(2.*2.)/128. - 700875.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/64. + 727125.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 874125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. - 9345.*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 1635375.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 1635375.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 588735.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/64. + 14875.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/128. - 1696625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 2039625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. + 9695.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. + 1696625.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/32. - 610785.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/32. - 14875.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. - 2039625.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. - 11655.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. + 734265.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/64. + 5355.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/128., 0.);
                case 4:
                  return sign * RealGradient(-125.*eta/4. - 30.*xi + 1500.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 7875.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 14000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 7875.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 9000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 21000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 21000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 7560.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 235./4. + 375.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 47250.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 84000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 47250.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 315.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 110250.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 110250.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 39690.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 875.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 196000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 110250.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 560.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 196000.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 70560.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 875.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 110250.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 315.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 39690.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 315.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                case 5:
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                case 6:
                  return sign * RealGradient(0., -2425.*xi/512. + 14325.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/64. - 42975.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/16. + 300825.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 100275.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. + 180495.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/32. - 105525.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/128. + 68075.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 58275.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. - 2425./512. + 316575.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/32. - 2216025.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 738675.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/16. - 1329615.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 7275.*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 204225.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/16. + 174825.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/32. + 1429575.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 476525.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. + 857745.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/32. - 50925.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/128. - 1223775.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 407925.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/16. - 734265.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 16975.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/32. - 30555.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/128.);
                case 7:
                  return sign * RealGradient(0., 75.*xi/32. - 525.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/4. + 1575.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 11025.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 7350.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 6615.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/2. + 5775.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/8. - 4725.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 4725.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8. + 75./32. - 17325.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 121275.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 40425.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 72765.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/4. - 225.*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 14175.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 14175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 66150.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 59535.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/2. + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/8. + 99225.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 33075.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 59535.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/4. - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/8.);
                case 8:
                  return sign * RealGradient(0., -425.*xi/512. + 3525.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/64. - 10575.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/16. + 74025.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 24675.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. + 44415.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/32. - 46725.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/128. + 48475.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 58275.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. - 425./512. + 140175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/32. - 981225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 327075.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/16. - 588735.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 1275.*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 145425.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/16. + 174825.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/32. + 1017975.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 339325.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. + 610785.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/32. - 8925.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/128. - 1223775.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 407925.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/16. - 734265.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 2975.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/32. - 5355.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/128.);
                case 9:
                  return sign * RealGradient(0., 25.*xi/4. - 300.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 12600.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 16800.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 7560.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 1575.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2800.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 1575.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 25./4. - 18900.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 66150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 88200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 150.*(xi + 1.)*(xi + 1.)/(2.*2.) + 33600.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 18900.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 117600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 156800.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 70560.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 525.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 66150.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 88200.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 700.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 315.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                case 10:
                  return sign * RealGradient(-25.*eta/4. + 300.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1575.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2800.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1575.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 3600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 12600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 16800.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 7560.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 25./4. + 150.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 18900.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 33600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 18900.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 66150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 88200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 39690.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 525.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 117600.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 66150.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 156800.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 70560.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 700.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 88200.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 39690.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 315.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                case 11:
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                case 12:
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                case 13:
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                case 14:
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                case 15:
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                case 16:
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                case 17:
                  return sign * RealGradient(0., 105.*eta/8. + 375.*xi/32. - 2625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/4. + 7875.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 18375.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 18375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. - 6615.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/2. + 28875.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/8. - 23625.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 23625.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8. + 765./32. - 1155.*(eta + 1.)*(eta + 1.)/(2.*2.)/8. - 86625.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 202125.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 202125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. + 72765.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/4. - 1125.*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 70875.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 70875.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. + 945.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 165375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 165375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. - 59535.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/2. + 2625.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/8. + 165375.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/8. - 165375.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. + 59535.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/4. - 2625.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/8.);
                case 18:
                  return sign * RealGradient(0., -2865.*eta/128. - 12125.*xi/512. + 71625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/64. - 214875.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/32. + 501375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 501375.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/32. + 180495.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/32. - 527625.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/128. + 340375.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 291375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. - 22615./512. + 21105.*((eta + 1.)*(eta + 1.)/(2.*2.))/128. + 1582875.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 3693375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 3693375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. - 1329615.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 36375.*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 1021125.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/32. + 874125.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. - 13615.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 2382625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 2382625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/32. + 857745.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/32. - 84875.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/128. - 2039625.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 11655.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/128. + 2039625.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. - 734265.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 84875.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. - 30555.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/128.);
                case 19:
                  return sign * RealGradient(0., 75.*eta + 625.*xi/4. - 3750.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 22500.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 52500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 52500.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 18900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 13125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 17500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 7875.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 875./4. - 525.*(eta + 1.)*(eta + 1.)/(2.*2.) - 78750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 183750.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 183750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 66150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 1875.*(xi + 1.)*(xi + 1.)/(2.*2.) + 105000.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 47250.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 700.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 245000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 245000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 88200.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 4375.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 110250.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 315.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 110250.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 4375.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                case 20:
                  return RealGradient(0., 975.*xi/8. - 2925.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 21150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 51825.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 52500.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 18900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 20475.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 13650.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 12285.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 975./8. - 74025.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 362775.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 183750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 66150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 3525.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 98700.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 44415.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 241850.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 245000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 88200.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 17275.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. + 217665.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. - 110250.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 4375.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                case 21:
                  return RealGradient(0., -25.*xi + 600.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 8325.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 30825.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 42000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 18900.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 2100.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 2800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1260.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 25. + 58275.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 215775.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 147000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 66150.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 2775.*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 38850.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 34965.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 143850.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 196000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 88200.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 10275.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. - 129465.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. + 88200.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 39690.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 3500.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                case 22:
                  return RealGradient(0., 225.*xi/4. - 1350.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2025.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4725.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 6300.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2835.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 225./4. - 23625.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 14175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 1125.*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 15750.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 14175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 9450.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 675.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. + 8505.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2.);
                case 23:
                  return RealGradient(0., -225.*xi/8. + 675.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 2700.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2025.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 3150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2835.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 225./8. + 9450.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 14175.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 225.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 12600.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 5670.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 9450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 675.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. - 8505.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2.);
                case 24:
                  return RealGradient(-975.*eta/8. + 2925.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 20475.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 13650.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 12285.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. - 21150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 51825.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 52500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 18900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 975./8. + 3525.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 74025.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 98700.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 44415.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 362775.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 183750.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 66150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 17275.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 241850.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 217665.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. - 245000.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 88200.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 4375.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 110250.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 39690.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                case 25:
                  return RealGradient(25.*eta - 600.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 2100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1260.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 8325.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 30825.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 42000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 18900.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 25. - 2775.*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 58275.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 38850.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 34965.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. + 215775.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 147000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 66150.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 10275.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 143850.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 129465.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 196000.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 88200.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 3500.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 88200.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                case 26:
                  return RealGradient(-225.*eta/4. + 1350.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 4725.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2835.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 3375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 2025.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 225./4. + 1125.*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 23625.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 15750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 14175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. - 14175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. - 675.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 9450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 8505.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2., 0.);
                case 27:
                  return RealGradient(225.*eta/8. - 675.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 4725.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 3150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2835.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 2700.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2025.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 225./8. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.) - 9450.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 12600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5670.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 14175.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. + 675.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 9450.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 8505.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2., 0.);
                case 28:
                  return RealGradient(-195.*eta/8. + 1170.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 12285.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 10920.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 12285.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. - 8460.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 20730.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 21000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 7560.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 195./8. + 705.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 44415.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 78960.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 44415.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 217665.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 110250.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 39690.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 3455.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 193480.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 217665.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. - 196000.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 70560.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 875.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 110250.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 39690.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 315.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                case 29:
                  return RealGradient(5.*eta - 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1260.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2240.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1260.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 3330.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 12330.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 16800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 7560.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 5. - 555.*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 34965.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 31080.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 34965.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. + 129465.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 88200.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 39690.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 2055.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 115080.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 129465.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 156800.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 70560.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 700.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 88200.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 315.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                case 30:
                  return RealGradient(-45.*eta/4. + 540.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 2835.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5040.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2835.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1350.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 810.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 45./4. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 14175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 12600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 14175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. - 8505.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. - 135.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 7560.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 8505.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2., 0.);
                case 31:
                  return RealGradient(45.*eta/8. - 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 2835.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 2520.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2835.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 1080.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 810.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 45./8. - 45.*(eta + 1.)*(eta + 1.)/(2.*2.) - 5670.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 10080.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5670.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 8505.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. + 135.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 7560.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 8505.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2., 0.);
                case 32:
                  return RealGradient(0., 195.*xi/8. - 1170.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 8460.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 20730.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 21000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 7560.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 12285.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 10920.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 12285.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 195./8. - 44415.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 217665.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 110250.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 705.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 78960.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 44415.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 193480.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 196000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 70560.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 3455.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. + 217665.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. - 110250.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 875.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 315.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                case 33:
                  return RealGradient(0., -5.*xi + 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 3330.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 12330.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 16800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 7560.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 1260.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 2240.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1260.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 5. + 34965.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 129465.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 88200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 39690.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 555.*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 31080.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 34965.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 115080.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 156800.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 70560.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 2055.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. - 129465.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. + 88200.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 39690.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 700.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 315.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                case 34:
                  return RealGradient(0., 45.*xi/4. - 540.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1350.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 810.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2835.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 5040.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2835.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 45./4. - 14175.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 8505.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 225.*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 12600.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 14175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 7560.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 135.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. + 8505.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2.);
                case 35:
                  return RealGradient(0., -45.*xi/8. + 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1080.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 810.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2835.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 2520.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2835.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 45./8. + 5670.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8505.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 45.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 10080.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 5670.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 7560.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 135.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. - 8505.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2.);
                case 36:
                  return RealGradient(36.*eta - 288.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 240.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 2376.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 6120.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 6300.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 2268.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 36. - 594.*(eta + 1.)*(eta + 1.)/(2.*2.) - 1980.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5100.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5250.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1890.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 1530.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 567.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                case 37:
                  return RealGradient(12.*eta - 192.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 240.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 1584.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 4080.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1512.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 12. - 198.*(eta + 1.)*(eta + 1.)/(2.*2.) - 1980.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5100.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5250.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1890.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 510.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 525.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 189.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                case 38:
                  return RealGradient(-6.*eta + 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 990.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 2550.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2625.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 945.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 6. + 99.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 990.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2550.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2625.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 945.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 255.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. - 189.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/2., 0.);
                case 39:
                  return RealGradient(0., 36.*xi - 288.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 2376.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 6300.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 2268.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 240.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 36. - 1980.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5100.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5250.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 1890.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 594.*(xi + 1.)*(xi + 1.)/(2.*2.) + 1530.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 567.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                case 40:
                  return RealGradient(0., 12.*xi - 192.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1584.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4080.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 1512.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 240.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 12. - 1980.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5100.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5250.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 1890.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 198.*(xi + 1.)*(xi + 1.)/(2.*2.) + 510.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 189.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                case 41:
                  return RealGradient(0., -6.*xi + 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 990.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2550.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2625.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 945.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 120.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 6. + 990.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2550.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2625.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 945.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 99.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 255.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 525.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. - 189.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/2.);
                case 42:
                  return RealGradient(0., -9.*xi/2. + 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 864.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 3600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5040.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 2268.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 30.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 9./2. + 720.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 1890.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 216.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 900.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1260.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 567.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                case 43:
                  return RealGradient(0., -3.*xi/2. + 24.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 576.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3360.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 1512.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 30.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 3./2. + 720.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 1890.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 72.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 300.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 420.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 189.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                case 44:
                  return RealGradient(0., 3.*xi/4. - 15.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 360.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 945.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 15.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 3./4. - 360.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 1500.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2100.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 945.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 36.*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 210.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 189.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/2.);
                case 45:
                  return RealGradient(-9.*eta/2. + 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 30.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 864.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 3600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5040.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 2268.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 9./2. + 216.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 720.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1890.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 1260.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 567.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                case 46:
                  return RealGradient(-3.*eta/2. + 24.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 30.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 576.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 2400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3360.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1512.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 3./2. + 72.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 720.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1890.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 300.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 420.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 189.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                case 47:
                  return RealGradient(3.*eta/4. - 15.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 15.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 360.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 1500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 945.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 3./4. - 36.*(eta + 1.)*(eta + 1.)/(2.*2.) - 360.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 1500.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2100.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 945.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 150.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 210.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 189.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/2., 0.);
                case 48:
                  return RealGradient(0., 18.*xi - 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 324.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 18. - 270.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 81.*(xi + 1.)*(xi + 1.)/(2.*2.) + 45.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 49:
                  return RealGradient(0., -9.*xi/2. + 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 216.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 30.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 9./2. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 54.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 45.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                case 50:
                  return RealGradient(-18.*eta + 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 324.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 18. + 81.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 270.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 45.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                case 51:
                  return RealGradient(9.*eta/2. - 36.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 30.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 216.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 9./2. - 54.*(eta + 1.)*(eta + 1.)/(2.*2.) - 180.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 45.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                case 52:
                  return RealGradient(-6.*eta + 96.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 216.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 6. + 27.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 270.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 15.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                case 53:
                  return RealGradient(3.*eta/2. - 24.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 30.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 144.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 120.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3./2. - 18.*(eta + 1.)*(eta + 1.)/(2.*2.) - 180.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 15.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                case 54:
                  return RealGradient(0., 6.*xi - 96.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 216.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 120.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 6. - 270.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 27.*(xi + 1.)*(xi + 1.)/(2.*2.) + 15.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 55:
                  return RealGradient(0., -3.*xi/2. + 24.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 144.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 120.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 30.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 3./2. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 18.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 15.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                case 56:
                  return RealGradient(2.*eta + 2. - 9.*(eta + 1.)*(eta + 1.)/(2.*2.) + 5.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                case 57:
                  return RealGradient(0., 2.*xi + 2. - 9.*(xi + 1.)*(xi + 1.)/(2.*2.) + 5.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                case 58:
                  return RealGradient(0., -xi/2. - 1./2. + 6.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 5.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                case 59:
                  return RealGradient(-eta/2. - 1./2. + 6.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 5.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch(ii)
                {
                case 0:
                  return sign * RealGradient(2800.*eta*xi - 375.*eta - 6300.*eta*xi*xi + 5040.*eta*(xi*xi*xi) - 1050.*eta*xi*xi*xi*xi - 300.*xi - 8400.*xi*eta*eta + 10080.*xi*(eta*eta*eta) - 4200.*xi*eta*eta*eta*eta + 25. + 1750.*(eta*eta) + 11340.*(eta*eta)*(xi*xi) - 4200.*eta*eta*xi*xi*xi + 1050.*(xi*xi) - 6300.*xi*xi*eta*eta*eta - 3500.*eta*eta*eta - 1400.*xi*xi*xi + 3150.*(eta*eta*eta*eta) + 630.*(xi*xi*xi*xi) - 1050.*eta*eta*eta*eta*eta, -700.*eta*xi + 4200.*eta*(xi*xi) - 7560.*eta*xi*xi*xi + 4200.*eta*(xi*xi*xi*xi) + 75.*xi + 2100.*xi*(eta*eta) - 2520.*xi*eta*eta*eta + 1050.*xi*(eta*eta*eta*eta) - 7560.*eta*eta*xi*xi + 6300.*(eta*eta)*(xi*xi*xi) - 700.*xi*xi + 4200.*(xi*xi)*(eta*eta*eta) + 2100.*(xi*xi*xi) - 2520.*xi*xi*xi*xi + 1050.*(xi*xi*xi*xi*xi));
                case 1:
                  return sign * RealGradient(-12145.*eta*xi/16. + 695.*eta/128. + 136185.*eta*(xi*xi)/64. - 6825.*eta*xi*xi*xi/4. + 19425.*eta*(xi*xi*xi*xi)/64. + 2865.*xi/32. + 7245.*xi*(eta*eta)/4. - 25515.*xi*eta*eta*eta/16. + 14175.*xi*(eta*eta*eta*eta)/32. - 485./128. + 11235.*(eta*eta)/64. - 240975.*eta*eta*xi*xi/64. + 48825.*(eta*eta)*(xi*xi*xi)/32. - 21105.*xi*xi/64. + 127575.*(xi*xi)*(eta*eta*eta)/64. - 42525.*eta*eta*eta/64. + 13615.*(xi*xi*xi)/32. + 104895.*(eta*eta*eta*eta)/128. - 11655.*xi*xi*xi*xi/64. - 42525.*eta*eta*eta*eta*eta/128., 3045.*eta*xi/32. - 39375.*eta*xi*xi/32. + 84105.*eta*(xi*xi*xi)/32. - 48825.*eta*xi*xi*xi*xi/32. - 2395.*xi/128. + 2835.*xi*(eta*eta)/64. - 14175.*xi*eta*eta*eta/32. + 42525.*xi*(eta*eta*eta*eta)/128. + 25515.*(eta*eta)*(xi*xi)/16. - 127575.*eta*eta*xi*xi*xi/64. + 1715.*(xi*xi)/8. - 14175.*xi*xi*eta*eta*eta/32. - 41755.*xi*xi*xi/64. + 48615.*(xi*xi*xi*xi)/64. - 19425.*xi*xi*xi*xi*xi/64.);
                case 2:
                  return sign * RealGradient(55.*eta/8. - 3255.*eta*xi*xi/4. + 1260.*eta*(xi*xi*xi) - 1575.*eta*xi*xi*xi*xi/4. - 105.*xi/2. + 840.*xi*(eta*eta) - 1575.*xi*eta*eta*eta + 1575.*xi*(eta*eta*eta*eta)/2. + 15./8. - 175.*eta*eta/4. + 945.*(eta*eta)*(xi*xi)/4. - 1575.*eta*eta*xi*xi*xi/2. + 1155.*(xi*xi)/4. + 1575.*(xi*xi)*(eta*eta*eta)/4. + 35.*(eta*eta*eta)/4. - 945.*xi*xi*xi/2. + 735.*(eta*eta*eta*eta)/8. + 945.*(xi*xi*xi*xi)/4. - 525.*eta*eta*eta*eta*eta/8., 35.*eta*xi/2. + 105.*eta*(xi*xi)/2. - 1575.*eta*xi*xi*xi/2. + 1575.*eta*(xi*xi*xi*xi)/2. + 85.*xi/8. - 525.*xi*eta*eta/4. + 105.*xi*(eta*eta*eta)/2. + 525.*xi*(eta*eta*eta*eta)/8. + 945.*(eta*eta)*(xi*xi) - 1575.*eta*eta*xi*xi*xi/4. - 315.*xi*xi/2. - 1575.*xi*xi*eta*eta*eta/2. + 2485.*(xi*xi*xi)/4. - 3465.*xi*xi*xi*xi/4. + 1575.*(xi*xi*xi*xi*xi)/4.);
                case 3:
                  return sign * RealGradient(1855.*eta*xi/16. - 825.*eta/128. - 16695.*eta*xi*xi/64. - 945.*eta*xi*xi*xi/4. + 19425.*eta*(xi*xi*xi*xi)/64. + 705.*xi/32. - 1155.*xi*eta*eta/4. - 315.*xi*eta*eta*eta/16. + 5775.*xi*(eta*eta*eta*eta)/32. - 85./128. + 595.*(eta*eta)/64. + 76545.*(eta*eta)*(xi*xi)/64. - 9975.*eta*eta*xi*xi*xi/32. - 9345.*xi*xi/64. - 48825.*xi*xi*eta*eta*eta/64. + 595.*(eta*eta*eta)/64. + 9695.*(xi*xi*xi)/32. - 945.*eta*eta*eta*eta/128. - 11655.*xi*xi*xi*xi/64. - 525.*eta*eta*eta*eta*eta/128., -875.*eta*xi/32. + 9345.*eta*(xi*xi)/32. - 21735.*eta*xi*xi*xi/32. + 9975.*eta*(xi*xi*xi*xi)/32. - 555.*xi/128. + 1155.*xi*(eta*eta)/64. + 945.*xi*(eta*eta*eta)/32. + 525.*xi*(eta*eta*eta*eta)/128. - 4725.*eta*eta*xi*xi/16. + 48825.*(eta*eta)*(xi*xi*xi)/64. + 595.*(xi*xi)/8. - 5775.*xi*xi*eta*eta*eta/32. - 22155.*xi*xi*xi/64. + 36855.*(xi*xi*xi*xi)/64. - 19425.*xi*xi*xi*xi*xi/64.);
                case 4:
                  return sign * RealGradient(140.*eta*xi - 5.*eta - 840.*eta*xi*xi + 1680.*eta*(xi*xi*xi) - 1050.*eta*xi*xi*xi*xi - 120.*xi + 5. + 630.*(xi*xi) - 1120.*xi*xi*xi + 630.*(xi*xi*xi*xi), 25.*xi - 350.*xi*xi + 1400.*(xi*xi*xi) - 2100.*xi*xi*xi*xi + 1050.*(xi*xi*xi*xi*xi));
                case 5:
                  return sign * RealGradient(140.*eta*xi - 5.*eta - 840.*eta*xi*xi + 1680.*eta*(xi*xi*xi) - 1050.*eta*xi*xi*xi*xi, 25.*xi - 350.*xi*xi + 1400.*(xi*xi*xi) - 2100.*xi*xi*xi*xi + 1050.*(xi*xi*xi*xi*xi));
                case 6:
                  return sign * RealGradient(735.*eta*xi/4. - 10.*eta - 2835.*eta*xi*xi/4. + 14175.*eta*(xi*xi*xi)/16. - 42525.*eta*xi*xi*xi*xi/128. - 1575.*xi*eta*eta/2. + 12285.*xi*(eta*eta*eta)/16. - 1575.*xi*eta*eta*eta*eta/8. + 385.*(eta*eta)/8. + 76545.*(eta*eta)*(xi*xi)/32. - 14175.*eta*eta*xi*xi*xi/8. - 42525.*xi*xi*eta*eta*eta/32. - 245.*eta*eta*eta/4. + 1785.*(eta*eta*eta*eta)/64. - 525.*eta*eta*eta*eta*eta/128., -455.*eta*xi/4. + 2205.*eta*(xi*xi)/2. - 42525.*eta*xi*xi*xi/16. + 14175.*eta*(xi*xi*xi*xi)/8. + 20.*xi + 525.*xi*(eta*eta)/4. - 735.*xi*eta*eta*eta/16. + 525.*xi*(eta*eta*eta*eta)/128. - 31185.*eta*eta*xi*xi/32. + 42525.*(eta*eta)*(xi*xi*xi)/32. - 1785.*xi*xi/8. + 1575.*(xi*xi)*(eta*eta*eta)/8. + 2835.*(xi*xi*xi)/4. - 53865.*xi*xi*xi*xi/64. + 42525.*(xi*xi*xi*xi*xi)/128.);
                case 7:
                  return sign * RealGradient(175.*eta*xi - 15.*eta - 420.*eta*xi*xi + 315.*eta*(xi*xi*xi) - 525.*eta*xi*xi*xi*xi/8. - 1260.*xi*eta*eta + 2205.*xi*(eta*eta*eta) - 1050.*xi*eta*eta*eta*eta + 245.*(eta*eta)/2. + 4725.*(eta*eta)*(xi*xi)/2. - 1050.*eta*eta*xi*xi*xi - 4725.*xi*xi*eta*eta*eta/2. - 280.*eta*eta*eta + 945.*(eta*eta*eta*eta)/4. - 525.*eta*eta*eta*eta*eta/8., -175.*eta*xi + 1260.*eta*(xi*xi) - 2205.*eta*xi*xi*xi + 1050.*eta*(xi*xi*xi*xi) + 15.*xi + 420.*xi*(eta*eta) - 315.*xi*eta*eta*eta + 525.*xi*(eta*eta*eta*eta)/8. - 4725.*eta*eta*xi*xi/2. + 4725.*(eta*eta)*(xi*xi*xi)/2. - 245.*xi*xi/2. + 1050.*(xi*xi)*(eta*eta*eta) + 280.*(xi*xi*xi) - 945.*xi*xi*xi*xi/4. + 525.*(xi*xi*xi*xi*xi)/8.);
                case 8:
                  return sign * RealGradient(455.*eta*xi/4. - 20.*eta - 525.*eta*xi*xi/4. + 735.*eta*(xi*xi*xi)/16. - 525.*eta*xi*xi*xi*xi/128. - 2205.*xi*eta*eta/2. + 42525.*xi*(eta*eta*eta)/16. - 14175.*xi*eta*eta*eta*eta/8. + 1785.*(eta*eta)/8. + 31185.*(eta*eta)*(xi*xi)/32. - 1575.*eta*eta*xi*xi*xi/8. - 42525.*xi*xi*eta*eta*eta/32. - 2835.*eta*eta*eta/4. + 53865.*(eta*eta*eta*eta)/64. - 42525.*eta*eta*eta*eta*eta/128., -735.*eta*xi/4. + 1575.*eta*(xi*xi)/2. - 12285.*eta*xi*xi*xi/16. + 1575.*eta*(xi*xi*xi*xi)/8. + 10.*xi + 2835.*xi*(eta*eta)/4. - 14175.*xi*eta*eta*eta/16. + 42525.*xi*(eta*eta*eta*eta)/128. - 76545.*eta*eta*xi*xi/32. + 42525.*(eta*eta)*(xi*xi*xi)/32. - 385.*xi*xi/8. + 14175.*(xi*xi)*(eta*eta*eta)/8. + 245.*(xi*xi*xi)/4. - 1785.*xi*xi*xi*xi/64. + 525.*(xi*xi*xi*xi*xi)/128.);
                case 9:
                  return sign * RealGradient(-25.*eta + 350.*(eta*eta) - 1400.*eta*eta*eta + 2100.*(eta*eta*eta*eta) - 1050.*eta*eta*eta*eta*eta, -140.*eta*xi + 5.*xi + 840.*xi*(eta*eta) - 1680.*xi*eta*eta*eta + 1050.*xi*(eta*eta*eta*eta));
                case 10:
                  return sign * RealGradient(-25.*eta + 350.*(eta*eta) - 1400.*eta*eta*eta + 2100.*(eta*eta*eta*eta) - 1050.*eta*eta*eta*eta*eta, -140.*eta*xi + 120.*eta + 5.*xi + 840.*xi*(eta*eta) - 1680.*xi*eta*eta*eta + 1050.*xi*(eta*eta*eta*eta) - 5. - 630.*eta*eta + 1120.*(eta*eta*eta) - 630.*eta*eta*eta*eta);
                case 11:
                  return sign * RealGradient(875.*eta*xi/32. + 555.*eta/128. - 1155.*eta*xi*xi/64. - 945.*eta*xi*xi*xi/32. - 525.*eta*xi*xi*xi*xi/128. - 9345.*xi*eta*eta/32. + 21735.*xi*(eta*eta*eta)/32. - 9975.*xi*eta*eta*eta*eta/32. - 595.*eta*eta/8. + 4725.*(eta*eta)*(xi*xi)/16. + 5775.*(eta*eta)*(xi*xi*xi)/32. - 48825.*xi*xi*eta*eta*eta/64. + 22155.*(eta*eta*eta)/64. - 36855.*eta*eta*eta*eta/64. + 19425.*(eta*eta*eta*eta*eta)/64., -1855.*eta*xi/16. - 705.*eta/32. + 1155.*eta*(xi*xi)/4. + 315.*eta*(xi*xi*xi)/16. - 5775.*eta*xi*xi*xi*xi/32. + 825.*xi/128. + 16695.*xi*(eta*eta)/64. + 945.*xi*(eta*eta*eta)/4. - 19425.*xi*eta*eta*eta*eta/64. + 85./128. + 9345.*(eta*eta)/64. - 76545.*eta*eta*xi*xi/64. + 48825.*(eta*eta)*(xi*xi*xi)/64. - 595.*xi*xi/64. + 9975.*(xi*xi)*(eta*eta*eta)/32. - 9695.*eta*eta*eta/32. - 595.*xi*xi*xi/64. + 11655.*(eta*eta*eta*eta)/64. + 945.*(xi*xi*xi*xi)/128. + 525.*(xi*xi*xi*xi*xi)/128.);
                case 12:
                  return sign * RealGradient(-35.*eta*xi/2. - 85.*eta/8. + 525.*eta*(xi*xi)/4. - 105.*eta*xi*xi*xi/2. - 525.*eta*xi*xi*xi*xi/8. - 105.*xi*eta*eta/2. + 1575.*xi*(eta*eta*eta)/2. - 1575.*xi*eta*eta*eta*eta/2. + 315.*(eta*eta)/2. - 945.*eta*eta*xi*xi + 1575.*(eta*eta)*(xi*xi*xi)/2. + 1575.*(xi*xi)*(eta*eta*eta)/4. - 2485.*eta*eta*eta/4. + 3465.*(eta*eta*eta*eta)/4. - 1575.*eta*eta*eta*eta*eta/4., 105.*eta/2. - 840.*eta*xi*xi + 1575.*eta*(xi*xi*xi) - 1575.*eta*xi*xi*xi*xi/2. - 55.*xi/8. + 3255.*xi*(eta*eta)/4. - 1260.*xi*eta*eta*eta + 1575.*xi*(eta*eta*eta*eta)/4. - 15./8. - 1155.*eta*eta/4. - 945.*eta*eta*xi*xi/4. - 1575.*eta*eta*xi*xi*xi/4. + 175.*(xi*xi)/4. + 1575.*(xi*xi)*(eta*eta*eta)/2. + 945.*(eta*eta*eta)/2. - 35.*xi*xi*xi/4. - 945.*eta*eta*eta*eta/4. - 735.*xi*xi*xi*xi/8. + 525.*(xi*xi*xi*xi*xi)/8.);
                case 13:
                  return sign * RealGradient(-3045.*eta*xi/32. + 2395.*eta/128. - 2835.*eta*xi*xi/64. + 14175.*eta*(xi*xi*xi)/32. - 42525.*eta*xi*xi*xi*xi/128. + 39375.*xi*(eta*eta)/32. - 84105.*xi*eta*eta*eta/32. + 48825.*xi*(eta*eta*eta*eta)/32. - 1715.*eta*eta/8. - 25515.*eta*eta*xi*xi/16. + 14175.*(eta*eta)*(xi*xi*xi)/32. + 127575.*(xi*xi)*(eta*eta*eta)/64. + 41755.*(eta*eta*eta)/64. - 48615.*eta*eta*eta*eta/64. + 19425.*(eta*eta*eta*eta*eta)/64., 12145.*eta*xi/16. - 2865.*eta/32. - 7245.*eta*xi*xi/4. + 25515.*eta*(xi*xi*xi)/16. - 14175.*eta*xi*xi*xi*xi/32. - 695.*xi/128. - 136185.*xi*eta*eta/64. + 6825.*xi*(eta*eta*eta)/4. - 19425.*xi*eta*eta*eta*eta/64. + 485./128. + 21105.*(eta*eta)/64. + 240975.*(eta*eta)*(xi*xi)/64. - 127575.*eta*eta*xi*xi*xi/64. - 11235.*xi*xi/64. - 48825.*xi*xi*eta*eta*eta/32. - 13615.*eta*eta*eta/32. + 42525.*(xi*xi*xi)/64. + 11655.*(eta*eta*eta*eta)/64. - 104895.*xi*xi*xi*xi/128. + 42525.*(xi*xi*xi*xi*xi)/128.);
                case 14:
                  return sign * RealGradient(700.*eta*xi - 75.*eta - 2100.*eta*xi*xi + 2520.*eta*(xi*xi*xi) - 1050.*eta*xi*xi*xi*xi - 4200.*xi*eta*eta + 7560.*xi*(eta*eta*eta) - 4200.*xi*eta*eta*eta*eta + 700.*(eta*eta) + 7560.*(eta*eta)*(xi*xi) - 4200.*eta*eta*xi*xi*xi - 6300.*xi*xi*eta*eta*eta - 2100.*eta*eta*eta + 2520.*(eta*eta*eta*eta) - 1050.*eta*eta*eta*eta*eta, -2800.*eta*xi + 300.*eta + 8400.*eta*(xi*xi) - 10080.*eta*xi*xi*xi + 4200.*eta*(xi*xi*xi*xi) + 375.*xi + 6300.*xi*(eta*eta) - 5040.*xi*eta*eta*eta + 1050.*xi*(eta*eta*eta*eta) - 25. - 1050.*eta*eta - 11340.*eta*eta*xi*xi + 6300.*(eta*eta)*(xi*xi*xi) - 1750.*xi*xi + 4200.*(xi*xi)*(eta*eta*eta) + 1400.*(eta*eta*eta) + 3500.*(xi*xi*xi) - 630.*eta*eta*eta*eta - 3150.*xi*xi*xi*xi + 1050.*(xi*xi*xi*xi*xi));
                case 15:
                  return RealGradient(-19600.*eta*xi + 3500.*eta + 35280.*eta*(xi*xi) - 23520.*eta*xi*xi*xi + 4200.*eta*(xi*xi*xi*xi) + 94080.*xi*(eta*eta) - 141120.*xi*eta*eta*eta + 67200.*xi*(eta*eta*eta*eta) - 24500.*eta*eta - 105840.*eta*eta*xi*xi + 33600.*(eta*eta)*(xi*xi*xi) + 75600.*(xi*xi)*(eta*eta*eta) + 58800.*(eta*eta*eta) - 58800.*eta*eta*eta*eta + 21000.*(eta*eta*eta*eta*eta), 9800.*eta*xi - 47040.*eta*xi*xi + 70560.*eta*(xi*xi*xi) - 33600.*eta*xi*xi*xi*xi - 700.*xi - 35280.*xi*eta*eta + 47040.*xi*(eta*eta*eta) - 21000.*xi*eta*eta*eta*eta + 105840.*(eta*eta)*(xi*xi) - 75600.*eta*eta*xi*xi*xi + 4900.*(xi*xi) - 67200.*xi*xi*eta*eta*eta - 11760.*xi*xi*xi + 11760.*(xi*xi*xi*xi) - 4200.*xi*xi*xi*xi*xi);
                case 16:
                  return RealGradient(9800.*eta*xi - 700.*eta - 35280.*eta*xi*xi + 47040.*eta*(xi*xi*xi) - 21000.*eta*xi*xi*xi*xi - 47040.*xi*eta*eta + 70560.*xi*(eta*eta*eta) - 33600.*xi*eta*eta*eta*eta + 4900.*(eta*eta) + 105840.*(eta*eta)*(xi*xi) - 67200.*eta*eta*xi*xi*xi - 75600.*xi*xi*eta*eta*eta - 11760.*eta*eta*eta + 11760.*(eta*eta*eta*eta) - 4200.*eta*eta*eta*eta*eta, -19600.*eta*xi + 94080.*eta*(xi*xi) - 141120.*eta*xi*xi*xi + 67200.*eta*(xi*xi*xi*xi) + 3500.*xi + 35280.*xi*(eta*eta) - 23520.*xi*eta*eta*eta + 4200.*xi*(eta*eta*eta*eta) - 105840.*eta*eta*xi*xi + 75600.*(eta*eta)*(xi*xi*xi) - 24500.*xi*xi + 33600.*(xi*xi)*(eta*eta*eta) + 58800.*(xi*xi*xi) - 58800.*xi*xi*xi*xi + 21000.*(xi*xi*xi*xi*xi));
                case 17:
                  return RealGradient(6440.*eta*xi - 280.*eta - 30240.*eta*xi*xi + 43680.*eta*(xi*xi*xi) - 16800.*eta*xi*xi*xi*xi - 6720.*xi*eta*eta + 280.*(eta*eta) + 30240.*(eta*eta)*(xi*xi) - 33600.*eta*eta*xi*xi*xi, -1120.*eta*xi + 13440.*eta*(xi*xi) - 40320.*eta*xi*xi*xi + 33600.*eta*(xi*xi*xi*xi) + 560.*xi - 7280.*xi*xi + 26880.*(xi*xi*xi) - 36960.*xi*xi*xi*xi + 16800.*(xi*xi*xi*xi*xi));
                case 18:
                  return RealGradient(-3640.*eta*xi + 140.*eta + 20160.*eta*(xi*xi) - 36960.*eta*xi*xi*xi + 21000.*eta*(xi*xi*xi*xi) + 3360.*xi*(eta*eta) - 140.*eta*eta - 15120.*eta*eta*xi*xi + 16800.*(eta*eta)*(xi*xi*xi), 560.*eta*xi - 6720.*eta*xi*xi + 20160.*eta*(xi*xi*xi) - 16800.*eta*xi*xi*xi*xi - 700.*xi + 9100.*(xi*xi) - 33600.*xi*xi*xi + 46200.*(xi*xi*xi*xi) - 21000.*xi*xi*xi*xi*xi);
                case 19:
                  return RealGradient(560.*eta*xi - 700.*eta - 6720.*xi*eta*eta + 20160.*xi*(eta*eta*eta) - 16800.*xi*eta*eta*eta*eta + 9100.*(eta*eta) - 33600.*eta*eta*eta + 46200.*(eta*eta*eta*eta) - 21000.*eta*eta*eta*eta*eta, -3640.*eta*xi + 3360.*eta*(xi*xi) + 140.*xi + 20160.*xi*(eta*eta) - 36960.*xi*eta*eta*eta + 21000.*xi*(eta*eta*eta*eta) - 15120.*eta*eta*xi*xi - 140.*xi*xi + 16800.*(xi*xi)*(eta*eta*eta));
                case 20:
                  return RealGradient(-1120.*eta*xi + 560.*eta + 13440.*xi*(eta*eta) - 40320.*xi*eta*eta*eta + 33600.*xi*(eta*eta*eta*eta) - 7280.*eta*eta + 26880.*(eta*eta*eta) - 36960.*eta*eta*eta*eta + 16800.*(eta*eta*eta*eta*eta), 6440.*eta*xi - 6720.*eta*xi*xi - 280.*xi - 30240.*xi*eta*eta + 43680.*xi*(eta*eta*eta) - 16800.*xi*eta*eta*eta*eta + 30240.*(eta*eta)*(xi*xi) + 280.*(xi*xi) - 33600.*xi*xi*eta*eta*eta);
                case 21:
                  return RealGradient(17920.*eta*xi/3. - 420.*eta - 17920.*eta*xi*xi + 156800.*eta*(xi*xi*xi)/9. - 44800.*eta*xi*xi*xi*xi/9. - 29120.*xi*eta*eta + 116480.*xi*(eta*eta*eta)/3. - 140000.*xi*eta*eta*eta*eta/9. + 7420.*(eta*eta)/3. + 62720.*(eta*eta)*(xi*xi) - 291200.*eta*eta*xi*xi*xi/9. - 44800.*xi*xi*eta*eta*eta - 4480.*eta*eta*eta + 28840.*(eta*eta*eta*eta)/9. - 7000.*eta*eta*eta*eta*eta/9., -10360.*eta*xi/3. + 28000.*eta*(xi*xi) - 170240.*eta*xi*xi*xi/3. + 291200.*eta*(xi*xi*xi*xi)/9. + 420.*xi + 6720.*xi*(eta*eta) - 39200.*xi*eta*eta*eta/9. + 7000.*xi*(eta*eta*eta*eta)/9. - 40880.*eta*eta*xi*xi + 44800.*(eta*eta)*(xi*xi*xi) - 12460.*xi*xi/3. + 140000.*(xi*xi)*(eta*eta*eta)/9. + 35840.*(xi*xi*xi)/3. - 118720.*xi*xi*xi*xi/9. + 44800.*(xi*xi*xi*xi*xi)/9.);
                case 22:
                  return RealGradient(-12880.*eta*xi/3. + 280.*eta + 14560.*eta*(xi*xi) - 152320.*eta*xi*xi*xi/9. + 56000.*eta*(xi*xi*xi*xi)/9. + 22400.*xi*(eta*eta) - 91840.*xi*eta*eta*eta/3. + 112000.*xi*(eta*eta*eta*eta)/9. - 5320.*eta*eta/3. - 54880.*eta*eta*xi*xi + 313600.*(eta*eta)*(xi*xi*xi)/9. + 39200.*(xi*xi)*(eta*eta*eta) + 3360.*(eta*eta*eta) - 22400.*eta*eta*eta*eta/9. + 5600.*(eta*eta*eta*eta*eta)/9., 12040.*eta*xi/3. - 31360.*eta*xi*xi + 185920.*eta*(xi*xi*xi)/3. - 313600.*eta*xi*xi*xi*xi/9. - 560.*xi - 6720.*xi*eta*eta + 34720.*xi*(eta*eta*eta)/9. - 5600.*xi*eta*eta*eta*eta/9. + 38080.*(eta*eta)*(xi*xi) - 39200.*eta*eta*xi*xi*xi + 16240.*(xi*xi)/3. - 112000.*xi*xi*eta*eta*eta/9. - 45920.*xi*xi*xi/3. + 150080.*(xi*xi*xi*xi)/9. - 56000.*xi*xi*xi*xi*xi/9.);
                case 23:
                  return RealGradient(12040.*eta*xi/3. - 560.*eta - 6720.*eta*xi*xi + 34720.*eta*(xi*xi*xi)/9. - 5600.*eta*xi*xi*xi*xi/9. - 31360.*xi*eta*eta + 185920.*xi*(eta*eta*eta)/3. - 313600.*xi*eta*eta*eta*eta/9. + 16240.*(eta*eta)/3. + 38080.*(eta*eta)*(xi*xi) - 112000.*eta*eta*xi*xi*xi/9. - 39200.*xi*xi*eta*eta*eta - 45920.*eta*eta*eta/3. + 150080.*(eta*eta*eta*eta)/9. - 56000.*eta*eta*eta*eta*eta/9., -12880.*eta*xi/3. + 22400.*eta*(xi*xi) - 91840.*eta*xi*xi*xi/3. + 112000.*eta*(xi*xi*xi*xi)/9. + 280.*xi + 14560.*xi*(eta*eta) - 152320.*xi*eta*eta*eta/9. + 56000.*xi*(eta*eta*eta*eta)/9. - 54880.*eta*eta*xi*xi + 39200.*(eta*eta)*(xi*xi*xi) - 5320.*xi*xi/3. + 313600.*(xi*xi)*(eta*eta*eta)/9. + 3360.*(xi*xi*xi) - 22400.*xi*xi*xi*xi/9. + 5600.*(xi*xi*xi*xi*xi)/9.);
                case 24:
                  return RealGradient(-10360.*eta*xi/3. + 420.*eta + 6720.*eta*(xi*xi) - 39200.*eta*xi*xi*xi/9. + 7000.*eta*(xi*xi*xi*xi)/9. + 28000.*xi*(eta*eta) - 170240.*xi*eta*eta*eta/3. + 291200.*xi*(eta*eta*eta*eta)/9. - 12460.*eta*eta/3. - 40880.*eta*eta*xi*xi + 140000.*(eta*eta)*(xi*xi*xi)/9. + 44800.*(xi*xi)*(eta*eta*eta) + 35840.*(eta*eta*eta)/3. - 118720.*eta*eta*eta*eta/9. + 44800.*(eta*eta*eta*eta*eta)/9., 17920.*eta*xi/3. - 29120.*eta*xi*xi + 116480.*eta*(xi*xi*xi)/3. - 140000.*eta*xi*xi*xi*xi/9. - 420.*xi - 17920.*xi*eta*eta + 156800.*xi*(eta*eta*eta)/9. - 44800.*xi*eta*eta*eta*eta/9. + 62720.*(eta*eta)*(xi*xi) - 44800.*eta*eta*xi*xi*xi + 7420.*(xi*xi)/3. - 291200.*xi*xi*eta*eta*eta/9. - 4480.*xi*xi*xi + 28840.*(xi*xi*xi*xi)/9. - 7000.*xi*xi*xi*xi*xi/9.);
                case 25:
                  return RealGradient(-12880.*eta*xi/9. - 700.*eta/9. + 5600.*eta*(xi*xi) - 49280.*eta*xi*xi*xi/9. + 11200.*eta*(xi*xi*xi*xi)/9. - 15680.*xi*eta*eta/3. + 51520.*xi*(eta*eta*eta)/3. - 95200.*xi*eta*eta*eta*eta/9. + 25900.*(eta*eta)/9. - 1120.*eta*eta*xi*xi + 22400.*(eta*eta)*(xi*xi*xi)/9. - 5600.*xi*xi*eta*eta*eta - 28000.*eta*eta*eta/3. + 93800.*(eta*eta*eta*eta)/9. - 35000.*eta*eta*eta*eta*eta/9., -10360.*eta*xi/9. + 7840.*eta*(xi*xi)/3. + 2240.*eta*(xi*xi*xi)/3. - 22400.*eta*xi*xi*xi*xi/9. + 140.*xi/9. + 5600.*xi*(eta*eta) - 75040.*xi*eta*eta*eta/9. + 35000.*xi*(eta*eta*eta*eta)/9. - 12880.*eta*eta*xi*xi + 5600.*(eta*eta)*(xi*xi*xi) + 3220.*(xi*xi)/9. + 95200.*(xi*xi)*(eta*eta*eta)/9. - 5600.*xi*xi*xi/3. + 24640.*(xi*xi*xi*xi)/9. - 11200.*xi*xi*xi*xi*xi/9.);
                case 26:
                  return RealGradient(-9520.*eta*xi/9. + 1400.*eta/9. - 1120.*eta*xi*xi + 71680.*eta*(xi*xi*xi)/9. - 56000.*eta*xi*xi*xi*xi/9. + 44800.*xi*(eta*eta)/3. - 82880.*xi*eta*eta*eta/3. + 123200.*xi*(eta*eta*eta*eta)/9. - 14840.*eta*eta/9. - 25760.*eta*eta*xi*xi + 89600.*(eta*eta)*(xi*xi*xi)/9. + 28000.*(xi*xi)*(eta*eta*eta) + 12320.*(eta*eta*eta)/3. - 34720.*eta*eta*eta*eta/9. + 11200.*(eta*eta*eta*eta*eta)/9., 51800.*eta*xi/9. - 69440.*eta*xi*xi/3. + 82880.*eta*(xi*xi*xi)/3. - 89600.*eta*xi*xi*xi*xi/9. + 560.*xi/9. - 13440.*xi*eta*eta + 79520.*xi*(eta*eta*eta)/9. - 11200.*xi*eta*eta*eta*eta/9. + 40320.*(eta*eta)*(xi*xi) - 28000.*eta*eta*xi*xi*xi - 24080.*xi*xi/9. - 123200.*xi*xi*eta*eta*eta/9. + 32480.*(xi*xi*xi)/3. - 129920.*xi*xi*xi*xi/9. + 56000.*(xi*xi*xi*xi*xi)/9.);
                case 27:
                  return RealGradient(2800.*eta*xi/9. + 700.*eta/9. - 560.*eta*xi*xi - 1120.*eta*xi*xi*xi/9. + 1400.*eta*(xi*xi*xi*xi)/9. - 4480.*xi*eta*eta/3. - 11200.*xi*eta*eta*eta/3. + 44800.*xi*(eta*eta*eta*eta)/9. - 13300.*eta*eta/9. + 6160.*(eta*eta)*(xi*xi) - 22400.*eta*eta*xi*xi*xi/9. - 2800.*xi*xi*eta*eta*eta + 19600.*(eta*eta*eta)/3. - 81200.*eta*eta*eta*eta/9. + 35000.*(eta*eta*eta*eta*eta)/9., 5320.*eta*xi/9. + 2240.*eta*(xi*xi)/3. - 12320.*eta*xi*xi*xi/3. + 22400.*eta*(xi*xi*xi*xi)/9. - 140.*xi/9. - 3920.*xi*eta*eta + 64960.*xi*(eta*eta*eta)/9. - 35000.*xi*eta*eta*eta*eta/9. + 2800.*(eta*eta)*(xi*xi) + 2800.*(eta*eta)*(xi*xi*xi) - 700.*xi*xi/9. - 44800.*xi*xi*eta*eta*eta/9. + 560.*(xi*xi*xi)/3. + 560.*(xi*xi*xi*xi)/9. - 1400.*xi*xi*xi*xi*xi/9.);
                case 28:
                  return RealGradient(280.*eta*xi/9. - 980.*eta/9. + 1680.*eta*(xi*xi) - 11200.*eta*xi*xi*xi/9. - 7000.*eta*xi*xi*xi*xi/9. - 11200.*xi*eta*eta/3. + 52640.*xi*(eta*eta*eta)/3. - 123200.*xi*eta*eta*eta*eta/9. + 13580.*(eta*eta)/9. - 9520.*eta*eta*xi*xi + 112000.*(eta*eta)*(xi*xi*xi)/9. - 2800.*xi*xi*eta*eta*eta - 16240.*eta*eta*eta/3. + 59920.*(eta*eta*eta*eta)/9. - 23800.*eta*eta*eta*eta*eta/9., -8960.*eta*xi/9. - 17920.*eta*xi*xi/3. + 58240.*eta*(xi*xi*xi)/3. - 112000.*eta*xi*xi*xi*xi/9. - 140.*xi/9. + 9520.*xi*(eta*eta) - 99680.*xi*eta*eta*eta/9. + 23800.*xi*(eta*eta*eta*eta)/9. - 15120.*eta*eta*xi*xi + 2800.*(eta*eta)*(xi*xi*xi) + 4340.*(xi*xi)/9. + 123200.*(xi*xi)*(eta*eta*eta)/9. - 560.*xi*xi*xi - 6160.*xi*xi*xi*xi/9. + 7000.*(xi*xi*xi*xi*xi)/9.);
                case 29:
                  return RealGradient(51800.*eta*xi/9. + 560.*eta/9. - 13440.*eta*xi*xi + 79520.*eta*(xi*xi*xi)/9. - 11200.*eta*xi*xi*xi*xi/9. - 69440.*xi*eta*eta/3. + 82880.*xi*(eta*eta*eta)/3. - 89600.*xi*eta*eta*eta*eta/9. - 24080.*eta*eta/9. + 40320.*(eta*eta)*(xi*xi) - 123200.*eta*eta*xi*xi*xi/9. - 28000.*xi*xi*eta*eta*eta + 32480.*(eta*eta*eta)/3. - 129920.*eta*eta*eta*eta/9. + 56000.*(eta*eta*eta*eta*eta)/9., -9520.*eta*xi/9. + 44800.*eta*(xi*xi)/3. - 82880.*eta*xi*xi*xi/3. + 123200.*eta*(xi*xi*xi*xi)/9. + 1400.*xi/9. - 1120.*xi*eta*eta + 71680.*xi*(eta*eta*eta)/9. - 56000.*xi*eta*eta*eta*eta/9. - 25760.*eta*eta*xi*xi + 28000.*(eta*eta)*(xi*xi*xi) - 14840.*xi*xi/9. + 89600.*(xi*xi)*(eta*eta*eta)/9. + 12320.*(xi*xi*xi)/3. - 34720.*xi*xi*xi*xi/9. + 11200.*(xi*xi*xi*xi*xi)/9.);
                case 30:
                  return RealGradient(-10360.*eta*xi/9. + 140.*eta/9. + 5600.*eta*(xi*xi) - 75040.*eta*xi*xi*xi/9. + 35000.*eta*(xi*xi*xi*xi)/9. + 7840.*xi*(eta*eta)/3. + 2240.*xi*(eta*eta*eta)/3. - 22400.*xi*eta*eta*eta*eta/9. + 3220.*(eta*eta)/9. - 12880.*eta*eta*xi*xi + 95200.*(eta*eta)*(xi*xi*xi)/9. + 5600.*(xi*xi)*(eta*eta*eta) - 5600.*eta*eta*eta/3. + 24640.*(eta*eta*eta*eta)/9. - 11200.*eta*eta*eta*eta*eta/9., -12880.*eta*xi/9. - 15680.*eta*xi*xi/3. + 51520.*eta*(xi*xi*xi)/3. - 95200.*eta*xi*xi*xi*xi/9. - 700.*xi/9. + 5600.*xi*(eta*eta) - 49280.*xi*eta*eta*eta/9. + 11200.*xi*(eta*eta*eta*eta)/9. - 1120.*eta*eta*xi*xi - 5600.*eta*eta*xi*xi*xi + 25900.*(xi*xi)/9. + 22400.*(xi*xi)*(eta*eta*eta)/9. - 28000.*xi*xi*xi/3. + 93800.*(xi*xi*xi*xi)/9. - 35000.*xi*xi*xi*xi*xi/9.);
                case 31:
                  return RealGradient(-8960.*eta*xi/9. - 140.*eta/9. + 9520.*eta*(xi*xi) - 99680.*eta*xi*xi*xi/9. + 23800.*eta*(xi*xi*xi*xi)/9. - 17920.*xi*eta*eta/3. + 58240.*xi*(eta*eta*eta)/3. - 112000.*xi*eta*eta*eta*eta/9. + 4340.*(eta*eta)/9. - 15120.*eta*eta*xi*xi + 123200.*(eta*eta)*(xi*xi*xi)/9. + 2800.*(xi*xi)*(eta*eta*eta) - 560.*eta*eta*eta - 6160.*eta*eta*eta*eta/9. + 7000.*(eta*eta*eta*eta*eta)/9., 280.*eta*xi/9. - 11200.*eta*xi*xi/3. + 52640.*eta*(xi*xi*xi)/3. - 123200.*eta*xi*xi*xi*xi/9. - 980.*xi/9. + 1680.*xi*(eta*eta) - 11200.*xi*eta*eta*eta/9. - 7000.*xi*eta*eta*eta*eta/9. - 9520.*eta*eta*xi*xi - 2800.*eta*eta*xi*xi*xi + 13580.*(xi*xi)/9. + 112000.*(xi*xi)*(eta*eta*eta)/9. - 16240.*xi*xi*xi/3. + 59920.*(xi*xi*xi*xi)/9. - 23800.*xi*xi*xi*xi*xi/9.);
                case 32:
                  return RealGradient(5320.*eta*xi/9. - 140.*eta/9. - 3920.*eta*xi*xi + 64960.*eta*(xi*xi*xi)/9. - 35000.*eta*xi*xi*xi*xi/9. + 2240.*xi*(eta*eta)/3. - 12320.*xi*eta*eta*eta/3. + 22400.*xi*(eta*eta*eta*eta)/9. - 700.*eta*eta/9. + 2800.*(eta*eta)*(xi*xi) - 44800.*eta*eta*xi*xi*xi/9. + 2800.*(xi*xi)*(eta*eta*eta) + 560.*(eta*eta*eta)/3. + 560.*(eta*eta*eta*eta)/9. - 1400.*eta*eta*eta*eta*eta/9., 2800.*eta*xi/9. - 4480.*eta*xi*xi/3. - 11200.*eta*xi*xi*xi/3. + 44800.*eta*(xi*xi*xi*xi)/9. + 700.*xi/9. - 560.*xi*eta*eta - 1120.*xi*eta*eta*eta/9. + 1400.*xi*(eta*eta*eta*eta)/9. + 6160.*(eta*eta)*(xi*xi) - 2800.*eta*eta*xi*xi*xi - 13300.*xi*xi/9. - 22400.*xi*xi*eta*eta*eta/9. + 19600.*(xi*xi*xi)/3. - 81200.*xi*xi*xi*xi/9. + 35000.*(xi*xi*xi*xi*xi)/9.);
                case 33:
                  return RealGradient(-6440.*eta*xi/9. + 280.*eta/9. + 1680.*eta*(xi*xi) - 4480.*eta*xi*xi*xi/3. + 1400.*eta*(xi*xi*xi*xi)/3. + 19040.*xi*(eta*eta)/3. - 11200.*xi*eta*eta*eta + 5600.*xi*(eta*eta*eta*eta) - 2800.*eta*eta/9. - 9520.*eta*eta*xi*xi + 11200.*(eta*eta)*(xi*xi*xi)/3. + 8400.*(xi*xi)*(eta*eta*eta) + 560.*(eta*eta*eta) - 280.*eta*eta*eta*eta, 6160.*eta*xi/9. - 14560.*eta*xi*xi/3. + 7840.*eta*(xi*xi*xi) - 11200.*eta*xi*xi*xi*xi/3. - 560.*xi/9. - 1680.*xi*eta*eta + 1120.*xi*(eta*eta*eta) + 10080.*(eta*eta)*(xi*xi) - 8400.*eta*eta*xi*xi*xi + 4760.*(xi*xi)/9. - 5600.*xi*xi*eta*eta*eta - 3920.*xi*xi*xi/3. + 3920.*(xi*xi*xi*xi)/3. - 1400.*xi*xi*xi*xi*xi/3.);
                case 34:
                  return RealGradient(6160.*eta*xi/9. - 560.*eta/9. - 1680.*eta*xi*xi + 1120.*eta*(xi*xi*xi) - 14560.*xi*eta*eta/3. + 7840.*xi*(eta*eta*eta) - 11200.*xi*eta*eta*eta*eta/3. + 4760.*(eta*eta)/9. + 10080.*(eta*eta)*(xi*xi) - 5600.*eta*eta*xi*xi*xi - 8400.*xi*xi*eta*eta*eta - 3920.*eta*eta*eta/3. + 3920.*(eta*eta*eta*eta)/3. - 1400.*eta*eta*eta*eta*eta/3., -6440.*eta*xi/9. + 19040.*eta*(xi*xi)/3. - 11200.*eta*xi*xi*xi + 5600.*eta*(xi*xi*xi*xi) + 280.*xi/9. + 1680.*xi*(eta*eta) - 4480.*xi*eta*eta*eta/3. + 1400.*xi*(eta*eta*eta*eta)/3. - 9520.*eta*eta*xi*xi + 8400.*(eta*eta)*(xi*xi*xi) - 2800.*xi*xi/9. + 11200.*(xi*xi)*(eta*eta*eta)/3. + 560.*(xi*xi*xi) - 280.*xi*xi*xi*xi);
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          } // end switch (type)
      } // end case FIFTH
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 2D FE order!: " << totalorder);
    }
#else // LIBMESH_DIM > 1
  libmesh_ignore(elem, order, i, p, add_p_level);
  libmesh_not_implemented();
#endif
}

shape() [67/195]

RealGradient libMesh::FE< 3, NEDELEC_ONE >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 28 of file fe_nedelec_one_shape_3D.C.

{
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = elem->positive_edge_orientation(i) ? 1 : -1;
 
  const Real xi   = p(0);
  const Real eta  = p(1);
  const Real zeta = p(2);
 
  switch (totalorder)
    {
      // linear Nedelec (first kind) shape functions
    case FIRST:
      {
        switch (elem->type())
          {
          case HEX20:
          case HEX27:
            {
              // Even with a loose inverse_map tolerance we ought to
              // be nearly on the element interior in master
              // coordinates
              libmesh_assert_less_equal ( std::fabs(xi),   1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(eta),  1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(zeta), 1.0+10*TOLERANCE );
 
              switch(i)
                {
                case 0:
                  return sign * RealGradient( -0.125*(1.0-eta-zeta+eta*zeta), 0.0, 0.0 );
                case 1:
                  return sign * RealGradient( 0.0, -0.125*(1.0+xi-zeta-xi*zeta), 0.0 );
                case 2:
                  return sign * RealGradient( 0.125*(1.0+eta-zeta-eta*zeta), 0.0, 0.0 );
                case 3:
                  return sign * RealGradient( 0.0, -0.125*(1.0-xi-zeta+xi*zeta), 0.0 );
                case 4:
                  return sign * RealGradient( 0.0, 0.0, -0.125*(1.0-xi-eta+xi*eta) );
                case 5:
                  return sign * RealGradient( 0.0, 0.0, -0.125*(1.0+xi-eta-xi*eta) );
                case 6:
                  return sign * RealGradient( 0.0, 0.0, -0.125*(1.0+xi+eta+xi*eta) );
                case 7:
                  return sign * RealGradient( 0.0, 0.0, -0.125*(1.0-xi+eta-xi*eta) );
                case 8:
                  return sign * RealGradient( -0.125*(1.0-eta+zeta-eta*zeta), 0.0, 0.0 );
                case 9:
                  return sign * RealGradient( 0.0, -0.125*(1.0+xi+zeta+xi*zeta), 0.0 );
                case 10:
                  return sign * RealGradient( 0.125*(1.0+eta+zeta+eta*zeta), 0.0, 0.0 );
                case 11:
                  return sign * RealGradient( 0.0, -0.125*(1.0-xi+zeta-xi*zeta), 0.0 );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          case TET10:
          case TET14:
            {
              switch(i)
                {
                case 0:
                  return sign * RealGradient( -1.0+eta+zeta, -xi, -xi );
                case 1:
                  return sign * RealGradient( eta, -xi, 0.0 );
                case 2:
                  return sign * RealGradient( -eta, -1.0+xi+zeta, -eta );
                case 3:
                  return sign * RealGradient( -zeta, -zeta, -1.0+xi+eta );
                case 4:
                  return sign * RealGradient( zeta, 0.0, -xi );
                case 5:
                  return sign * RealGradient( 0.0, zeta, -eta );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, p, add_p_level);
  libmesh_not_implemented();
#endif
}

shape() [68/195]

Real libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 44 of file fe_rational_shape_1D.C.

{
  libmesh_assert(elem);
 
  // FEType object for the non-rational basis underlying this one
  FEType fe_type(order, _underlying_fe_family);
 
  return rational_fe_shape(*elem, fe_type, i, p, add_p_level);
}

shape() [69/195]

Real libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 42 of file fe_rational_shape_2D.C.

{
  libmesh_assert(elem);
 
  // FEType object for the non-rational basis underlying this one
  FEType fe_type(order, _underlying_fe_family);
 
  return rational_fe_shape(*elem, fe_type, i, p, add_p_level);
}

shape() [70/195]

Real libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 42 of file fe_rational_shape_3D.C.

{
  libmesh_assert(elem);
 
  // FEType object for the non-rational basis underlying this one
  FEType fe_type(order, _underlying_fe_family);
 
  return rational_fe_shape(*elem, fe_type, i, p, add_p_level);
}

shape() [71/195]

RealGradient libMesh::FE< 2, RAVIART_THOMAS >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 30 of file fe_raviart_shape_2D.C.

{
  RealGradient ND1 = FE<2,NEDELEC_ONE>::shape(elem, order, i, p, add_p_level);
  return RealGradient(-ND1(1), ND1(0));
}

shape() [72/195]

RealGradient libMesh::FE< 2, L2_RAVIART_THOMAS >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 41 of file fe_raviart_shape_2D.C.

{
  return FE<2,RAVIART_THOMAS>::shape(elem, order, i, p, add_p_level);
}

shape() [73/195]

RealGradient libMesh::FE< 3, RAVIART_THOMAS >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 28 of file fe_raviart_shape_3D.C.

{
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = elem->positive_face_orientation(i) ? 1 : -1;
 
  const Real xi   = p(0);
  const Real eta  = p(1);
  const Real zeta = p(2);
 
  switch (totalorder)
    {
      // linear Raviart-Thomas shape functions
    case FIRST:
      {
        switch (elem->type())
          {
          case HEX27:
            {
              // Even with a loose inverse_map tolerance we ought to
              // be nearly on the element interior in master
              // coordinates
              libmesh_assert_less_equal ( std::fabs(xi),   1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(eta),  1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(zeta), 1.0+10*TOLERANCE );
 
              switch(i)
                {
                case 0:
                  return sign * RealGradient( 0.0, 0.0, 0.125*(zeta-1.0) );
                case 1:
                  return sign * RealGradient( 0.0, 0.125*(eta-1.0), 0.0 );
                case 2:
                  return sign * RealGradient( 0.125*(xi+1.0), 0.0, 0.0 );
                case 3:
                  return sign * RealGradient( 0.0, 0.125*(1.0+eta), 0.0 );
                case 4:
                  return sign * RealGradient( 0.125*(xi-1.0), 0.0, 0.0 );
                case 5:
                  return sign * RealGradient( 0.0, 0.0, 0.125*(1.0+zeta) );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          case TET14:
            {
              switch(i)
                {
                case 0:
                  return sign * RealGradient( 2.0*xi, 2.0*eta, 2.0*zeta-2.0 );
                case 1:
                  return sign * RealGradient( 2.0*xi, 2.0*eta-2.0, 2.0*zeta );
                case 2:
                  return sign * RealGradient( 2.0*xi, 2.0*eta, 2.0*zeta );
                case 3:
                  return sign * RealGradient( 2.0*xi-2.0, 2.0*eta, 2.0*zeta );
 
                default:
                  libmesh_error_msg("Invalid i = " << i);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, p, add_p_level);
  libmesh_not_implemented();
#endif
}

shape() [74/195]

RealGradient libMesh::FE< 3, L2_RAVIART_THOMAS >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 118 of file fe_raviart_shape_3D.C.

{
  return FE<3,RAVIART_THOMAS>::shape(elem, order, i, p, add_p_level);
}

shape() [75/195]

Real libMesh::FE< 2, SUBDIVISION >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 735 of file fe_subdivision_2D.C.

{
  libmesh_assert(elem);
  const Order totalorder = order + add_p_level*elem->p_level();
  return FE<2,SUBDIVISION>::shape(elem->type(), totalorder, i, p);
}

shape() [76/195]

Real libMesh::FE< 1, SZABAB >::shape ( const Elem *  elem, const Order  order, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 83 of file fe_szabab_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape(elem->type(), order + add_p_level*elem->p_level(), i, p);
}

shape() [77/195]

Real libMesh::FE< 3, CLOUGH >::shape ( const Elem *  libmesh_dbg_varelem, const Order  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 48 of file fe_clough_shape_3D.C.

{
  libmesh_assert(elem);
 
  libmesh_not_implemented();
  return 0.;
}

shape() [78/195]

Real libMesh::FE< 1, L2_HIERARCHIC >::shape ( const ElemType  elem_type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 78 of file fe_hierarchic_shape_1D.C.

{
  return fe_hierarchic_1D_shape(elem_type, order, i, p);
}

shape() [79/195]

static OutputShape libMesh::FE< Dim, T >::shape ( const ElemType  t, const Order  o, const unsigned int  i, const Point &  p  )

staticinherited

Returns

The value of the \( i^{th} \) shape function at point p. This method allows you to specify the dimension, element type, and order directly. This allows the method to be static.

On a p-refined element, o should be the total order of the element.

shape() [80/195]

RealGradient libMesh::FE< 0, L2_HIERARCHIC_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 155 of file fe_hierarchic_vec.C.

{
  return FE<0,HIERARCHIC_VEC>::shape(type, order, i, p);
}

shape() [81/195]

RealGradient libMesh::FE< 1, HIERARCHIC_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 178 of file fe_hierarchic_vec.C.

{
  Real value = FE<1,HIERARCHIC>::shape( type, order, i, p );
  return libMesh::RealGradient( value );
}

shape() [82/195]

RealGradient libMesh::FE< 1, L2_HIERARCHIC_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 202 of file fe_hierarchic_vec.C.

{
  return FE<1,HIERARCHIC_VEC>::shape(type, order, i, p);
}

shape() [83/195]

RealGradient libMesh::FE< 2, HIERARCHIC_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 225 of file fe_hierarchic_vec.C.

{
  Real value = FE<2,HIERARCHIC>::shape( type, order, i/2, p );
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape() [84/195]

RealGradient libMesh::FE< 2, L2_HIERARCHIC_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 292 of file fe_hierarchic_vec.C.

{
  return FE<2,HIERARCHIC_VEC>::shape(type, order, i, p);
}

shape() [85/195]

RealGradient libMesh::FE< 3, HIERARCHIC_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 316 of file fe_hierarchic_vec.C.

{
  Real value = FE<3,HIERARCHIC>::shape( type, order, i/3, p );
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape() [86/195]

RealGradient libMesh::FE< 3, L2_HIERARCHIC_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 393 of file fe_hierarchic_vec.C.

{
  return FE<3,HIERARCHIC_VEC>::shape(type, order, i, p);
}

shape() [87/195]

Real libMesh::FE< 2, L2_LAGRANGE >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 84 of file fe_lagrange_shape_2D.C.

{
  return fe_lagrange_2D_shape<L2_LAGRANGE>(type, nullptr, order, i, p);
}

shape() [88/195]

Real libMesh::FE< 3, LAGRANGE >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 419 of file fe_lagrange_shape_3D.C.

{
  return fe_lagrange_3D_shape<LAGRANGE>(type, order, nullptr, i, p);
}

shape() [89/195]

Real libMesh::FE< 3, L2_LAGRANGE >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 430 of file fe_lagrange_shape_3D.C.

{
  return fe_lagrange_3D_shape<L2_LAGRANGE>(type, order, nullptr, i, p);
}

shape() [90/195]

RealGradient libMesh::FE< 0, L2_LAGRANGE_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 695 of file fe_lagrange_vec.C.

{
  return FE<0,LAGRANGE_VEC>::shape(type, order, i, p);
}

shape() [91/195]

RealGradient libMesh::FE< 1, LAGRANGE_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 718 of file fe_lagrange_vec.C.

{
  Real value = FE<1,LAGRANGE>::shape( type, order, i, p );
  return libMesh::RealGradient( value );
}

shape() [92/195]

RealGradient libMesh::FE< 1, L2_LAGRANGE_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 742 of file fe_lagrange_vec.C.

{
  return FE<1,LAGRANGE_VEC>::shape(type, order, i, p);
}

shape() [93/195]

RealGradient libMesh::FE< 2, LAGRANGE_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 765 of file fe_lagrange_vec.C.

{
  Real value = FE<2,LAGRANGE>::shape( type, order, i/2, p );
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape() [94/195]

RealGradient libMesh::FE< 2, L2_LAGRANGE_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 832 of file fe_lagrange_vec.C.

{
  return FE<2,LAGRANGE_VEC>::shape(type, order, i, p);
}

shape() [95/195]

RealGradient libMesh::FE< 3, LAGRANGE_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 856 of file fe_lagrange_vec.C.

{
  Real value = FE<3,LAGRANGE>::shape( type, order, i/3, p );
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape() [96/195]

RealGradient libMesh::FE< 3, L2_LAGRANGE_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 933 of file fe_lagrange_vec.C.

{
  return FE<3,LAGRANGE_VEC>::shape(type, order, i, p);
}

shape() [97/195]

RealVectorValue libMesh::FE< 1, MONOMIAL_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 186 of file fe_monomial_vec.C.

{
  Real value = FE<1, MONOMIAL>::shape(type, order, i, p);
  return libMesh::RealVectorValue(value);
}

shape() [98/195]

RealVectorValue libMesh::FE< 2, MONOMIAL_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 223 of file fe_monomial_vec.C.

{
  Real value = FE<2, MONOMIAL>::shape(type, order, i / 2, p);
 
  switch (i % 2)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape() [99/195]

RealVectorValue libMesh::FE< 3, MONOMIAL_VEC >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 303 of file fe_monomial_vec.C.

{
  Real value = FE<3, MONOMIAL>::shape(type, order, i / 3, p);
 
  switch (i % 3)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    case 2:
      return libMesh::RealVectorValue(Real(0), Real(0), value);
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape() [100/195]

Real libMesh::FE< 2, SUBDIVISION >::shape ( const ElemType  type, const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 709 of file fe_subdivision_2D.C.

{
  switch (order)
    {
    case FOURTH:
      {
        switch (type)
          {
          case TRI3SUBDIVISION:
            libmesh_assert_less(i, 12);
            return FESubdivision::regular_shape(i,p(0),p(1));
          default:
            libmesh_error_msg("ERROR: Unsupported element type == " << Utility::enum_to_string(type));
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order == " << order);
    }
}

shape() [101/195]

Real libMesh::FE< 1, L2_LAGRANGE >::shape ( const ElemType  , const Order  order, const unsigned int  i, const Point &  p  )

inherited

Definition at line 43 of file fe_lagrange_shape_1D.C.

{
  return fe_lagrange_1D_shape(order, i, p(0));
}

shape() [102/195]

Real libMesh::FE< 1, SIDE_HIERARCHIC >::shape ( const ElemType  , const Order  , const unsigned int  i, const Point &  p  )

inherited

Definition at line 89 of file fe_hierarchic_shape_1D.C.

{
  unsigned int right_side = p(0) > 0; // 0 false, 1 true
  return (right_side == i);
}

shape() [103/195]

Real libMesh::FE< 0, L2_HIERARCHIC >::shape ( const ElemType  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &    )

inherited

Definition at line 47 of file fe_hierarchic_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [104/195]

Real libMesh::FE< 0, LAGRANGE >::shape ( const ElemType  , const Order  , const unsigned int  libmesh_dbg_vari, const Point &    )

inherited

Definition at line 44 of file fe_lagrange_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [105/195]

Real libMesh::FE< 2, BERNSTEIN >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 393 of file fe_bernstein_shape_2D.C.

{
  libmesh_error_msg("Bernstein polynomials require the element type \nbecause edge orientation is needed.");
  return 0.;
}

shape() [106/195]

Real libMesh::FE< 3, BERNSTEIN >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 894 of file fe_bernstein_shape_3D.C.

{
  libmesh_error_msg("Bernstein polynomials require the element type \nbecause edge and face orientation is needed.");
  return 0.;
}

shape() [107/195]

Real libMesh::FE< 1, CLOUGH >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 281 of file fe_clough_shape_1D.C.

{
  libmesh_error_msg("Clough-Tocher elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape() [108/195]

Real libMesh::FE< 2, CLOUGH >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 1946 of file fe_clough_shape_2D.C.

{
  libmesh_error_msg("Clough-Tocher elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape() [109/195]

Real libMesh::FE< 1, HERMITE >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 234 of file fe_hermite_shape_1D.C.

{
  libmesh_error_msg("Hermite elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape() [110/195]

Real libMesh::FE< 2, HERMITE >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 248 of file fe_hermite_shape_2D.C.

{
  libmesh_error_msg("Hermite elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape() [111/195]

Real libMesh::FE< 3, HERMITE >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 443 of file fe_hermite_shape_3D.C.

{
  libmesh_error_msg("Hermite elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape() [112/195]

Real libMesh::FE< 0, SIDE_HIERARCHIC >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 59 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No side variables in 0D!");
  return 1.;
}

shape() [113/195]

Real libMesh::FE< 2, L2_HIERARCHIC >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 149 of file fe_hierarchic_shape_2D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge orientation.");
  return 0.;
}

shape() [114/195]

Real libMesh::FE< 2, SIDE_HIERARCHIC >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 161 of file fe_hierarchic_shape_2D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge orientation.");
  return 0.;
}

shape() [115/195]

Real libMesh::FE< 3, L2_HIERARCHIC >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 1177 of file fe_hierarchic_shape_3D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge/face orientation.");
  return 0.;
}

shape() [116/195]

Real libMesh::FE< 3, SIDE_HIERARCHIC >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 1189 of file fe_hierarchic_shape_3D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge/face orientation.");
  return 0.;
}

shape() [117/195]

RealGradient libMesh::FE< 0, NEDELEC_ONE >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 457 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape() [118/195]

RealGradient libMesh::FE< 1, NEDELEC_ONE >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 484 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape() [119/195]

RealGradient libMesh::FE< 2, NEDELEC_ONE >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 685 of file fe_nedelec_one_shape_2D.C.

{
  libmesh_error_msg("Nedelec elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape() [120/195]

RealGradient libMesh::FE< 3, NEDELEC_ONE >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 136 of file fe_nedelec_one_shape_3D.C.

{
  libmesh_error_msg("Nedelec elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape() [121/195]

Real libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 61 of file fe_rational_shape_1D.C.

{
  libmesh_error_msg("Rational bases require the real element \nto query nodal weighting.");
  return 0.;
}

shape() [122/195]

Real libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 59 of file fe_rational_shape_2D.C.

{
  libmesh_error_msg("Rational bases require the real element \nto query nodal weighting.");
  return 0.;
}

shape() [123/195]

Real libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 59 of file fe_rational_shape_3D.C.

{
  libmesh_error_msg("Rational bases require the real element \nto query nodal weighting.");
  return 0.;
}

shape() [124/195]

RealGradient libMesh::FE< 0, RAVIART_THOMAS >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 549 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape() [125/195]

RealGradient libMesh::FE< 0, L2_RAVIART_THOMAS >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 555 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape() [126/195]

RealGradient libMesh::FE< 1, RAVIART_THOMAS >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 598 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape() [127/195]

RealGradient libMesh::FE< 1, L2_RAVIART_THOMAS >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 604 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape() [128/195]

RealGradient libMesh::FE< 2, RAVIART_THOMAS >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 51 of file fe_raviart_shape_2D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape() [129/195]

RealGradient libMesh::FE< 2, L2_RAVIART_THOMAS >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 61 of file fe_raviart_shape_2D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape() [130/195]

RealGradient libMesh::FE< 3, RAVIART_THOMAS >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 129 of file fe_raviart_shape_3D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}

shape() [131/195]

RealGradient libMesh::FE< 3, L2_RAVIART_THOMAS >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 140 of file fe_raviart_shape_3D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}

shape() [132/195]

Real libMesh::FE< 2, SZABAB >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 644 of file fe_szabab_shape_2D.C.

{
  libmesh_error_msg("Szabo-Babuska polynomials require the element type \nbecause edge orientation is needed.");
  return 0.;
}

shape() [133/195]

Real libMesh::FE< 1, XYZ >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 84 of file fe_xyz_shape_1D.C.

{
  libmesh_error_msg("XYZ polynomials require the element.");
  return 0.;
}

shape() [134/195]

Real libMesh::FE< 2, XYZ >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 148 of file fe_xyz_shape_2D.C.

{
  libmesh_error_msg("XYZ polynomials require the element.");
  return 0.;
}

shape() [135/195]

Real libMesh::FE< 3, XYZ >::shape ( const ElemType  , const Order  , const unsigned int  , const Point &    )

inherited

Definition at line 216 of file fe_xyz_shape_3D.C.

{
  libmesh_error_msg("XYZ polynomials require the element.");
  return 0.;
}

shape() [136/195]

Real libMesh::FE< 1, BERNSTEIN >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 208 of file fe_bernstein_shape_1D.C.

{
  libmesh_assert(elem);
  return FE<1,BERNSTEIN>::shape
    (elem->type(),
     fet.order + add_p_level*elem->p_level(), i, p);
}

shape() [137/195]

Real libMesh::FE< 2, BERNSTEIN >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 404 of file fe_bernstein_shape_2D.C.

{
  return FE<2,BERNSTEIN>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [138/195]

Real libMesh::FE< 3, BERNSTEIN >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 905 of file fe_bernstein_shape_3D.C.

{
  return FE<3,BERNSTEIN>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [139/195]

Real libMesh::FE< 1, CLOUGH >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 291 of file fe_clough_shape_1D.C.

{
  return FE<1,CLOUGH>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [140/195]

Real libMesh::FE< 2, CLOUGH >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1957 of file fe_clough_shape_2D.C.

{
  return FE<2,CLOUGH>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [141/195]

Real libMesh::FE< 1, HERMITE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 245 of file fe_hermite_shape_1D.C.

{
  return FE<1,HERMITE>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [142/195]

Real libMesh::FE< 2, HERMITE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 259 of file fe_hermite_shape_2D.C.

{
  return FE<2,HERMITE>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [143/195]

Real libMesh::FE< 3, HERMITE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 453 of file fe_hermite_shape_3D.C.

{
  return FE<3,HERMITE>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [144/195]

Real libMesh::FE< 1, HIERARCHIC >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 115 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_hierarchic_1D_shape(elem->type(), fet.order + add_p_level*elem->p_level(), i, p);
}

shape() [145/195]

Real libMesh::FE< 1, L2_HIERARCHIC >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 142 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_hierarchic_1D_shape(elem->type(), fet.order + add_p_level*elem->p_level(), i, p);
}

shape() [146/195]

Real libMesh::FE< 2, HIERARCHIC >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 185 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape<HIERARCHIC>(elem, fet.order, i, p, add_p_level);
}

shape() [147/195]

Real libMesh::FE< 2, L2_HIERARCHIC >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 207 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape<L2_HIERARCHIC>(elem, fet.order, i, p, add_p_level);
}

shape() [148/195]

Real libMesh::FE< 2, SIDE_HIERARCHIC >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 391 of file fe_hierarchic_shape_2D.C.

{
  return FE<2,SIDE_HIERARCHIC>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [149/195]

Real libMesh::FE< 3, HIERARCHIC >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1212 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape<HIERARCHIC>(elem, fet.order, i, p, add_p_level);
}

shape() [150/195]

Real libMesh::FE< 3, L2_HIERARCHIC >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1236 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape<L2_HIERARCHIC>(elem, fet.order, i, p, add_p_level);
}

shape() [151/195]

Real libMesh::FE< 3, SIDE_HIERARCHIC >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1498 of file fe_hierarchic_shape_3D.C.

{
  return FE<3,SIDE_HIERARCHIC>::shape(elem,fet.order, i, p, add_p_level);
}

shape() [152/195]

Real libMesh::FE< 1, LAGRANGE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 67 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_1D_shape(fet.order + add_p_level*elem->p_level(), i, p(0));
}

shape() [153/195]

Real libMesh::FE< 1, L2_LAGRANGE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 90 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_1D_shape(fet.order + add_p_level*elem->p_level(), i, p(0));
}

shape() [154/195]

Real libMesh::FE< 2, LAGRANGE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 123 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_2D_shape<LAGRANGE>(elem->type(), elem, fet.order + add_p_level*elem->p_level(), i, p);
}

shape() [155/195]

Real libMesh::FE< 2, L2_LAGRANGE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 136 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_2D_shape<L2_LAGRANGE>(elem->type(), elem, fet.order + add_p_level*elem->p_level(), i, p);
}

shape() [156/195]

Real libMesh::FE< 3, LAGRANGE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 471 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_3D_shape<LAGRANGE>(elem->type(), fet.order + add_p_level*elem->p_level(), elem, i, p);
}

shape() [157/195]

Real libMesh::FE< 3, L2_LAGRANGE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 484 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_3D_shape<L2_LAGRANGE>(elem->type(), fet.order + add_p_level*elem->p_level(), elem, i, p);
}

shape() [158/195]

Real libMesh::FE< 1, MONOMIAL >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 85 of file fe_monomial_shape_1D.C.

{
  libmesh_assert(elem);
  return FE<1,MONOMIAL>::shape(elem->type(), fet.order + add_p_level*elem->p_level(), i, p);
}

shape() [159/195]

Real libMesh::FE< 2, MONOMIAL >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 136 of file fe_monomial_shape_2D.C.

{
  libmesh_assert(elem);
  // by default call the orientation-independent shape functions
  return FE<2,MONOMIAL>::shape(elem->type(), fet.order + add_p_level*elem->p_level(), i, p);
}

shape() [160/195]

Real libMesh::FE< 3, MONOMIAL >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 205 of file fe_monomial_shape_3D.C.

{
  libmesh_assert(elem);
  // by default call the orientation-independent shape functions
  return FE<3,MONOMIAL>::shape(elem->type(), fet.order + add_p_level*elem->p_level(), i, p);
}

shape() [161/195]

RealGradient libMesh::FE< 2, NEDELEC_ONE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 696 of file fe_nedelec_one_shape_2D.C.

{
  return FE<2,NEDELEC_ONE>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [162/195]

RealGradient libMesh::FE< 3, NEDELEC_ONE >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 147 of file fe_nedelec_one_shape_3D.C.

{
  return FE<3,NEDELEC_ONE>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [163/195]

Real libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 72 of file fe_rational_shape_1D.C.

{
  libmesh_assert(elem);
  return FE<1,RATIONAL_BERNSTEIN>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [164/195]

Real libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 71 of file fe_rational_shape_2D.C.

{
  return FE<2,RATIONAL_BERNSTEIN>::shape
    (elem, fet.order, i, p, add_p_level);
}

shape() [165/195]

Real libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 69 of file fe_rational_shape_3D.C.

{
  return FE<3,RATIONAL_BERNSTEIN>::shape
    (elem, fet.order, i, p, add_p_level);
}

shape() [166/195]

RealGradient libMesh::FE< 2, RAVIART_THOMAS >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 71 of file fe_raviart_shape_2D.C.

{
  return FE<2,RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [167/195]

RealGradient libMesh::FE< 2, L2_RAVIART_THOMAS >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 81 of file fe_raviart_shape_2D.C.

{
  return FE<2,L2_RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [168/195]

RealGradient libMesh::FE< 3, RAVIART_THOMAS >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 151 of file fe_raviart_shape_3D.C.

{
  return FE<3,RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [169/195]

RealGradient libMesh::FE< 3, L2_RAVIART_THOMAS >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 162 of file fe_raviart_shape_3D.C.

{
  return FE<3,L2_RAVIART_THOMAS>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [170/195]

Real libMesh::FE< 2, SUBDIVISION >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 748 of file fe_subdivision_2D.C.

{
  libmesh_assert(elem);
  const Order totalorder = fet.order + add_p_level*elem->p_level();
  return FE<2,SUBDIVISION>::shape(elem->type(), totalorder, i, p);
}

shape() [171/195]

Real libMesh::FE< 1, SZABAB >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 96 of file fe_szabab_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape(elem->type(), fet.order + add_p_level*elem->p_level(), i, p);
}

shape() [172/195]

Real libMesh::FE< 2, SZABAB >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 656 of file fe_szabab_shape_2D.C.

{
  return FE<2,SZABAB>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [173/195]

Real libMesh::FE< 1, XYZ >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 97 of file fe_xyz_shape_1D.C.

{
  return FE<1,XYZ>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [174/195]

Real libMesh::FE< 2, XYZ >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 160 of file fe_xyz_shape_2D.C.

{
  return FE<2,XYZ>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [175/195]

Real libMesh::FE< 3, XYZ >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 228 of file fe_xyz_shape_3D.C.

{
  return FE<3,XYZ>::shape(elem, fet.order, i, p, add_p_level);
}

shape() [176/195]

static OutputShape libMesh::FE< Dim, T >::shape ( const FEType  fet, const Elem *  elem, const unsigned int  i, const Point &  p, const bool  add_p_level = true  )

staticinherited

Returns

The value of the \( i^{th} \) shape function at point p. This method allows you to specify the dimension and element type directly. The order is given by the FEType. This allows the method to be static.

On a p-refined element, o should be the base order of the element if add_p_level is left true, or can be the base order of the element if add_p_level is set to false.

shape() [177/195]

Real libMesh::FE< 1, SIDE_HIERARCHIC >::shape ( const FEType  , const Elem *  , const unsigned int  i, const Point &  p, const bool    )

inherited

Definition at line 166 of file fe_hierarchic_shape_1D.C.

{
  unsigned int right_side = p(0) > 0; // 0 false, 1 true
  return (right_side == i);
}

shape() [178/195]

Real libMesh::FE< 0, BERNSTEIN >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 57 of file fe_bernstein_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [179/195]

Real libMesh::FE< 0, CLOUGH >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 58 of file fe_clough_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [180/195]

Real libMesh::FE< 0, HERMITE >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 57 of file fe_hermite_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [181/195]

Real libMesh::FE< 0, HIERARCHIC >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 110 of file fe_hierarchic_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [182/195]

Real libMesh::FE< 0, L2_HIERARCHIC >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 123 of file fe_hierarchic_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [183/195]

Real libMesh::FE< 0, L2_LAGRANGE >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 81 of file fe_lagrange_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [184/195]

Real libMesh::FE< 0, LAGRANGE >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 93 of file fe_lagrange_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [185/195]

Real libMesh::FE< 0, MONOMIAL >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 58 of file fe_monomial_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [186/195]

Real libMesh::FE< 0, RATIONAL_BERNSTEIN >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 57 of file fe_rational_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [187/195]

Real libMesh::FE< 0, SZABAB >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 58 of file fe_szabab_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [188/195]

Real libMesh::FE< 0, XYZ >::shape ( const FEType  , const Elem *  , const unsigned int  libmesh_dbg_vari, const Point &  , const bool    )

inherited

Definition at line 59 of file fe_xyz_shape_0D.C.

{
  libmesh_assert_less (i, 1);
  return 1.;
}

shape() [189/195]

Real libMesh::FE< 0, SIDE_HIERARCHIC >::shape ( const FEType  , const Elem *  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 136 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No side variables in 0D!");
  return 1.;
}

shape() [190/195]

Real libMesh::FE< 0, SCALAR >::shape ( const FEType  , const Elem *  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 53 of file fe_scalar_shape_0D.C.

{
  return 1.;
}

shape() [191/195]

Real libMesh::FE< 1, SCALAR >::shape ( const FEType  , const Elem *  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 55 of file fe_scalar_shape_1D.C.

{
  return 0.;
}

shape() [192/195]

Real libMesh::FE< 2, SCALAR >::shape ( const FEType  , const Elem *  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 54 of file fe_scalar_shape_2D.C.

{
  return 1.;
}

shape() [193/195]

Real libMesh::FE< 3, SCALAR >::shape ( const FEType  , const Elem *  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 54 of file fe_scalar_shape_3D.C.

{
  return 1.;
}

shape() [194/195]

Real libMesh::FE< 3, SZABAB >::shape ( const FEType  , const Elem *  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 60 of file fe_szabab_shape_3D.C.

{
  libmesh_error_msg("Szabo-Babuska polynomials are not defined in 3D");
  return 0;
}

shape() [195/195]

Real libMesh::FE< 3, CLOUGH >::shape ( const FEType  , const Elem *  libmesh_dbg_varelem, const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 62 of file fe_clough_shape_3D.C.

{
  libmesh_assert(elem);
 
  libmesh_not_implemented();
  return 0.;
}

shape_deriv() [1/233]

Real libMesh::FE< 0, BERNSTEIN >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 83 of file fe_bernstein_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [2/233]

Real libMesh::FE< 0, CLOUGH >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 84 of file fe_clough_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [3/233]

Real libMesh::FE< 0, HERMITE >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 84 of file fe_hermite_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [4/233]

Real libMesh::FE< 0, HIERARCHIC >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 162 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [5/233]

Real libMesh::FE< 0, L2_HIERARCHIC >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 203 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [6/233]

Real libMesh::FE< 0, SIDE_HIERARCHIC >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 243 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [7/233]

Real libMesh::FE< 1, SIDE_HIERARCHIC >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 275 of file fe_hierarchic_shape_1D.C.

{
  return 0;
}

shape_deriv() [8/233]

Real libMesh::FE< 0, L2_LAGRANGE >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 118 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [9/233]

Real libMesh::FE< 0, LAGRANGE >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 145 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [10/233]

Real libMesh::FE< 0, MONOMIAL >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 85 of file fe_monomial_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [11/233]

RealGradient libMesh::FE< 0, NEDELEC_ONE >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 467 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape_deriv() [12/233]

RealGradient libMesh::FE< 1, NEDELEC_ONE >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 494 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape_deriv() [13/233]

Real libMesh::FE< 0, RATIONAL_BERNSTEIN >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 82 of file fe_rational_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [14/233]

RealGradient libMesh::FE< 0, RAVIART_THOMAS >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 565 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_deriv() [15/233]

RealGradient libMesh::FE< 0, L2_RAVIART_THOMAS >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 573 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_deriv() [16/233]

RealGradient libMesh::FE< 1, RAVIART_THOMAS >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 614 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_deriv() [17/233]

RealGradient libMesh::FE< 1, L2_RAVIART_THOMAS >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 622 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_deriv() [18/233]

Real libMesh::FE< 0, SCALAR >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 73 of file fe_scalar_shape_0D.C.

{
  return 0.;
}

shape_deriv() [19/233]

Real libMesh::FE< 1, SCALAR >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 76 of file fe_scalar_shape_1D.C.

{
  return 0.;
}

shape_deriv() [20/233]

Real libMesh::FE< 2, SCALAR >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 75 of file fe_scalar_shape_2D.C.

{
  return 0.;
}

shape_deriv() [21/233]

Real libMesh::FE< 3, SCALAR >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 74 of file fe_scalar_shape_3D.C.

{
  return 0.;
}

shape_deriv() [22/233]

Real libMesh::FE< 0, SZABAB >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 85 of file fe_szabab_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [23/233]

Real libMesh::FE< 3, SZABAB >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 85 of file fe_szabab_shape_3D.C.

{
  libmesh_error_msg("Szabo-Babuska polynomials are not defined in 3D");
  return 0.;
}

shape_deriv() [24/233]

Real libMesh::FE< 0, XYZ >::shape_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 85 of file fe_xyz_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [25/233]

Real libMesh::FE< 2, XYZ >::shape_deriv ( const Elem *  elem, const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  j, const Point &  point_in, const bool  libmesh_dbg_varadd_p_level  )

inherited

Definition at line 174 of file fe_xyz_shape_2D.C.

{
#if LIBMESH_DIM > 1
 
 
  libmesh_assert_less (j, 2);
  libmesh_assert(elem);
 
  Point avg = elem->vertex_average();
  Point max_distance = Point(0.,0.,0.);
  for (const Point & p : elem->node_ref_range())
    for (unsigned int d = 0; d < 2; d++)
      {
        const Real distance = std::abs(avg(d) - p(d));
        max_distance(d) = std::max(distance, max_distance(d));
      }
 
  const Real x  = point_in(0);
  const Real y  = point_in(1);
  const Real xc = avg(0);
  const Real yc = avg(1);
  const Real distx = max_distance(0);
  const Real disty = max_distance(1);
  const Real dx = (x - xc)/distx;
  const Real dy = (y - yc)/disty;
 
#ifndef NDEBUG
  // totalorder is only used in the assertion below, so
  // we avoid declaring it when asserts are not active.
  const unsigned int totalorder = order + add_p_level * elem->p_level();
#endif
  libmesh_assert_less (i, (totalorder+1)*(totalorder+2)/2);
 
  // monomials. since they are hierarchic we only need one case block.
 
  switch (j)
    {
      // d()/dx
    case 0:
      {
        switch (i)
          {
            // constants
          case 0:
            return 0.;
 
            // linears
          case 1:
            return 1./distx;
 
          case 2:
            return 0.;
 
            // quadratics
          case 3:
            return 2.*dx/distx;
 
          case 4:
            return dy/distx;
 
          case 5:
            return 0.;
 
            // cubics
          case 6:
            return 3.*dx*dx/distx;
 
          case 7:
            return 2.*dx*dy/distx;
 
          case 8:
            return dy*dy/distx;
 
          case 9:
            return 0.;
 
            // quartics
          case 10:
            return 4.*dx*dx*dx/distx;
 
          case 11:
            return 3.*dx*dx*dy/distx;
 
          case 12:
            return 2.*dx*dy*dy/distx;
 
          case 13:
            return dy*dy*dy/distx;
 
          case 14:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            unsigned int i2 = i - (o*(o+1)/2);
            Real val = o - i2;
            for (unsigned int index=i2+1; index < o; index++)
              val *= dx;
            for (unsigned int index=0; index != i2; index++)
              val *= dy;
            return val/distx;
          }
      }
 
 
      // d()/dy
    case 1:
      {
        switch (i)
          {
            // constants
          case 0:
            return 0.;
 
            // linears
          case 1:
            return 0.;
 
          case 2:
            return 1./disty;
 
            // quadratics
          case 3:
            return 0.;
 
          case 4:
            return dx/disty;
 
          case 5:
            return 2.*dy/disty;
 
            // cubics
          case 6:
            return 0.;
 
          case 7:
            return dx*dx/disty;
 
          case 8:
            return 2.*dx*dy/disty;
 
          case 9:
            return 3.*dy*dy/disty;
 
            // quartics
          case 10:
            return 0.;
 
          case 11:
            return dx*dx*dx/disty;
 
          case 12:
            return 2.*dx*dx*dy/disty;
 
          case 13:
            return 3.*dx*dy*dy/disty;
 
          case 14:
            return 4.*dy*dy*dy/disty;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            unsigned int i2 = i - (o*(o+1)/2);
            Real val = i2;
            for (unsigned int index=i2; index != o; index++)
              val *= dx;
            for (unsigned int index=1; index <= i2; index++)
              val *= dy;
            return val/disty;
          }
      }
 
 
    default:
      libmesh_error_msg("Invalid j = " << j);
    }
 
#else // LIBMESH_DIM <= 1
  libmesh_assert(true || order || add_p_level);
  libmesh_ignore(elem, i, j, point_in);
  libmesh_not_implemented();
#endif
}

shape_deriv() [26/233]

Real libMesh::FE< 3, XYZ >::shape_deriv ( const Elem *  elem, const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  j, const Point &  point_in, const bool  libmesh_dbg_varadd_p_level  )

inherited

Definition at line 242 of file fe_xyz_shape_3D.C.

{
#if LIBMESH_DIM == 3
 
  libmesh_assert(elem);
  libmesh_assert_less (j, 3);
 
  Point avg = elem->vertex_average();
  Point max_distance = Point(0.,0.,0.);
  for (auto p : make_range(elem->n_nodes()))
    for (unsigned int d = 0; d < 3; d++)
      {
        const Real distance = std::abs(avg(d) - elem->point(p)(d));
        max_distance(d) = std::max(distance, max_distance(d));
      }
 
  const Real x  = point_in(0);
  const Real y  = point_in(1);
  const Real z  = point_in(2);
  const Real xc = avg(0);
  const Real yc = avg(1);
  const Real zc = avg(2);
  const Real distx = max_distance(0);
  const Real disty = max_distance(1);
  const Real distz = max_distance(2);
  const Real dx = (x - xc)/distx;
  const Real dy = (y - yc)/disty;
  const Real dz = (z - zc)/distz;
 
#ifndef NDEBUG
  // totalorder is only used in the assertion below, so
  // we avoid declaring it when asserts are not active.
  const unsigned int totalorder = order + add_p_level*elem->p_level();
#endif
  libmesh_assert_less (i, (totalorder+1) * (totalorder+2) *
                       (totalorder+3)/6);
 
  switch (j)
    {
      // d()/dx
    case 0:
      {
        switch (i)
          {
            // constant
          case 0:
            return 0.;
 
            // linear
          case 1:
            return 1./distx;
 
          case 2:
            return 0.;
 
          case 3:
            return 0.;
 
            // quadratic
          case 4:
            return 2.*dx/distx;
 
          case 5:
            return dy/distx;
 
          case 6:
            return 0.;
 
          case 7:
            return dz/distx;
 
          case 8:
            return 0.;
 
          case 9:
            return 0.;
 
            // cubic
          case 10:
            return 3.*dx*dx/distx;
 
          case 11:
            return 2.*dx*dy/distx;
 
          case 12:
            return dy*dy/distx;
 
          case 13:
            return 0.;
 
          case 14:
            return 2.*dx*dz/distx;
 
          case 15:
            return dy*dz/distx;
 
          case 16:
            return 0.;
 
          case 17:
            return dz*dz/distx;
 
          case 18:
            return 0.;
 
          case 19:
            return 0.;
 
            // quartics
          case 20:
            return 4.*dx*dx*dx/distx;
 
          case 21:
            return 3.*dx*dx*dy/distx;
 
          case 22:
            return 2.*dx*dy*dy/distx;
 
          case 23:
            return dy*dy*dy/distx;
 
          case 24:
            return 0.;
 
          case 25:
            return 3.*dx*dx*dz/distx;
 
          case 26:
            return 2.*dx*dy*dz/distx;
 
          case 27:
            return dy*dy*dz/distx;
 
          case 28:
            return 0.;
 
          case 29:
            return 2.*dx*dz*dz/distx;
 
          case 30:
            return dy*dz*dz/distx;
 
          case 31:
            return 0.;
 
          case 32:
            return dz*dz*dz/distx;
 
          case 33:
            return 0.;
 
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            unsigned int i2 = i - (o*(o+1)*(o+2)/6);
            unsigned int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const unsigned int nx = block - i2;
            const unsigned int ny = o - nx - nz;
            Real val = nx;
            for (unsigned int index=1; index < nx; index++)
              val *= dx;
            for (unsigned int index=0; index != ny; index++)
              val *= dy;
            for (unsigned int index=0; index != nz; index++)
              val *= dz;
            return val/distx;
          }
      }
 
 
      // d()/dy
    case 1:
      {
        switch (i)
          {
            // constant
          case 0:
            return 0.;
 
            // linear
          case 1:
            return 0.;
 
          case 2:
            return 1./disty;
 
          case 3:
            return 0.;
 
            // quadratic
          case 4:
            return 0.;
 
          case 5:
            return dx/disty;
 
          case 6:
            return 2.*dy/disty;
 
          case 7:
            return 0.;
 
          case 8:
            return dz/disty;
 
          case 9:
            return 0.;
 
            // cubic
          case 10:
            return 0.;
 
          case 11:
            return dx*dx/disty;
 
          case 12:
            return 2.*dx*dy/disty;
 
          case 13:
            return 3.*dy*dy/disty;
 
          case 14:
            return 0.;
 
          case 15:
            return dx*dz/disty;
 
          case 16:
            return 2.*dy*dz/disty;
 
          case 17:
            return 0.;
 
          case 18:
            return dz*dz/disty;
 
          case 19:
            return 0.;
 
            // quartics
          case 20:
            return 0.;
 
          case 21:
            return dx*dx*dx/disty;
 
          case 22:
            return 2.*dx*dx*dy/disty;
 
          case 23:
            return 3.*dx*dy*dy/disty;
 
          case 24:
            return 4.*dy*dy*dy/disty;
 
          case 25:
            return 0.;
 
          case 26:
            return dx*dx*dz/disty;
 
          case 27:
            return 2.*dx*dy*dz/disty;
 
          case 28:
            return 3.*dy*dy*dz/disty;
 
          case 29:
            return 0.;
 
          case 30:
            return dx*dz*dz/disty;
 
          case 31:
            return 2.*dy*dz*dz/disty;
 
          case 32:
            return 0.;
 
          case 33:
            return dz*dz*dz/disty;
 
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            unsigned int i2 = i - (o*(o+1)*(o+2)/6);
            unsigned int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const unsigned int nx = block - i2;
            const unsigned int ny = o - nx - nz;
            Real val = ny;
            for (unsigned int index=0; index != nx; index++)
              val *= dx;
            for (unsigned int index=1; index < ny; index++)
              val *= dy;
            for (unsigned int index=0; index != nz; index++)
              val *= dz;
            return val/disty;
          }
      }
 
 
      // d()/dz
    case 2:
      {
        switch (i)
          {
            // constant
          case 0:
            return 0.;
 
            // linear
          case 1:
            return 0.;
 
          case 2:
            return 0.;
 
          case 3:
            return 1./distz;
 
            // quadratic
          case 4:
            return 0.;
 
          case 5:
            return 0.;
 
          case 6:
            return 0.;
 
          case 7:
            return dx/distz;
 
          case 8:
            return dy/distz;
 
          case 9:
            return 2.*dz/distz;
 
            // cubic
          case 10:
            return 0.;
 
          case 11:
            return 0.;
 
          case 12:
            return 0.;
 
          case 13:
            return 0.;
 
          case 14:
            return dx*dx/distz;
 
          case 15:
            return dx*dy/distz;
 
          case 16:
            return dy*dy/distz;
 
          case 17:
            return 2.*dx*dz/distz;
 
          case 18:
            return 2.*dy*dz/distz;
 
          case 19:
            return 3.*dz*dz/distz;
 
            // quartics
          case 20:
            return 0.;
 
          case 21:
            return 0.;
 
          case 22:
            return 0.;
 
          case 23:
            return 0.;
 
          case 24:
            return 0.;
 
          case 25:
            return dx*dx*dx/distz;
 
          case 26:
            return dx*dx*dy/distz;
 
          case 27:
            return dx*dy*dy/distz;
 
          case 28:
            return dy*dy*dy/distz;
 
          case 29:
            return 2.*dx*dx*dz/distz;
 
          case 30:
            return 2.*dx*dy*dz/distz;
 
          case 31:
            return 2.*dy*dy*dz/distz;
 
          case 32:
            return 3.*dx*dz*dz/distz;
 
          case 33:
            return 3.*dy*dz*dz/distz;
 
          case 34:
            return 4.*dz*dz*dz/distz;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            unsigned int i2 = i - (o*(o+1)*(o+2)/6);
            unsigned int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const unsigned int nx = block - i2;
            const unsigned int ny = o - nx - nz;
            Real val = nz;
            for (unsigned int index=0; index != nx; index++)
              val *= dx;
            for (unsigned int index=0; index != ny; index++)
              val *= dy;
            for (unsigned int index=1; index < nz; index++)
              val *= dz;
            return val/distz;
          }
      }
 
 
    default:
      libmesh_error_msg("Invalid j = " << j);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_assert(true || order || add_p_level);
  libmesh_ignore(elem, i, j, point_in);
  libmesh_not_implemented();
#endif
}

shape_deriv() [27/233]

Real libMesh::FE< 1, XYZ >::shape_deriv ( const Elem *  elem, const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  libmesh_dbg_varj, const Point &  point_in, const bool  libmesh_dbg_varadd_p_level  )

inherited

Definition at line 108 of file fe_xyz_shape_1D.C.

{
  libmesh_assert(elem);
  libmesh_assert_less_equal (i, order + add_p_level * elem->p_level());
 
  // only d()/dxi in 1D!
 
  libmesh_assert_equal_to (j, 0);
 
  Point avg = elem->vertex_average();
  Real max_distance = 0.;
  for (const Point & p : elem->node_ref_range())
    {
      const Real distance = std::abs(avg(0) - p(0));
      max_distance = std::max(distance, max_distance);
    }
 
  const Real x  = point_in(0);
  const Real xc = avg(0);
  const Real dx = (x - xc)/max_distance;
 
  // monomials. since they are hierarchic we only need one case block.
  switch (i)
    {
    case 0:
      return 0.;
 
    case 1:
      return 1./max_distance;
 
    case 2:
      return 2.*dx/max_distance;
 
    case 3:
      return 3.*dx*dx/max_distance;
 
    case 4:
      return 4.*dx*dx*dx/max_distance;
 
    default:
      Real val = i;
      for (unsigned int index = 1; index != i; ++index)
        val *= dx;
      return val/max_distance;
    }
}

shape_deriv() [28/233]

Real libMesh::FE< 1, HERMITE >::shape_deriv ( const Elem *  elem, const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  , const Point &  p, const bool  libmesh_dbg_varadd_p_level  )

inherited

Definition at line 256 of file fe_hermite_shape_1D.C.

{
  libmesh_assert(elem);
 
  // Coefficient naming: d(1)d(2n) is the coefficient of the
  // global shape function corresponding to value 1 in terms of the
  // local shape function corresponding to normal derivative 2
  Real d1xd1x, d2xd2x;
 
  hermite_compute_coefs(elem, d1xd1x, d2xd2x);
 
  const ElemType type = elem->type();
 
#ifndef NDEBUG
  const unsigned int totalorder =
    order + add_p_level * elem->p_level();
#endif
 
  switch (type)
    {
      // C1 functions on the C1 cubic edge
    case EDGE2:
    case EDGE3:
      {
        libmesh_assert_less (i, totalorder+1);
 
        switch (i)
          {
          case 0:
            return FEHermite<1>::hermite_raw_shape_deriv(0, p(0));
          case 1:
            return d1xd1x * FEHermite<1>::hermite_raw_shape_deriv(2, p(0));
          case 2:
            return FEHermite<1>::hermite_raw_shape_deriv(1, p(0));
          case 3:
            return d2xd2x * FEHermite<1>::hermite_raw_shape_deriv(3, p(0));
          default:
            return FEHermite<1>::hermite_raw_shape_deriv(i, p(0));
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
    }
}

shape_deriv() [29/233]

static OutputShape libMesh::FE< Dim, T >::shape_deriv ( const Elem *  elem, const Order  o, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level = true  )

staticinherited

Returns

The \( j^{th} \) derivative of the \( i^{th} \) shape function. You must specify element type, and order directly.

On a p-refined element, o should be the base order of the element if add_p_level is left true, or can be the base order of the element if add_p_level is set to false.

shape_deriv() [30/233]

RealGradient libMesh::FE< 3, RAVIART_THOMAS >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  , const bool  add_p_level  )

inherited

Definition at line 173 of file fe_raviart_shape_3D.C.

{
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
  libmesh_assert_less (j, 3);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = elem->positive_face_orientation(i) ? 1 : -1;
 
  switch (totalorder)
    {
      // linear Raviart-Thomas shape function first derivatives
    case FIRST:
      {
        switch (elem->type())
          {
          case HEX27:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(i)
                      {
                      case 0:
                      case 1:
                      case 3:
                      case 5:
                        return RealGradient();
                      case 2:
                      case 4:
                        return sign * RealGradient( 0.125, 0.0, 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(i)
                      {
                      case 0:
                      case 2:
                      case 4:
                      case 5:
                        return RealGradient();
                      case 1:
                      case 3:
                        return sign * RealGradient( 0.0, 0.125, 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 1
 
                  // d()/dzeta
                case 2:
                  {
                    switch(i)
                      {
                      case 1:
                      case 2:
                      case 3:
                      case 4:
                        return RealGradient();
                      case 0:
                      case 5:
                        return sign * RealGradient( 0.0, 0.0, 0.125 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TET14:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(i)
                    {
                    case 0:
                    case 1:
                    case 2:
                    case 3:
                      return sign * RealGradient( 2.0, 0.0, 0.0 );
 
                    default:
                      libmesh_error_msg("Invalid i = " << i);
                    } // switch(i)
 
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(i)
                    {
                    case 0:
                    case 1:
                    case 2:
                    case 3:
                      return sign * RealGradient( 0.0, 2.0, 0.0 );
 
                    default:
                      libmesh_error_msg("Invalid i = " << i);
                    } // switch(i)
 
                  } // j = 1
 
                  // d()/dzeta
                case 2:
                  {
                    switch(i)
                    {
                    case 0:
                    case 1:
                    case 2:
                    case 3:
                      return sign * RealGradient( 0.0, 0.0, 2.0 );
 
                    default:
                      libmesh_error_msg("Invalid i = " << i);
                    } // switch(i)
 
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, j, p, add_p_level);
  libmesh_not_implemented();
#endif
}

shape_deriv() [31/233]

Real libMesh::FE< 2, SUBDIVISION >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

shape_deriv() [32/233]

Real libMesh::FE< 1, BERNSTEIN >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 380 of file fe_bernstein_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,BERNSTEIN>::shape_deriv
    (elem->type(),
     order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [33/233]

Real libMesh::FE< 2, BERNSTEIN >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 416 of file fe_bernstein_shape_2D.C.

{
  libmesh_assert(elem);
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (type)
    {
      // Hierarchic shape functions on the quadrilateral.
    case QUAD4:
    case QUAD9:
    case QUADSHELL9:
      {
        // Compute quad shape functions as a tensor-product
        auto [i0, i1] = quad_i0_i1(i, totalorder, *elem);
 
        switch (j)
          {
            // d()/dxi
          case 0:
            return (FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i0, 0, p(0))*
                    FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1,    p(1)));
 
            // d()/deta
          case 1:
            return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0,    p(0))*
                    FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i1, 0, p(1)));
 
          default:
            libmesh_error_msg("Invalid shape function derivative j = " << j);
          }
      }
 
      // Bernstein shape functions on the 8-noded quadrilateral
      // is handled separately.
    case QUAD8:
    case QUADSHELL8:
      {
        libmesh_assert_less (totalorder, 3);
 
        const Real xi  = p(0);
        const Real eta = p(1);
 
        libmesh_assert_less (i, 8);
 
        //                                0  1  2  3  4  5  6  7  8
        static const unsigned int i0[] = {0, 1, 1, 0, 2, 1, 2, 0, 2};
        static const unsigned int i1[] = {0, 0, 1, 1, 0, 2, 1, 2, 2};
        static const Real scal[] = {-0.25, -0.25, -0.25, -0.25, 0.5, 0.5, 0.5, 0.5};
        switch (j)
          {
            // d()/dxi
          case 0:
            return (FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi)*
                    FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[i],    eta)
                    +scal[i]*
                    FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i0[8], 0, xi)*
                    FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[8],    eta));
 
            // d()/deta
          case 1:
            return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[i],    xi)*
                    FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta)
                    +scal[i]*
                    FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[8],    xi)*
                    FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i1[8], 0, eta));
 
          default:
            libmesh_error_msg("Invalid shape function derivative j = " << j);
          }
      }
 
    case TRI3:
    case TRISHELL3:
      libmesh_assert_less (totalorder, 2);
      libmesh_fallthrough();
    case TRI6:
    case TRI7:
      {
        return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<2,BERNSTEIN>::shape);
      }
 
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
    }
}

shape_deriv() [34/233]

Real libMesh::FE< 3, BERNSTEIN >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 915 of file fe_bernstein_shape_3D.C.

{
 
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  libmesh_assert_less (j, 3);
 
  switch (totalorder)
    {
      // 1st order Bernstein.
    case FIRST:
      {
        switch (type)
          {
            // Bernstein shape functions on the tetrahedron.
          case TET4:
          case TET10:
          case TET14:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<3,BERNSTEIN>::shape);
            }
 
 
            // Bernstein shape functions on the hexahedral.
          case HEX8:
          case HEX20:
          case HEX27:
            {
              libmesh_assert_less (i, 8);
 
              // Compute hex shape functions as a tensor-product
              const Real xi   = p(0);
              const Real eta  = p(1);
              const Real zeta = p(2);
 
              // The only way to make any sense of this
              // is to look at the mgflo/mg2/mgf documentation
              // and make the cut-out cube!
              //                                0  1  2  3  4  5  6  7
              static const unsigned int i0[] = {0, 1, 1, 0, 0, 1, 1, 0};
              static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 1, 1};
              static const unsigned int i2[] = {0, 0, 0, 0, 1, 1, 1, 1};
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return (FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[i],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i2[i],    zeta));
 
                  // d()/deta
                case 1:
                  return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[i],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i2[i],    zeta));
 
                  // d()/dzeta
                case 2:
                  return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[i],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[i],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i2[i], 0, zeta));
 
                default:
                  libmesh_error_msg("Invalid derivative index j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
 
 
 
    case SECOND:
      {
        switch (type)
          {
            // Bernstein shape functions on the tetrahedron.
          case TET10:
          case TET14:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<3,BERNSTEIN>::shape);
            }
 
            // Bernstein shape functions on the hexahedral.
          case HEX20:
            {
              libmesh_assert_less (i, 20);
 
              // Compute hex shape functions as a tensor-product
              const Real xi   = p(0);
              const Real eta  = p(1);
              const Real zeta = p(2);
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return (FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i0[i], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[i],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[i],    zeta)
                          +hex20_scal20[i]*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i0[20], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[20],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[20],    zeta)
                          +hex20_scal21[i]*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i0[21], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[21],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[21],    zeta)
                          +hex20_scal22[i]*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i0[22], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[22],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[22],    zeta)
                          +hex20_scal23[i]*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i0[23], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[23],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[23],    zeta)
                          +hex20_scal24[i]*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i0[24], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[24],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[24],    zeta)
                          +hex20_scal25[i]*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i0[25], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[25],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[25],    zeta)
                          +hex20_scal26[i]*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i0[26], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[26],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[26],    zeta));
 
                  // d()/deta
                case 1:
                  return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[i],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i1[i], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[i],    zeta)
                          +hex20_scal20[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[20],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i1[20], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[20],    zeta)
                          +hex20_scal21[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[21],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i1[21], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[21],    zeta)
                          +hex20_scal22[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[22],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i1[22], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[22],    zeta)
                          +hex20_scal23[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[23],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i1[23], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[23],    zeta)
                          +hex20_scal24[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[24],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i1[24], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[24],    zeta)
                          +hex20_scal25[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[25],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i1[25], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[25],    zeta)
                          +hex20_scal26[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[26],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i1[26], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i2[26],    zeta));
 
                  // d()/dzeta
                case 2:
                  return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[i],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[i],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i2[i], 0, zeta)
                          +hex20_scal20[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[20],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[20],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i2[20], 0, zeta)
                          +hex20_scal21[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[21],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[21],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i2[21], 0, zeta)
                          +hex20_scal22[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[22],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[22],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i2[22], 0, zeta)
                          +hex20_scal23[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[23],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[23],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i2[23], 0, zeta)
                          +hex20_scal24[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[24],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[24],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i2[24], 0, zeta)
                          +hex20_scal25[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[25],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[25],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i2[25], 0, zeta)
                          +hex20_scal26[i]*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i0[26],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, hex20_i1[26],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, hex20_i2[26], 0, zeta));
 
                default:
                  libmesh_error_msg("Invalid derivative index j = " << j);
                }
            }
 
            // Bernstein shape functions on the hexahedral.
          case HEX27:
            {
              libmesh_assert_less (i, 27);
 
              // Compute hex shape functions as a tensor-product
              const Real xi   = p(0);
              const Real eta  = p(1);
              const Real zeta = p(2);
 
              // The only way to make any sense of this
              // is to look at the mgflo/mg2/mgf documentation
              // and make the cut-out cube!
              //                                0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
              static const unsigned int i0[] = {0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 2, 0, 0, 1, 1, 0, 2, 1, 2, 0, 2, 2, 1, 2, 0, 2, 2};
              static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 2, 0, 0, 1, 1, 0, 2, 1, 2, 2, 0, 2, 1, 2, 2, 2};
              static const unsigned int i2[] = {0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, 0, 2, 2, 2, 2, 1, 2};
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return (FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[i],    eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i2[i],    zeta));
 
                  // d()/deta
                case 1:
                  return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[i],     xi)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i2[i],    zeta));
 
                  // d()/dzeta
                case 2:
                  return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[i],    xi)*
                          FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[i],    eta)*
                          FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i2[i], 0, zeta));
 
                default:
                  libmesh_error_msg("Invalid derivative index j = " << j);
                }
            }
 
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
 
 
      // 3rd-order Bernstein.
    case THIRD:
      {
        switch (type)
          {
 
            //     // Bernstein shape functions derivatives.
            //   case TET10:
            //     {
            //       // I have been lazy here and am using finite differences
            //       // to compute the derivatives!
            //       const Real eps = 1.e-4;
 
            //       libmesh_assert_less (i, 20);
            //       libmesh_assert_less (j, 3);
 
            // switch (j)
            // {
            //   //  d()/dxi
            // case 0:
            //   {
            //     const Point pp(p(0)+eps, p(1), p(2));
            //     const Point pm(p(0)-eps, p(1), p(2));
 
            //     return (FE<3,BERNSTEIN>::shape(elem, order, i, pp) -
            //     FE<3,BERNSTEIN>::shape(elem, order, i, pm))/2./eps;
            //   }
 
            //   // d()/deta
            // case 1:
            //   {
            //     const Point pp(p(0), p(1)+eps, p(2));
            //     const Point pm(p(0), p(1)-eps, p(2));
 
            //     return (FE<3,BERNSTEIN>::shape(elem, order, i, pp) -
            //     FE<3,BERNSTEIN>::shape(elem, order, i, pm))/2./eps;
            //   }
            //   // d()/dzeta
            // case 2:
            //   {
            //     const Point pp(p(0), p(1), p(2)+eps);
            //     const Point pm(p(0), p(1), p(2)-eps);
 
            //     return (FE<3,BERNSTEIN>::shape(elem, order, i, pp) -
            //     FE<3,BERNSTEIN>::shape(elem, order, i, pm))/2./eps;
            //   }
            // default:
            // libmesh_error_msg("Invalid derivative index j = " << j);
            // }
 
 
            //     }
 
 
            // Bernstein shape functions on the hexahedral.
          case HEX27:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<3,BERNSTEIN>::shape);
            }
 
            //       // Compute hex shape functions as a tensor-product
            //       const Real xi    = p(0);
            //       const Real eta   = p(1);
            //       const Real zeta  = p(2);
            //       Real xi_mapped   = p(0);
            //       Real eta_mapped  = p(1);
            //       Real zeta_mapped = p(2);
 
            //       // The only way to make any sense of this
            //       // is to look at the mgflo/mg2/mgf documentation
            //       // and make the cut-out cube!
            //       //  Nodes                         0  1  2  3  4  5  6  7  8  8  9  9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 20 20 21 21 21 21 22 22 22 22 23 23 23 23 24 24 24 24 25 25 25 25 26 26 26 26 26 26 26 26
            //       //  DOFS                          0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 18 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 60 62 63
            //       static const unsigned int i0[] = {0, 1, 1, 0, 0, 1, 1, 0, 2, 3, 1, 1, 2, 3, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 2, 3, 1, 1, 2, 3, 0, 0, 2, 3, 2, 3, 2, 3, 2, 3, 1, 1, 1, 1, 2, 3, 2, 3, 0, 0, 0, 0, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3};
            //       static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 3, 1, 1, 2, 3, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 2, 3, 1, 1, 2, 3, 2, 2, 3, 3, 0, 0, 0, 0, 2, 3, 2, 3, 1, 1, 1, 1, 2, 3, 2, 3, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3};
            //       static const unsigned int i2[] = {0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 2, 3, 2, 3, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3};
 
 
 
            //       // handle the edge orientation
            //       {
            // // Edge 0
            // if ((i1[i] == 0) && (i2[i] == 0))
            //   {
            //     if (elem->node_id(0) != std::min(elem->node_id(0), elem->node_id(1)))
            //       xi_mapped = -xi;
            //   }
            // // Edge 1
            // else if ((i0[i] == 1) && (i2[i] == 0))
            //   {
            //     if (elem->node_id(1) != std::min(elem->node_id(1), elem->node_id(2)))
            //       eta_mapped = -eta;
            //   }
            // // Edge 2
            // else if ((i1[i] == 1) && (i2[i] == 0))
            //   {
            //     if (elem->node_id(3) != std::min(elem->node_id(3), elem->node_id(2)))
            //       xi_mapped = -xi;
            //   }
            // // Edge 3
            // else if ((i0[i] == 0) && (i2[i] == 0))
            //   {
            //     if (elem->node_id(0) != std::min(elem->node_id(0), elem->node_id(3)))
            //       eta_mapped = -eta;
            //   }
            // // Edge 4
            // else if ((i0[i] == 0) && (i1[i] == 0))
            //   {
            //     if (elem->node_id(0) != std::min(elem->node_id(0), elem->node_id(4)))
            //       zeta_mapped = -zeta;
            //   }
            // // Edge 5
            // else if ((i0[i] == 1) && (i1[i] == 0))
            //   {
            //     if (elem->node_id(1) != std::min(elem->node_id(1), elem->node_id(5)))
            //       zeta_mapped = -zeta;
            //   }
            // // Edge 6
            // else if ((i0[i] == 1) && (i1[i] == 1))
            //   {
            //     if (elem->node_id(2) != std::min(elem->node_id(2), elem->node_id(6)))
            //       zeta_mapped = -zeta;
            //   }
            // // Edge 7
            // else if ((i0[i] == 0) && (i1[i] == 1))
            //   {
            //     if (elem->node_id(3) != std::min(elem->node_id(3), elem->node_id(7)))
            //       zeta_mapped = -zeta;
            //   }
            // // Edge 8
            // else if ((i1[i] == 0) && (i2[i] == 1))
            //   {
            //     if (elem->node_id(4) != std::min(elem->node_id(4), elem->node_id(5)))
            //       xi_mapped = -xi;
            //   }
            // // Edge 9
            // else if ((i0[i] == 1) && (i2[i] == 1))
            //   {
            //     if (elem->node_id(5) != std::min(elem->node_id(5), elem->node_id(6)))
            //       eta_mapped = -eta;
            //   }
            // // Edge 10
            // else if ((i1[i] == 1) && (i2[i] == 1))
            //   {
            //     if (elem->node_id(7) != std::min(elem->node_id(7), elem->node_id(6)))
            //       xi_mapped = -xi;
            //   }
            // // Edge 11
            // else if ((i0[i] == 0) && (i2[i] == 1))
            //   {
            //     if (elem->node_id(4) != std::min(elem->node_id(4), elem->node_id(7)))
            //       eta_mapped = -eta;
            //   }
            //       }
 
 
            //       // handle the face orientation
            //       {
            // // Face 0
            // if ((i2[i] == 0) && (i0[i] >= 2) && (i1[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(1),
            //    std::min(elem->node_id(2),
            //     std::min(elem->node_id(0),
            //      elem->node_id(3))));
            //     if (elem->node_id(0) == min_node)
            //       if (elem->node_id(1) == std::min(elem->node_id(1), elem->node_id(3)))
            // {
            //   // Case 1
            //   xi_mapped  = xi;
            //   eta_mapped = eta;
            // }
            //       else
            // {
            //   // Case 2
            //   xi_mapped  = eta;
            //   eta_mapped = xi;
            // }
 
            //     else if (elem->node_id(3) == min_node)
            //       if (elem->node_id(0) == std::min(elem->node_id(0), elem->node_id(2)))
            // {
            //   // Case 3
            //   xi_mapped  = -eta;
            //   eta_mapped = xi;
            // }
            //       else
            // {
            //   // Case 4
            //   xi_mapped  = xi;
            //   eta_mapped = -eta;
            // }
 
            //     else if (elem->node_id(2) == min_node)
            //       if (elem->node_id(3) == std::min(elem->node_id(3), elem->node_id(1)))
            // {
            //   // Case 5
            //   xi_mapped  = -xi;
            //   eta_mapped = -eta;
            // }
            //       else
            // {
            //   // Case 6
            //   xi_mapped  = -eta;
            //   eta_mapped = -xi;
            // }
 
            //     else if (elem->node_id(1) == min_node)
            //       if (elem->node_id(2) == std::min(elem->node_id(2), elem->node_id(0)))
            // {
            //   // Case 7
            //   xi_mapped  = eta;
            //   eta_mapped = -xi;
            // }
            //       else
            // {
            //   // Case 8
            //   xi_mapped  = -xi;
            //   eta_mapped = eta;
            // }
            //   }
 
 
            // // Face 1
            // else if ((i1[i] == 0) && (i0[i] >= 2) && (i2[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(0),
            //    std::min(elem->node_id(1),
            //     std::min(elem->node_id(5),
            //      elem->node_id(4))));
            //     if (elem->node_id(0) == min_node)
            //       if (elem->node_id(1) == std::min(elem->node_id(1), elem->node_id(4)))
            // {
            //   // Case 1
            //   xi_mapped   = xi;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 2
            //   xi_mapped   = zeta;
            //   zeta_mapped = xi;
            // }
 
            //     else if (elem->node_id(1) == min_node)
            //       if (elem->node_id(5) == std::min(elem->node_id(5), elem->node_id(0)))
            // {
            //   // Case 3
            //   xi_mapped   = zeta;
            //   zeta_mapped = -xi;
            // }
            //       else
            // {
            //   // Case 4
            //   xi_mapped   = -xi;
            //   zeta_mapped = zeta;
            // }
 
            //     else if (elem->node_id(5) == min_node)
            //       if (elem->node_id(4) == std::min(elem->node_id(4), elem->node_id(1)))
            // {
            //   // Case 5
            //   xi_mapped   = -xi;
            //   zeta_mapped = -zeta;
            // }
            //       else
            // {
            //   // Case 6
            //   xi_mapped   = -zeta;
            //   zeta_mapped = -xi;
            // }
 
            //     else if (elem->node_id(4) == min_node)
            //       if (elem->node_id(0) == std::min(elem->node_id(0), elem->node_id(5)))
            // {
            //   // Case 7
            //   xi_mapped   = -xi;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 8
            //   xi_mapped   = xi;
            //   zeta_mapped = -zeta;
            // }
            //   }
 
 
            // // Face 2
            // else if ((i0[i] == 1) && (i1[i] >= 2) && (i2[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(1),
            //    std::min(elem->node_id(2),
            //     std::min(elem->node_id(6),
            //      elem->node_id(5))));
            //     if (elem->node_id(1) == min_node)
            //       if (elem->node_id(2) == std::min(elem->node_id(2), elem->node_id(5)))
            // {
            //   // Case 1
            //   eta_mapped  = eta;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 2
            //   eta_mapped  = zeta;
            //   zeta_mapped = eta;
            // }
 
            //     else if (elem->node_id(2) == min_node)
            //       if (elem->node_id(6) == std::min(elem->node_id(6), elem->node_id(1)))
            // {
            //   // Case 3
            //   eta_mapped  = zeta;
            //   zeta_mapped = -eta;
            // }
            //       else
            // {
            //   // Case 4
            //   eta_mapped  = -eta;
            //   zeta_mapped = zeta;
            // }
 
            //     else if (elem->node_id(6) == min_node)
            //       if (elem->node_id(5) == std::min(elem->node_id(5), elem->node_id(2)))
            // {
            //   // Case 5
            //   eta_mapped  = -eta;
            //   zeta_mapped = -zeta;
            // }
            //       else
            // {
            //   // Case 6
            //   eta_mapped  = -zeta;
            //   zeta_mapped = -eta;
            // }
 
            //     else if (elem->node_id(5) == min_node)
            //       if (elem->node_id(1) == std::min(elem->node_id(1), elem->node_id(6)))
            // {
            //   // Case 7
            //   eta_mapped  = -zeta;
            //   zeta_mapped = eta;
            // }
            //       else
            // {
            //   // Case 8
            //   eta_mapped   = eta;
            //   zeta_mapped = -zeta;
            // }
            //   }
 
 
            // // Face 3
            // else if ((i1[i] == 1) && (i0[i] >= 2) && (i2[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(2),
            //    std::min(elem->node_id(3),
            //     std::min(elem->node_id(7),
            //      elem->node_id(6))));
            //     if (elem->node_id(3) == min_node)
            //       if (elem->node_id(2) == std::min(elem->node_id(2), elem->node_id(7)))
            // {
            //   // Case 1
            //   xi_mapped   = xi;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 2
            //   xi_mapped   = zeta;
            //   zeta_mapped = xi;
            // }
 
            //     else if (elem->node_id(7) == min_node)
            //       if (elem->node_id(3) == std::min(elem->node_id(3), elem->node_id(6)))
            // {
            //   // Case 3
            //   xi_mapped   = -zeta;
            //   zeta_mapped = xi;
            // }
            //       else
            // {
            //   // Case 4
            //   xi_mapped   = xi;
            //   zeta_mapped = -zeta;
            // }
 
            //     else if (elem->node_id(6) == min_node)
            //       if (elem->node_id(7) == std::min(elem->node_id(7), elem->node_id(2)))
            // {
            //   // Case 5
            //   xi_mapped   = -xi;
            //   zeta_mapped = -zeta;
            // }
            //       else
            // {
            //   // Case 6
            //   xi_mapped   = -zeta;
            //   zeta_mapped = -xi;
            // }
 
            //     else if (elem->node_id(2) == min_node)
            //       if (elem->node_id(6) == std::min(elem->node_id(3), elem->node_id(6)))
            // {
            //   // Case 7
            //   xi_mapped   = zeta;
            //   zeta_mapped = -xi;
            // }
            //       else
            // {
            //   // Case 8
            //   xi_mapped   = -xi;
            //   zeta_mapped = zeta;
            // }
            //   }
 
 
            // // Face 4
            // else if ((i0[i] == 0) && (i1[i] >= 2) && (i2[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(3),
            //    std::min(elem->node_id(0),
            //     std::min(elem->node_id(4),
            //      elem->node_id(7))));
            //     if (elem->node_id(0) == min_node)
            //       if (elem->node_id(3) == std::min(elem->node_id(3), elem->node_id(4)))
            // {
            //   // Case 1
            //   eta_mapped  = eta;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 2
            //   eta_mapped  = zeta;
            //   zeta_mapped = eta;
            // }
 
            //     else if (elem->node_id(4) == min_node)
            //       if (elem->node_id(0) == std::min(elem->node_id(0), elem->node_id(7)))
            // {
            //   // Case 3
            //   eta_mapped  = -zeta;
            //   zeta_mapped = eta;
            // }
            //       else
            // {
            //   // Case 4
            //   eta_mapped  = eta;
            //   zeta_mapped = -zeta;
            // }
 
            //     else if (elem->node_id(7) == min_node)
            //       if (elem->node_id(4) == std::min(elem->node_id(4), elem->node_id(3)))
            // {
            //   // Case 5
            //   eta_mapped  = -eta;
            //   zeta_mapped = -zeta;
            // }
            //       else
            // {
            //   // Case 6
            //   eta_mapped  = -zeta;
            //   zeta_mapped = -eta;
            // }
 
            //     else if (elem->node_id(3) == min_node)
            //       if (elem->node_id(7) == std::min(elem->node_id(7), elem->node_id(0)))
            // {
            //   // Case 7
            //   eta_mapped   = zeta;
            //   zeta_mapped = -eta;
            // }
            //       else
            // {
            //   // Case 8
            //   eta_mapped  = -eta;
            //   zeta_mapped = zeta;
            // }
            //   }
 
 
            // // Face 5
            // else if ((i2[i] == 1) && (i0[i] >= 2) && (i1[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(4),
            //    std::min(elem->node_id(5),
            //     std::min(elem->node_id(6),
            //      elem->node_id(7))));
            //     if (elem->node_id(4) == min_node)
            //       if (elem->node_id(5) == std::min(elem->node_id(5), elem->node_id(7)))
            // {
            //   // Case 1
            //   xi_mapped  = xi;
            //   eta_mapped = eta;
            // }
            //       else
            // {
            //   // Case 2
            //   xi_mapped  = eta;
            //   eta_mapped = xi;
            // }
 
            //     else if (elem->node_id(5) == min_node)
            //       if (elem->node_id(6) == std::min(elem->node_id(6), elem->node_id(4)))
            // {
            //   // Case 3
            //   xi_mapped  = eta;
            //   eta_mapped = -xi;
            // }
            //       else
            // {
            //   // Case 4
            //   xi_mapped  = -xi;
            //   eta_mapped = eta;
            // }
 
            //     else if (elem->node_id(6) == min_node)
            //       if (elem->node_id(7) == std::min(elem->node_id(7), elem->node_id(5)))
            // {
            //   // Case 5
            //   xi_mapped  = -xi;
            //   eta_mapped = -eta;
            // }
            //       else
            // {
            //   // Case 6
            //   xi_mapped  = -eta;
            //   eta_mapped = -xi;
            // }
 
            //     else if (elem->node_id(7) == min_node)
            //       if (elem->node_id(4) == std::min(elem->node_id(4), elem->node_id(6)))
            // {
            //   // Case 7
            //   xi_mapped  = -eta;
            //   eta_mapped = xi;
            // }
            //       else
            // {
            //   // Case 8
            //   xi_mapped  = xi;
            //   eta_mapped = eta;
            // }
            //   }
 
 
            //       }
 
 
 
            //       libmesh_assert_less (j, 3);
 
            //       switch (j)
            // {
            //   // d()/dxi
            // case 0:
            //   return (FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi_mapped)*
            //   FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[i],    eta_mapped)*
            //   FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i2[i],    zeta_mapped));
 
            //   // d()/deta
            // case 1:
            //   return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[i],    xi_mapped)*
            //   FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta_mapped)*
            //   FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i2[i],    zeta_mapped));
 
            //   // d()/dzeta
            // case 2:
            //   return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[i],    xi_mapped)*
            //   FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[i],    eta_mapped)*
            //   FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i2[i], 0, zeta_mapped));
 
            // default:
            // libmesh_error_msg("Invalid derivative index j = " << j);
            // }
 
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
      // 4th-order Bernstein.
    case FOURTH:
      {
        switch (type)
          {
 
            // Bernstein shape functions derivatives on the hexahedral.
          case HEX27:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<3,BERNSTEIN>::shape);
            }
 
            //       // Compute hex shape functions as a tensor-product
            //       const Real xi    = p(0);
            //       const Real eta   = p(1);
            //       const Real zeta  = p(2);
            //       Real xi_mapped   = p(0);
            //       Real eta_mapped  = p(1);
            //       Real zeta_mapped = p(2);
 
            //       // The only way to make any sense of this
            //       // is to look at the mgflo/mg2/mgf documentation
            //       // and make the cut-out cube!
            //       //  Nodes                         0  1  2  3  4  5  6  7  8  8  9  9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 20 20 21 21 21 21 22 22 22 22 23 23 23 23 24 24 24 24 25 25 25 25 26 26 26 26 26 26 26 26
            //       //  DOFS                          0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 18 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 60 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
            //       static const unsigned int i0[] = {0, 1, 1, 0, 0, 1, 1, 0, 2, 3, 4, 1, 1, 1, 2, 3, 4, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 2, 3, 4, 1, 1, 1, 2, 3, 4, 0, 0, 0, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4};
            //       static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 2, 3, 4, 1, 1, 1, 2, 3, 4, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 2, 3, 4, 1, 1, 1, 2, 3, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 4, 2, 3, 4, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4};
            //       static const unsigned int i2[] = {0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 3, 3, 3, 4, 4, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4};
 
 
 
            //       // handle the edge orientation
            //       {
            // // Edge 0
            // if ((i1[i] == 0) && (i2[i] == 0))
            //   {
            //     if (elem->node_id(0) != std::min(elem->node_id(0), elem->node_id(1)))
            //       xi_mapped = -xi;
            //   }
            // // Edge 1
            // else if ((i0[i] == 1) && (i2[i] == 0))
            //   {
            //     if (elem->node_id(1) != std::min(elem->node_id(1), elem->node_id(2)))
            //       eta_mapped = -eta;
            //   }
            // // Edge 2
            // else if ((i1[i] == 1) && (i2[i] == 0))
            //   {
            //     if (elem->node_id(3) != std::min(elem->node_id(3), elem->node_id(2)))
            //       xi_mapped = -xi;
            //   }
            // // Edge 3
            // else if ((i0[i] == 0) && (i2[i] == 0))
            //   {
            //     if (elem->node_id(0) != std::min(elem->node_id(0), elem->node_id(3)))
            //       eta_mapped = -eta;
            //   }
            // // Edge 4
            // else if ((i0[i] == 0) && (i1[i] == 0))
            //   {
            //     if (elem->node_id(0) != std::min(elem->node_id(0), elem->node_id(4)))
            //       zeta_mapped = -zeta;
            //   }
            // // Edge 5
            // else if ((i0[i] == 1) && (i1[i] == 0))
            //   {
            //     if (elem->node_id(1) != std::min(elem->node_id(1), elem->node_id(5)))
            //       zeta_mapped = -zeta;
            //   }
            // // Edge 6
            // else if ((i0[i] == 1) && (i1[i] == 1))
            //   {
            //     if (elem->node_id(2) != std::min(elem->node_id(2), elem->node_id(6)))
            //       zeta_mapped = -zeta;
            //   }
            // // Edge 7
            // else if ((i0[i] == 0) && (i1[i] == 1))
            //   {
            //     if (elem->node_id(3) != std::min(elem->node_id(3), elem->node_id(7)))
            //       zeta_mapped = -zeta;
            //   }
            // // Edge 8
            // else if ((i1[i] == 0) && (i2[i] == 1))
            //   {
            //     if (elem->node_id(4) != std::min(elem->node_id(4), elem->node_id(5)))
            //       xi_mapped = -xi;
            //   }
            // // Edge 9
            // else if ((i0[i] == 1) && (i2[i] == 1))
            //   {
            //     if (elem->node_id(5) != std::min(elem->node_id(5), elem->node_id(6)))
            //       eta_mapped = -eta;
            //   }
            // // Edge 10
            // else if ((i1[i] == 1) && (i2[i] == 1))
            //   {
            //     if (elem->node_id(7) != std::min(elem->node_id(7), elem->node_id(6)))
            //       xi_mapped = -xi;
            //   }
            // // Edge 11
            // else if ((i0[i] == 0) && (i2[i] == 1))
            //   {
            //     if (elem->node_id(4) != std::min(elem->node_id(4), elem->node_id(7)))
            //       eta_mapped = -eta;
            //   }
            //       }
 
 
            //       // handle the face orientation
            //       {
            // // Face 0
            // if ((i2[i] == 0) && (i0[i] >= 2) && (i1[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(1),
            //    std::min(elem->node_id(2),
            //     std::min(elem->node_id(0),
            //      elem->node_id(3))));
            //     if (elem->node_id(0) == min_node)
            //       if (elem->node_id(1) == std::min(elem->node_id(1), elem->node_id(3)))
            // {
            //   // Case 1
            //   xi_mapped  = xi;
            //   eta_mapped = eta;
            // }
            //       else
            // {
            //   // Case 2
            //   xi_mapped  = eta;
            //   eta_mapped = xi;
            // }
 
            //     else if (elem->node_id(3) == min_node)
            //       if (elem->node_id(0) == std::min(elem->node_id(0), elem->node_id(2)))
            // {
            //   // Case 3
            //   xi_mapped  = -eta;
            //   eta_mapped = xi;
            // }
            //       else
            // {
            //   // Case 4
            //   xi_mapped  = xi;
            //   eta_mapped = -eta;
            // }
 
            //     else if (elem->node_id(2) == min_node)
            //       if (elem->node_id(3) == std::min(elem->node_id(3), elem->node_id(1)))
            // {
            //   // Case 5
            //   xi_mapped  = -xi;
            //   eta_mapped = -eta;
            // }
            //       else
            // {
            //   // Case 6
            //   xi_mapped  = -eta;
            //   eta_mapped = -xi;
            // }
 
            //     else if (elem->node_id(1) == min_node)
            //       if (elem->node_id(2) == std::min(elem->node_id(2), elem->node_id(0)))
            // {
            //   // Case 7
            //   xi_mapped  = eta;
            //   eta_mapped = -xi;
            // }
            //       else
            // {
            //   // Case 8
            //   xi_mapped  = -xi;
            //   eta_mapped = eta;
            // }
            //   }
 
 
            // // Face 1
            // else if ((i1[i] == 0) && (i0[i] >= 2) && (i2[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(0),
            //    std::min(elem->node_id(1),
            //     std::min(elem->node_id(5),
            //      elem->node_id(4))));
            //     if (elem->node_id(0) == min_node)
            //       if (elem->node_id(1) == std::min(elem->node_id(1), elem->node_id(4)))
            // {
            //   // Case 1
            //   xi_mapped   = xi;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 2
            //   xi_mapped   = zeta;
            //   zeta_mapped = xi;
            // }
 
            //     else if (elem->node_id(1) == min_node)
            //       if (elem->node_id(5) == std::min(elem->node_id(5), elem->node_id(0)))
            // {
            //   // Case 3
            //   xi_mapped   = zeta;
            //   zeta_mapped = -xi;
            // }
            //       else
            // {
            //   // Case 4
            //   xi_mapped   = -xi;
            //   zeta_mapped = zeta;
            // }
 
            //     else if (elem->node_id(5) == min_node)
            //       if (elem->node_id(4) == std::min(elem->node_id(4), elem->node_id(1)))
            // {
            //   // Case 5
            //   xi_mapped   = -xi;
            //   zeta_mapped = -zeta;
            // }
            //       else
            // {
            //   // Case 6
            //   xi_mapped   = -zeta;
            //   zeta_mapped = -xi;
            // }
 
            //     else if (elem->node_id(4) == min_node)
            //       if (elem->node_id(0) == std::min(elem->node_id(0), elem->node_id(5)))
            // {
            //   // Case 7
            //   xi_mapped   = -xi;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 8
            //   xi_mapped   = xi;
            //   zeta_mapped = -zeta;
            // }
            //   }
 
 
            // // Face 2
            // else if ((i0[i] == 1) && (i1[i] >= 2) && (i2[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(1),
            //    std::min(elem->node_id(2),
            //     std::min(elem->node_id(6),
            //      elem->node_id(5))));
            //     if (elem->node_id(1) == min_node)
            //       if (elem->node_id(2) == std::min(elem->node_id(2), elem->node_id(5)))
            // {
            //   // Case 1
            //   eta_mapped  = eta;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 2
            //   eta_mapped  = zeta;
            //   zeta_mapped = eta;
            // }
 
            //     else if (elem->node_id(2) == min_node)
            //       if (elem->node_id(6) == std::min(elem->node_id(6), elem->node_id(1)))
            // {
            //   // Case 3
            //   eta_mapped  = zeta;
            //   zeta_mapped = -eta;
            // }
            //       else
            // {
            //   // Case 4
            //   eta_mapped  = -eta;
            //   zeta_mapped = zeta;
            // }
 
            //     else if (elem->node_id(6) == min_node)
            //       if (elem->node_id(5) == std::min(elem->node_id(5), elem->node_id(2)))
            // {
            //   // Case 5
            //   eta_mapped  = -eta;
            //   zeta_mapped = -zeta;
            // }
            //       else
            // {
            //   // Case 6
            //   eta_mapped  = -zeta;
            //   zeta_mapped = -eta;
            // }
 
            //     else if (elem->node_id(5) == min_node)
            //       if (elem->node_id(1) == std::min(elem->node_id(1), elem->node_id(6)))
            // {
            //   // Case 7
            //   eta_mapped  = -zeta;
            //   zeta_mapped = eta;
            // }
            //       else
            // {
            //   // Case 8
            //   eta_mapped   = eta;
            //   zeta_mapped = -zeta;
            // }
            //   }
 
 
            // // Face 3
            // else if ((i1[i] == 1) && (i0[i] >= 2) && (i2[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(2),
            //    std::min(elem->node_id(3),
            //     std::min(elem->node_id(7),
            //      elem->node_id(6))));
            //     if (elem->node_id(3) == min_node)
            //       if (elem->node_id(2) == std::min(elem->node_id(2), elem->node_id(7)))
            // {
            //   // Case 1
            //   xi_mapped   = xi;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 2
            //   xi_mapped   = zeta;
            //   zeta_mapped = xi;
            // }
 
            //     else if (elem->node_id(7) == min_node)
            //       if (elem->node_id(3) == std::min(elem->node_id(3), elem->node_id(6)))
            // {
            //   // Case 3
            //   xi_mapped   = -zeta;
            //   zeta_mapped = xi;
            // }
            //       else
            // {
            //   // Case 4
            //   xi_mapped   = xi;
            //   zeta_mapped = -zeta;
            // }
 
            //     else if (elem->node_id(6) == min_node)
            //       if (elem->node_id(7) == std::min(elem->node_id(7), elem->node_id(2)))
            // {
            //   // Case 5
            //   xi_mapped   = -xi;
            //   zeta_mapped = -zeta;
            // }
            //       else
            // {
            //   // Case 6
            //   xi_mapped   = -zeta;
            //   zeta_mapped = -xi;
            // }
 
            //     else if (elem->node_id(2) == min_node)
            //       if (elem->node_id(6) == std::min(elem->node_id(3), elem->node_id(6)))
            // {
            //   // Case 7
            //   xi_mapped   = zeta;
            //   zeta_mapped = -xi;
            // }
            //       else
            // {
            //   // Case 8
            //   xi_mapped   = -xi;
            //   zeta_mapped = zeta;
            // }
            //   }
 
 
            // // Face 4
            // else if ((i0[i] == 0) && (i1[i] >= 2) && (i2[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(3),
            //    std::min(elem->node_id(0),
            //     std::min(elem->node_id(4),
            //      elem->node_id(7))));
            //     if (elem->node_id(0) == min_node)
            //       if (elem->node_id(3) == std::min(elem->node_id(3), elem->node_id(4)))
            // {
            //   // Case 1
            //   eta_mapped  = eta;
            //   zeta_mapped = zeta;
            // }
            //       else
            // {
            //   // Case 2
            //   eta_mapped  = zeta;
            //   zeta_mapped = eta;
            // }
 
            //     else if (elem->node_id(4) == min_node)
            //       if (elem->node_id(0) == std::min(elem->node_id(0), elem->node_id(7)))
            // {
            //   // Case 3
            //   eta_mapped  = -zeta;
            //   zeta_mapped = eta;
            // }
            //       else
            // {
            //   // Case 4
            //   eta_mapped  = eta;
            //   zeta_mapped = -zeta;
            // }
 
            //     else if (elem->node_id(7) == min_node)
            //       if (elem->node_id(4) == std::min(elem->node_id(4), elem->node_id(3)))
            // {
            //   // Case 5
            //   eta_mapped  = -eta;
            //   zeta_mapped = -zeta;
            // }
            //       else
            // {
            //   // Case 6
            //   eta_mapped  = -zeta;
            //   zeta_mapped = -eta;
            // }
 
            //     else if (elem->node_id(3) == min_node)
            //       if (elem->node_id(7) == std::min(elem->node_id(7), elem->node_id(0)))
            // {
            //   // Case 7
            //   eta_mapped   = zeta;
            //   zeta_mapped = -eta;
            // }
            //       else
            // {
            //   // Case 8
            //   eta_mapped  = -eta;
            //   zeta_mapped = zeta;
            // }
            //   }
 
 
            // // Face 5
            // else if ((i2[i] == 1) && (i0[i] >= 2) && (i1[i] >= 2))
            //   {
            //     const unsigned int min_node = std::min(elem->node_id(4),
            //    std::min(elem->node_id(5),
            //     std::min(elem->node_id(6),
            //      elem->node_id(7))));
            //     if (elem->node_id(4) == min_node)
            //       if (elem->node_id(5) == std::min(elem->node_id(5), elem->node_id(7)))
            // {
            //   // Case 1
            //   xi_mapped  = xi;
            //   eta_mapped = eta;
            // }
            //       else
            // {
            //   // Case 2
            //   xi_mapped  = eta;
            //   eta_mapped = xi;
            // }
 
            //     else if (elem->node_id(5) == min_node)
            //       if (elem->node_id(6) == std::min(elem->node_id(6), elem->node_id(4)))
            // {
            //   // Case 3
            //   xi_mapped  = eta;
            //   eta_mapped = -xi;
            // }
            //       else
            // {
            //   // Case 4
            //   xi_mapped  = -xi;
            //   eta_mapped = eta;
            // }
 
            //     else if (elem->node_id(6) == min_node)
            //       if (elem->node_id(7) == std::min(elem->node_id(7), elem->node_id(5)))
            // {
            //   // Case 5
            //   xi_mapped  = -xi;
            //   eta_mapped = -eta;
            // }
            //       else
            // {
            //   // Case 6
            //   xi_mapped  = -eta;
            //   eta_mapped = -xi;
            // }
 
            //     else if (elem->node_id(7) == min_node)
            //       if (elem->node_id(4) == std::min(elem->node_id(4), elem->node_id(6)))
            // {
            //   // Case 7
            //   xi_mapped  = -eta;
            //   eta_mapped = xi;
            // }
            //       else
            // {
            //   // Case 8
            //   xi_mapped  = xi;
            //   eta_mapped = eta;
            // }
            //   }
 
 
            //       }
 
 
 
            //       libmesh_assert_less (j, 3);
 
            //       switch (j)
            // {
            //   // d()/dxi
            // case 0:
            //   return (FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi_mapped)*
            //   FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[i],    eta_mapped)*
            //   FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i2[i],    zeta_mapped));
 
            //   // d()/deta
            // case 1:
            //   return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[i],    xi_mapped)*
            //   FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta_mapped)*
            //   FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i2[i],    zeta_mapped));
 
            //   // d()/dzeta
            // case 2:
            //   return (FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i0[i],    xi_mapped)*
            //   FE<1,BERNSTEIN>::shape      (EDGE3, totalorder, i1[i],    eta_mapped)*
            //   FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i2[i], 0, zeta_mapped));
 
            // default:
            //   libmesh_error_msg("Invalid derivative index j = " << j);
            // }
 
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
 
    default:
      libmesh_error_msg("Invalid totalorder = " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, j, p, add_p_level);
  libmesh_not_implemented();
#endif
}

shape_deriv() [35/233]

Real libMesh::FE< 1, CLOUGH >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 317 of file fe_clough_shape_1D.C.

{
  libmesh_assert(elem);
 
  clough_compute_coefs(elem);
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (totalorder)
    {
      // 3rd-order C1 cubic element
    case THIRD:
      {
        switch (type)
          {
            // C1 functions on the C1 cubic edge
          case EDGE2:
          case EDGE3:
            {
              switch (i)
                {
                case 0:
                  return clough_raw_shape_deriv(0, j, p);
                case 1:
                  return clough_raw_shape_deriv(1, j, p);
                case 2:
                  return d1xd1x * clough_raw_shape_deriv(2, j, p);
                case 3:
                  return d2xd2x * clough_raw_shape_deriv(3, j, p);
                default:
                  libmesh_error_msg("Invalid shape function index i = " << i);
                }
            }
          default:
            libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
          }
      }
      // by default throw an error
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order = " << totalorder);
    }
}

shape_deriv() [36/233]

Real libMesh::FE< 2, CLOUGH >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1970 of file fe_clough_shape_2D.C.

{
  libmesh_assert(elem);
 
  CloughCoefs coefs;
  clough_compute_coefs(elem, coefs);
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (totalorder)
    {
      // 2nd-order restricted Clough-Tocher element
    case SECOND:
      {
        // There may be a bug in the 2nd order case; the 3rd order
        // Clough-Tocher elements are pretty uniformly better anyways
        // so use those instead.
        libmesh_experimental();
        switch (type)
          {
            // C1 functions on the Clough-Tocher triangle.
          case TRI6:
          case TRI7:
            {
              libmesh_assert_less (i, 9);
              // FIXME: it would be nice to calculate (and cache)
              // clough_raw_shape(j,p) only once per triangle, not 1-7
              // times
              switch (i)
                {
                  // Note: these DoF numbers are "scrambled" because my
                  // initial numbering conventions didn't match libMesh
                case 0:
                  return clough_raw_shape_deriv(0, j, p)
                    + coefs.d1d2n * clough_raw_shape_deriv(10, j, p)
                    + coefs.d1d3n * clough_raw_shape_deriv(11, j, p);
                case 3:
                  return clough_raw_shape_deriv(1, j, p)
                    + coefs.d2d3n * clough_raw_shape_deriv(11, j, p)
                    + coefs.d2d1n * clough_raw_shape_deriv(9, j, p);
                case 6:
                  return clough_raw_shape_deriv(2, j, p)
                    + coefs.d3d1n * clough_raw_shape_deriv(9, j, p)
                    + coefs.d3d2n * clough_raw_shape_deriv(10, j, p);
                case 1:
                  return coefs.d1xd1x * clough_raw_shape_deriv(3, j, p)
                    + coefs.d1xd1y * clough_raw_shape_deriv(4, j, p)
                    + coefs.d1xd2n * clough_raw_shape_deriv(10, j, p)
                    + coefs.d1xd3n * clough_raw_shape_deriv(11, j, p)
                    + 0.5 * coefs.N01x * coefs.d3nd3n * clough_raw_shape_deriv(11, j, p)
                    + 0.5 * coefs.N02x * coefs.d2nd2n * clough_raw_shape_deriv(10, j, p);
                case 2:
                  return coefs.d1yd1y * clough_raw_shape_deriv(4, j, p)
                    + coefs.d1yd1x * clough_raw_shape_deriv(3, j, p)
                    + coefs.d1yd2n * clough_raw_shape_deriv(10, j, p)
                    + coefs.d1yd3n * clough_raw_shape_deriv(11, j, p)
                    + 0.5 * coefs.N01y * coefs.d3nd3n * clough_raw_shape_deriv(11, j, p)
                    + 0.5 * coefs.N02y * coefs.d2nd2n * clough_raw_shape_deriv(10, j, p);
                case 4:
                  return coefs.d2xd2x * clough_raw_shape_deriv(5, j, p)
                    + coefs.d2xd2y * clough_raw_shape_deriv(6, j, p)
                    + coefs.d2xd3n * clough_raw_shape_deriv(11, j, p)
                    + coefs.d2xd1n * clough_raw_shape_deriv(9, j, p)
                    + 0.5 * coefs.N10x * coefs.d3nd3n * clough_raw_shape_deriv(11, j, p)
                    + 0.5 * coefs.N12x * coefs.d1nd1n * clough_raw_shape_deriv(9, j, p);
                case 5:
                  return coefs.d2yd2y * clough_raw_shape_deriv(6, j, p)
                    + coefs.d2yd2x * clough_raw_shape_deriv(5, j, p)
                    + coefs.d2yd3n * clough_raw_shape_deriv(11, j, p)
                    + coefs.d2yd1n * clough_raw_shape_deriv(9, j, p)
                    + 0.5 * coefs.N10y * coefs.d3nd3n * clough_raw_shape_deriv(11, j, p)
                    + 0.5 * coefs.N12y * coefs.d1nd1n * clough_raw_shape_deriv(9, j, p);
                case 7:
                  return coefs.d3xd3x * clough_raw_shape_deriv(7, j, p)
                    + coefs.d3xd3y * clough_raw_shape_deriv(8, j, p)
                    + coefs.d3xd1n * clough_raw_shape_deriv(9, j, p)
                    + coefs.d3xd2n * clough_raw_shape_deriv(10, j, p)
                    + 0.5 * coefs.N20x * coefs.d2nd2n * clough_raw_shape_deriv(10, j, p)
                    + 0.5 * coefs.N21x * coefs.d1nd1n * clough_raw_shape_deriv(9, j, p);
                case 8:
                  return coefs.d3yd3y * clough_raw_shape_deriv(8, j, p)
                    + coefs.d3yd3x * clough_raw_shape_deriv(7, j, p)
                    + coefs.d3yd1n * clough_raw_shape_deriv(9, j, p)
                    + coefs.d3yd2n * clough_raw_shape_deriv(10, j, p)
                    + 0.5 * coefs.N20y * coefs.d2nd2n * clough_raw_shape_deriv(10, j, p)
                    + 0.5 * coefs.N21y * coefs.d1nd1n * clough_raw_shape_deriv(9, j, p);
                default:
                  libmesh_error_msg("Invalid shape function index i = " << i);
                }
            }
          default:
            libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
          }
      }
      // 3rd-order Clough-Tocher element
    case THIRD:
      {
        switch (type)
          {
            // C1 functions on the Clough-Tocher triangle.
          case TRI6:
          case TRI7:
            {
              libmesh_assert_less (i, 12);
 
              // FIXME: it would be nice to calculate (and cache)
              // clough_raw_shape(j,p) only once per triangle, not 1-7
              // times
              switch (i)
                {
                  // Note: these DoF numbers are "scrambled" because my
                  // initial numbering conventions didn't match libMesh
                case 0:
                  return clough_raw_shape_deriv(0, j, p)
                    + coefs.d1d2n * clough_raw_shape_deriv(10, j, p)
                    + coefs.d1d3n * clough_raw_shape_deriv(11, j, p);
                case 3:
                  return clough_raw_shape_deriv(1, j, p)
                    + coefs.d2d3n * clough_raw_shape_deriv(11, j, p)
                    + coefs.d2d1n * clough_raw_shape_deriv(9, j, p);
                case 6:
                  return clough_raw_shape_deriv(2, j, p)
                    + coefs.d3d1n * clough_raw_shape_deriv(9, j, p)
                    + coefs.d3d2n * clough_raw_shape_deriv(10, j, p);
                case 1:
                  return coefs.d1xd1x * clough_raw_shape_deriv(3, j, p)
                    + coefs.d1xd1y * clough_raw_shape_deriv(4, j, p)
                    + coefs.d1xd2n * clough_raw_shape_deriv(10, j, p)
                    + coefs.d1xd3n * clough_raw_shape_deriv(11, j, p);
                case 2:
                  return coefs.d1yd1y * clough_raw_shape_deriv(4, j, p)
                    + coefs.d1yd1x * clough_raw_shape_deriv(3, j, p)
                    + coefs.d1yd2n * clough_raw_shape_deriv(10, j, p)
                    + coefs.d1yd3n * clough_raw_shape_deriv(11, j, p);
                case 4:
                  return coefs.d2xd2x * clough_raw_shape_deriv(5, j, p)
                    + coefs.d2xd2y * clough_raw_shape_deriv(6, j, p)
                    + coefs.d2xd3n * clough_raw_shape_deriv(11, j, p)
                    + coefs.d2xd1n * clough_raw_shape_deriv(9, j, p);
                case 5:
                  return coefs.d2yd2y * clough_raw_shape_deriv(6, j, p)
                    + coefs.d2yd2x * clough_raw_shape_deriv(5, j, p)
                    + coefs.d2yd3n * clough_raw_shape_deriv(11, j, p)
                    + coefs.d2yd1n * clough_raw_shape_deriv(9, j, p);
                case 7:
                  return coefs.d3xd3x * clough_raw_shape_deriv(7, j, p)
                    + coefs.d3xd3y * clough_raw_shape_deriv(8, j, p)
                    + coefs.d3xd1n * clough_raw_shape_deriv(9, j, p)
                    + coefs.d3xd2n * clough_raw_shape_deriv(10, j, p);
                case 8:
                  return coefs.d3yd3y * clough_raw_shape_deriv(8, j, p)
                    + coefs.d3yd3x * clough_raw_shape_deriv(7, j, p)
                    + coefs.d3yd1n * clough_raw_shape_deriv(9, j, p)
                    + coefs.d3yd2n * clough_raw_shape_deriv(10, j, p);
                case 10:
                  return coefs.d1nd1n * clough_raw_shape_deriv(9, j, p);
                case 11:
                  return coefs.d2nd2n * clough_raw_shape_deriv(10, j, p);
                case 9:
                  return coefs.d3nd3n * clough_raw_shape_deriv(11, j, p);
 
                default:
                  libmesh_error_msg("Invalid shape function index i = " << i);
                }
            }
          default:
            libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
          }
      }
      // by default throw an error
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order = " << order);
    }
}

shape_deriv() [37/233]

Real libMesh::FE< 2, HERMITE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 270 of file fe_hermite_shape_2D.C.

{
  libmesh_assert(elem);
  libmesh_assert (j == 0 || j == 1);
 
  std::vector<std::vector<Real>> dxdxi(2, std::vector<Real>(2, 0));
 
#ifdef DEBUG
  std::vector<Real> dxdeta(2), dydxi(2);
#endif
 
  hermite_compute_coefs(elem,dxdxi
#ifdef DEBUG
                        ,dxdeta,dydxi
#endif
                        );
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (type)
    {
    case QUAD4:
    case QUADSHELL4:
      libmesh_assert_less (totalorder, 4);
      libmesh_fallthrough();
    case QUAD8:
    case QUADSHELL8:
    case QUAD9:
    case QUADSHELL9:
      {
        libmesh_assert_less (i, (totalorder+1u)*(totalorder+1u));
 
        std::vector<unsigned int> bases1D;
 
        Real coef = hermite_bases_2D(bases1D, dxdxi, totalorder, i);
 
        switch (j)
          {
          case 0:
            return coef *
              FEHermite<1>::hermite_raw_shape_deriv(bases1D[0],p(0)) *
              FEHermite<1>::hermite_raw_shape(bases1D[1],p(1));
          case 1:
            return coef *
              FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
              FEHermite<1>::hermite_raw_shape_deriv(bases1D[1],p(1));
          default:
            libmesh_error_msg("Invalid derivative index j = " << j);
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
    }
}

shape_deriv() [38/233]

Real libMesh::FE< 3, HERMITE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 465 of file fe_hermite_shape_3D.C.

{
  libmesh_assert(elem);
  libmesh_assert (j == 0 || j == 1 || j == 2);
 
  std::vector<std::vector<Real>> dxdxi(3, std::vector<Real>(2, 0));
 
#ifdef DEBUG
  std::vector<Real> dydxi(2), dzdeta(2), dxdzeta(2);
  std::vector<Real> dzdxi(2), dxdeta(2), dydzeta(2);
#endif //DEBUG
 
  hermite_compute_coefs(elem, dxdxi
#ifdef DEBUG
                        , dydxi, dzdeta, dxdzeta, dzdxi, dxdeta, dydzeta
#endif
                        );
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (totalorder)
    {
      // 3rd-order tricubic Hermite functions
    case THIRD:
      {
        switch (type)
          {
          case HEX8:
          case HEX20:
          case HEX27:
            {
              libmesh_assert_less (i, 64);
 
              std::vector<unsigned int> bases1D;
 
              Real coef = hermite_bases_3D(bases1D, dxdxi, totalorder, i);
 
              switch (j) // Derivative type
                {
                case 0:
                  return coef *
                    FEHermite<1>::hermite_raw_shape_deriv(bases1D[0],p(0)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[1],p(1)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[2],p(2));
                  break;
                case 1:
                  return coef *
                    FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
                    FEHermite<1>::hermite_raw_shape_deriv(bases1D[1],p(1)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[2],p(2));
                  break;
                case 2:
                  return coef *
                    FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[1],p(1)) *
                    FEHermite<1>::hermite_raw_shape_deriv(bases1D[2],p(2));
                  break;
                default:
                  libmesh_error_msg("Invalid shape function derivative j = " << j);
                }
 
            }
          default:
            libmesh_error_msg("ERROR: Unsupported element type " << Utility::enum_to_string(type));
          }
      }
      // by default throw an error
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order " << totalorder);
    }
}

shape_deriv() [39/233]

Real libMesh::FE< 1, HIERARCHIC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 214 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_hierarchic_1D_shape_deriv(elem->type(),
                                      order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [40/233]

Real libMesh::FE< 1, L2_HIERARCHIC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 245 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_hierarchic_1D_shape_deriv(elem->type(),
                                      order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [41/233]

Real libMesh::FE< 2, HIERARCHIC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 441 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape_deriv<HIERARCHIC>(elem, order, i, j, p, add_p_level);
}

shape_deriv() [42/233]

Real libMesh::FE< 2, L2_HIERARCHIC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 467 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape_deriv<L2_HIERARCHIC>(elem, order, i, j, p, add_p_level);
}

shape_deriv() [43/233]

Real libMesh::FE< 2, SIDE_HIERARCHIC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 492 of file fe_hierarchic_shape_2D.C.

{
  libmesh_assert(elem);
 
  const ElemType type = elem->type();
 
  const Order totalorder = order + add_p_level*elem->p_level();
 
  if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
    return 0;
 
  const unsigned int dofs_per_side = totalorder+1u;
 
  switch (type)
    {
    case TRI6:
    case TRI7:
      {
        return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<2,SIDE_HIERARCHIC>::shape);
      }
#if 0
      {
        libmesh_assert_less(i, 3*dofs_per_side);
        libmesh_assert_less (j, 2);
 
        // Flip odd degree of freedom values if necessary
        // to keep continuity on sides.  We'll flip xi/eta rather than
        // flipping phi, so that we can use this to handle the "nodal"
        // degrees of freedom too.
        Real f = 1.;
 
        const Real zeta1 = p(0);
        const Real zeta2 = p(1);
        const Real zeta0 = 1. - zeta1 - zeta2;
 
        if (zeta1 > zeta2 && zeta0 > zeta2) // side 0
          {
            if (j == 1) // d/deta is perpendicular here
              return 0;
 
            if (i >= dofs_per_side)
              return 0;
 
            if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
              return 0;
 
            if ((i < 2 || i % 2) &&
                elem->positive_edge_orientation(0))
              f = -1;
 
            return f*FE<1,HIERARCHIC>::shape_deriv(EDGE3, totalorder, i, 0, f*(zeta1-zeta0));
          }
        else if (zeta1 > zeta0 && zeta2 > zeta0) // side 1
          {
            if (i < dofs_per_side ||
                i >= 2*dofs_per_side)
              return 0;
 
            if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
              return 0;
 
            const unsigned int side_i = i - dofs_per_side;
 
            if ((side_i < 2 || side_i % 2) &&
                elem->positive_edge_orientation(1))
              f = -1;
 
            Real g = 1;
            if (j == 0) // 2D d/dxi is in the opposite direction on this edge
              g = -1;
 
            return f*g*FE<1,HIERARCHIC>::shape_deriv(EDGE3, totalorder, side_i, 0, f*(zeta2-zeta1));
          }
        else // side 2
          {
            libmesh_assert (zeta2 >= zeta1 && zeta0 >= zeta1); // On a corner???
 
            if (j == 0) // d/dxi is perpendicular here
              return 0;
 
            if (i < 2*dofs_per_side)
              return 0;
 
            if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
              return 0;
 
            const unsigned int side_i = i - 2*dofs_per_side;
 
            if ((side_i < 2 || side_i % 2) &&
                elem->positive_edge_orientation(2))
              f = -1;
 
            return -f*FE<1,HIERARCHIC>::shape_deriv(EDGE3, totalorder, side_i, 0, f*(zeta0-zeta2));
          }
      }
#endif
    case QUAD8:
    case QUADSHELL8:
    case QUAD9:
    case QUADSHELL9:
      {
        libmesh_assert_less(i, 4*dofs_per_side);
 
        // Flip odd degree of freedom values if necessary
        // to keep continuity on sides.  We'll flip xi/eta rather than
        // flipping phi, so that we can use this to handle the "nodal"
        // degrees of freedom too.
        Real f = 1.;
 
        const Real xi = p(0), eta = p(1);
        if (eta < xi)
          {
            if (eta < -xi) // side 0
              {
                if (i >= dofs_per_side)
                  return 0;
                if (j != 0)
                  return 0;
                if ((i < 2 || i % 2) &&
                    elem->positive_edge_orientation(0))
                  f = -1;
 
                return f*FE<1,HIERARCHIC>::shape_deriv(EDGE3, totalorder, i, 0, f*xi);
              }
            else           // side 1
              {
                if (i < dofs_per_side ||
                    i >= 2*dofs_per_side)
                  return 0;
                if (j != 1)
                  return 0;
 
                const unsigned int side_i = i - dofs_per_side;
 
                if ((side_i < 2 || side_i % 2) &&
                    elem->positive_edge_orientation(1))
                  f = -1;
 
                return f*FE<1,HIERARCHIC>::shape_deriv(EDGE3, totalorder, side_i, 0, f*eta);
              }
          }
        else // xi < eta
          {
            if (eta > -xi)    // side 2
              {
                if (i < 2*dofs_per_side ||
                    i >= 3*dofs_per_side)
                  return 0;
                if (j != 0)
                  return 0;
 
                const unsigned int side_i = i - 2*dofs_per_side;
 
                if ((side_i < 2 || side_i % 2) &&
                    !elem->positive_edge_orientation(2))
                  f = -1;
 
                return f*FE<1,HIERARCHIC>::shape_deriv(EDGE3, totalorder, side_i, 0, f*xi);
              }
            else           // side 3
              {
                if (i < 3*dofs_per_side)
                  return 0;
                if (j != 1)
                  return 0;
 
                const unsigned int side_i = i - 3*dofs_per_side;
 
                if ((side_i < 2 || side_i % 2) &&
                    !elem->positive_edge_orientation(3))
                  f = -1;
 
                return f*FE<1,HIERARCHIC>::shape_deriv(EDGE3, totalorder, side_i, 0, f*eta);
              }
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(elem->type()));
    }
  return 0;
}

shape_deriv() [44/233]

Real libMesh::FE< 3, HIERARCHIC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1548 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape_deriv<HIERARCHIC>(elem, order, i, j, p, add_p_level);
}

shape_deriv() [45/233]

Real libMesh::FE< 3, L2_HIERARCHIC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1573 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape_deriv<L2_HIERARCHIC>(elem, order, i, j, p, add_p_level);
}

shape_deriv() [46/233]

Real libMesh::FE< 3, SIDE_HIERARCHIC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1598 of file fe_hierarchic_shape_3D.C.

{
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
  const ElemType type = elem->type();
 
  const Order totalorder = order + add_p_level*elem->p_level();
 
  if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
    return 0; // constants have zero derivative
 
  switch (type)
    {
    case HEX27:
      {
        // I need to debug the p>2 case here...
        if (totalorder > 2)
          return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<3,SIDE_HIERARCHIC>::shape);
 
        const unsigned int dofs_per_side = (totalorder+1u)*(totalorder+1u);
        libmesh_assert_less(i, 6*dofs_per_side);
 
        const unsigned int sidenum = cube_side(p);
        if (sidenum > 5)
          return std::numeric_limits<Real>::quiet_NaN();
 
        const unsigned int dof_offset = sidenum * dofs_per_side;
 
        if (i < dof_offset) // i is on a previous side
          return 0;
 
        if (i >= dof_offset + dofs_per_side) // i is on a later side
          return 0;
 
        unsigned int side_i = i - dof_offset;
 
        std::unique_ptr<const Elem> side = elem->build_side_ptr(sidenum);
 
        Point sidep = cube_side_point(sidenum, p);
 
        cube_remap(side_i, *side, totalorder, sidep);
 
        // What direction on the side corresponds to the derivative
        // direction we want?
        unsigned int sidej = 100;
 
        // Do we need a -1 here to flip that direction?
        Real f = 1.;
 
        switch (j)
          {
          case 0: // d()/dxi
            {
              switch (sidenum)
                {
                case 0:
                  sidej = 1;
                  break;
                case 1:
                  sidej = 0;
                  break;
                case 2:
                  return 0;
                case 3:
                  sidej = 0;
                  f = -1;
                  break;
                case 4:
                  return 0;
                case 5:
                  sidej = 0;
                  break;
                default:
                  libmesh_error();
                }
              break;
            }
          case 1: // d()/deta
            {
              switch (sidenum)
                {
                case 0:
                  sidej = 0;
                  break;
                case 1:
                  return 0;
                case 2:
                  sidej = 0;
                  break;
                case 3:
                  return 0;
                case 4:
                  sidej = 0;
                  f = -1;
                  break;
                case 5:
                  sidej = 1;
                  break;
                default:
                  libmesh_error();
                }
              break;
            }
          case 2: // d()/dzeta
            {
              switch (sidenum)
                {
                case 0:
                  return 0;
                case 1:
                case 2:
                case 3:
                case 4:
                  sidej = 1;
                  break;
                case 5:
                  return 0;
                default:
                  libmesh_error();
                }
              break;
            }
 
          default:
            libmesh_error_msg("Invalid derivative index j = " << j);
          }
 
        return f * FE<2,HIERARCHIC>::shape_deriv(side.get(), order,
                                                 side_i, sidej, sidep,
                                                 add_p_level);
      }
 
    case TET14:
    case PRISM20:
    case PRISM21:
      {
        return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<3,SIDE_HIERARCHIC>::shape);
      }
 
    default:
      libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, j, p, add_p_level);
  libmesh_not_implemented();
#endif
}

shape_deriv() [47/233]

RealGradient libMesh::FE< 0, HIERARCHIC_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 425 of file fe_hierarchic_vec.C.

{
  const Real value = FE<0,HIERARCHIC>::shape_deriv(elem, order, i, j, p, add_p_level);
  return libMesh::RealGradient( value );
}

shape_deriv() [48/233]

RealGradient libMesh::FE< 0, L2_HIERARCHIC_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 454 of file fe_hierarchic_vec.C.

{
  return FE<0,HIERARCHIC_VEC>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [49/233]

RealGradient libMesh::FE< 1, HIERARCHIC_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 482 of file fe_hierarchic_vec.C.

{
  Real value = FE<1,HIERARCHIC>::shape_deriv(elem, order, i, j, p, add_p_level);
  return libMesh::RealGradient( value );
}

shape_deriv() [50/233]

RealGradient libMesh::FE< 1, L2_HIERARCHIC_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 510 of file fe_hierarchic_vec.C.

{
  return FE<1,HIERARCHIC_VEC>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [51/233]

RealGradient libMesh::FE< 2, HIERARCHIC_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 552 of file fe_hierarchic_vec.C.

{
  const Real value = FE<2,HIERARCHIC>::shape_deriv(elem, order, i/2, j, p, add_p_level);
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_deriv() [52/233]

RealGradient libMesh::FE< 2, L2_HIERARCHIC_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 607 of file fe_hierarchic_vec.C.

{
  return FE<2,HIERARCHIC_VEC>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [53/233]

RealGradient libMesh::FE< 3, HIERARCHIC_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 653 of file fe_hierarchic_vec.C.

{
  const Real value = FE<3,HIERARCHIC>::shape_deriv(elem, order, i/3, j, p, add_p_level);
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_deriv() [54/233]

RealGradient libMesh::FE< 3, L2_HIERARCHIC_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 716 of file fe_hierarchic_vec.C.

{
  return FE<3,HIERARCHIC_VEC>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [55/233]

Real libMesh::FE< 1, LAGRANGE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 127 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_lagrange_1D_shape_deriv(order + add_p_level*elem->p_level(), i, j, p(0));
}

shape_deriv() [56/233]

Real libMesh::FE< 1, L2_LAGRANGE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 142 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_lagrange_1D_shape_deriv(order + add_p_level*elem->p_level(), i, j, p(0));
}

shape_deriv() [57/233]

Real libMesh::FE< 2, LAGRANGE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 172 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape functions
  return fe_lagrange_2D_shape_deriv<LAGRANGE>(elem->type(), elem, order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [58/233]

Real libMesh::FE< 2, L2_LAGRANGE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 188 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape functions
  return fe_lagrange_2D_shape_deriv<L2_LAGRANGE>(elem->type(), elem, order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [59/233]

Real libMesh::FE< 3, LAGRANGE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 519 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape function derivatives
  return fe_lagrange_3D_shape_deriv<LAGRANGE>(elem->type(), order + add_p_level*elem->p_level(), elem, i, j, p);
}

shape_deriv() [60/233]

Real libMesh::FE< 3, L2_LAGRANGE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 534 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape function derivatives
  return fe_lagrange_3D_shape_deriv<L2_LAGRANGE>(elem->type(), order + add_p_level*elem->p_level(), elem, i, j, p);
}

shape_deriv() [61/233]

RealGradient libMesh::FE< 0, LAGRANGE_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 965 of file fe_lagrange_vec.C.

{
  Real value = FE<0,LAGRANGE>::shape_deriv( elem->type(), order + add_p_level*elem->p_level(), i, j, p);
  return libMesh::RealGradient( value );
}

shape_deriv() [62/233]

RealGradient libMesh::FE< 0, L2_LAGRANGE_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 993 of file fe_lagrange_vec.C.

{
  return FE<0,LAGRANGE_VEC>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [63/233]

RealGradient libMesh::FE< 1, LAGRANGE_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1021 of file fe_lagrange_vec.C.

{
  Real value = FE<1,LAGRANGE>::shape_deriv( elem->type(), order + add_p_level*elem->p_level(), i, j, p);
  return libMesh::RealGradient( value );
}

shape_deriv() [64/233]

RealGradient libMesh::FE< 1, L2_LAGRANGE_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1048 of file fe_lagrange_vec.C.

{
  return FE<1,LAGRANGE_VEC>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [65/233]

RealGradient libMesh::FE< 2, LAGRANGE_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1090 of file fe_lagrange_vec.C.

{
  Real value = FE<2,LAGRANGE>::shape_deriv( elem->type(), order + add_p_level*elem->p_level(), i/2, j, p );
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_deriv() [66/233]

RealGradient libMesh::FE< 2, L2_LAGRANGE_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1145 of file fe_lagrange_vec.C.

{
  return FE<2,LAGRANGE_VEC>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [67/233]

RealGradient libMesh::FE< 3, LAGRANGE_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1190 of file fe_lagrange_vec.C.

{
  Real value = FE<3,LAGRANGE>::shape_deriv( elem->type(), order + add_p_level*elem->p_level(), i/3, j, p );
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_deriv() [68/233]

RealGradient libMesh::FE< 3, L2_LAGRANGE_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1252 of file fe_lagrange_vec.C.

{
  return FE<3,LAGRANGE_VEC>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [69/233]

Real libMesh::FE< 1, MONOMIAL >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 140 of file fe_monomial_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,MONOMIAL>::shape_deriv(elem->type(),
                                     order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [70/233]

Real libMesh::FE< 2, MONOMIAL >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 324 of file fe_monomial_shape_2D.C.

{
  libmesh_assert(elem);
 
  // by default call the orientation-independent shape functions
  return FE<2,MONOMIAL>::shape_deriv(elem->type(), order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [71/233]

Real libMesh::FE< 3, MONOMIAL >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 659 of file fe_monomial_shape_3D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape function derivatives
  return FE<3,MONOMIAL>::shape_deriv(elem->type(), order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [72/233]

RealVectorValue libMesh::FE< 0, MONOMIAL_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 405 of file fe_monomial_vec.C.

{
  Real value = FE<0, MONOMIAL>::shape_deriv(
      elem->type(), order + add_p_level*elem->p_level(), i, j, p);
  return libMesh::RealVectorValue(value);
}

shape_deriv() [73/233]

RealVectorValue libMesh::FE< 1, MONOMIAL_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 450 of file fe_monomial_vec.C.

{
  Real value = FE<1, MONOMIAL>::shape_deriv(
      elem->type(), order + add_p_level*elem->p_level(), i, j, p);
  return libMesh::RealVectorValue(value);
}

shape_deriv() [74/233]

RealVectorValue libMesh::FE< 2, MONOMIAL_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 508 of file fe_monomial_vec.C.

{
  Real value = FE<2, MONOMIAL>::shape_deriv(
      elem->type(), order + add_p_level*elem->p_level(), i / 2, j, p);
 
  switch (i % 2)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape_deriv() [75/233]

RealVectorValue libMesh::FE< 3, MONOMIAL_VEC >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 597 of file fe_monomial_vec.C.

{
  Real value = FE<3, MONOMIAL>::shape_deriv(
      elem->type(), order + add_p_level*elem->p_level(), i / 3, j, p);
 
  switch (i % 3)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    case 2:
      return libMesh::RealVectorValue(Real(0), Real(0), value);
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape_deriv() [76/233]

RealGradient libMesh::FE< 2, NEDELEC_ONE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 706 of file fe_nedelec_one_shape_2D.C.

{
#if LIBMESH_DIM > 1
  libmesh_assert(elem);
  libmesh_assert_less (j, 2);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = i >= totalorder * elem->n_edges() || elem->positive_edge_orientation(i / totalorder) ? 1 : -1;
  const unsigned int ii = sign > 0 ? i : (i / totalorder * 2 + 1) * totalorder - 1 - i;
 
  const Real xi  = p(0);
  const Real eta = p(1);
 
  switch (totalorder)
    {
      // linear Nedelec (first kind) shape function first derivatives
    case FIRST:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                      case 2:
                        return RealGradient();
                      case 1:
                      case 3:
                        return sign * RealGradient( 0.0, -0.25 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(ii)
                      {
                      case 1:
                      case 3:
                        return RealGradient();
                      case 0:
                      case 2:
                        return sign * RealGradient( 0.25 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return sign * RealGradient( 0.0, -1.0 );
 
                  // d()/deta
                case 1:
                  return sign * RealGradient( 1.0 );
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
 
      // quadratic Nedelec (first kind) shape function first derivatives
    case SECOND:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              // Even with a loose inverse_map tolerance we ought to
              // be nearly on the element interior in master
              // coordinates
              libmesh_assert_less_equal ( std::fabs(xi), 1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(eta), 1.0+10*TOLERANCE );
 
              const Real x = 0.5 * (xi + 1.0);
              const Real y = 0.5 * (eta + 1.0);
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient( 0.25*(-18.0*y*y+24.0*y-6.0), 0.0 );
                      case 1:
                        return sign * RealGradient( 0.25*( 18.0*y*y-24.0*y+6.0), 0.0 );
                      case 2:
                        return sign * RealGradient( 0.0, 0.25*(-36.0*x*y+24.0*x+12.0*y-8.0) );
                      case 3:
                        return sign * RealGradient( 0.0, 0.25*( 36.0*x*y-12.0*x-12.0*y+4.0) );
                      case 4:
                        return sign * RealGradient( 0.25*(-18.0*y*y+12.0*y), 0.0 );
                      case 5:
                        return sign * RealGradient( 0.25*( 18.0*y*y-12.0*y), 0.0 );
                      case 6:
                        return sign * RealGradient( 0.0, 0.25*(-36.0*x*y+12.0*x+24.0*y-8.0) );
                      case 7:
                        return sign * RealGradient( 0.0, 0.25*( 36.0*x*y-24.0*x-24.0*y+16.0) );
                      case 8:
                        return RealGradient( 0.0, 1.5*(6.0*x*y-4.0*x-3.0*y+2.0) );
                      case 9:
                        return RealGradient( 1.5*y*(-3.0*y+3.0), 0.0 );
                      case 10:
                        return RealGradient( 1.5*y*(3.0*y-3.0), 0.0 );
                      case 11:
                        return RealGradient( 0.0, 1.5*(-6.0*x*y+2.0*x+3.0*y-1.0) );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient( 0.25*(-36.0*x*y+24.0*x+24.0*y-16.0), 0.0 );
                      case 1:
                        return sign * RealGradient( 0.25*( 36.0*x*y-24.0*x-12.0*y+8.0), 0.0 );
                      case 2:
                        return sign * RealGradient( 0.0, 0.25*x*(-18.0*x+12.0) );
                      case 3:
                        return sign * RealGradient( 0.0, 0.25*x*( 18.0*x-12.0) );
                      case 4:
                        return sign * RealGradient( 0.25*(-36.0*x*y+12.0*x+12.0*y-4.0), 0.0 );
                      case 5:
                        return sign * RealGradient( 0.25*( 36.0*x*y-12.0*x-24.0*y+8.0), 0.0 );
                      case 6:
                        return sign * RealGradient( 0.0, 0.25*(-18.0*x*x+24.0*x-6.0) );
                      case 7:
                        return sign * RealGradient( 0.0, 0.25*( 18.0*x*x-24.0*x+6.0) );
                      case 8:
                        return RealGradient( 0.0, 1.5*x*(3.0*x-3.0) );
                      case 9:
                        return RealGradient( 1.5*(-6.0*x*y+3.0*x+4.0*y-2.0), 0.0 );
                      case 10:
                        return RealGradient( 1.5*(6.0*x*y-3.0*x-2.0*y+1.0), 0.0 );
                      case 11:
                        return RealGradient( 0.0, 1.5*x*(-3.0*x+3.0) );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient( 8.0*eta-6.0, -16.0*xi-8.0*eta+6.0 );
                      case 1:
                        return sign * RealGradient( -8.0*eta+6.0, 16.0*xi-4.0 );
                      case 2:
                        return sign * RealGradient( -8.0*eta, 16.0*xi-4.0 );
                      case 3:
                        return sign * RealGradient( 0.0, 8.0*eta-2.0 );
                      case 4:
                        return sign * RealGradient( 0.0, 8.0*eta-2.0 );
                      case 5:
                        return sign * RealGradient( 8.0*eta, -16.0*xi-8.0*eta+12.0 );
                      case 6:
                        return RealGradient( -8.0*eta, 16.0*xi+16.0*eta-8.0 );
                      case 7:
                        return RealGradient( 16.0*eta, -32.0*xi-8.0*eta+16.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient( 8.0*xi+16.0*eta-12.0, -8.0*xi );
                      case 1:
                        return sign * RealGradient( -8.0*xi+2.0, 0.0 );
                      case 2:
                        return sign * RealGradient( 2.0-8.0*xi, 0.0 );
                      case 3:
                        return sign * RealGradient( 4.0-16.0*eta, 8.0*xi );
                      case 4:
                        return sign * RealGradient( 4.0-16.0*eta,8.0*xi-6.0 );
                      case 5:
                        return sign * RealGradient( 8.0*xi+16*eta-6.0,-8.0*xi+6.0 );
                      case 6:
                        return RealGradient( -8.0*xi-32.0*eta+16.0, 16.0*xi );
                      case 7:
                        return RealGradient( 16.0*xi+16.0*eta-8.0,-8.0*xi );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
 
      // cubic Nedelec (first kind) shape function first derivatives
    case THIRD:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(81.*eta/2. + 15.*xi/2. - 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 39. - 162.*(eta + 1.)*(eta + 1.)/(2.*2.) + 90.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 1:
                        return sign * RealGradient(-135.*eta/8. - 15.*xi/4. + 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 135.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 75.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 135./8. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2., 0.);
                      case 2:
                        return sign * RealGradient(27.*eta + 15.*xi/2. - 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 57./2. - 108.*(eta + 1.)*(eta + 1.)/(2.*2.) + 60.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 3:
                        return sign * RealGradient(0., -27.*eta/2. - 27.*xi + 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 135./4. + 45.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 135.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 4:
                        return sign * RealGradient(0., 45.*eta/8. + 9.*xi/2. - 90.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. + 90.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 9. - 45.*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. - 45.*(xi + 1.)*(xi + 1.)/(2.*2.)/4.);
                      case 5:
                        return sign * RealGradient(0., -9.*eta - 9.*xi + 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 63./4. + 45.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 45.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 6:
                        return sign * RealGradient(9.*eta - 45.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 9. - 72.*(eta + 1.)*(eta + 1.)/(2.*2.) + 60.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 7:
                        return sign * RealGradient(-45.*eta/8. + 45.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 90.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 75.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 45./8. + 45.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2., 0.);
                      case 8:
                        return sign * RealGradient(27.*eta/2. - 45.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 27./2. - 108.*(eta + 1.)*(eta + 1.)/(2.*2.) + 90.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 9:
                        return sign * RealGradient(0., -27.*eta - 27.*xi/2. + 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 135./4. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 45.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 10:
                        return sign * RealGradient(0., 135.*eta/8. + 27.*xi/4. - 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. + 135.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 81./4. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. - 45.*(xi + 1.)*(xi + 1.)/(2.*2.)/4.);
                      case 11:
                        return sign * RealGradient(0., -81.*eta/2. - 81.*xi/2. + 324.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 243./4. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 135.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 12:
                        return RealGradient(0., -36.*eta - 81.*xi/2. + 324.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 117./2. + 60.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 135.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 13:
                        return RealGradient(0., 9.*eta + 27.*xi - 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 63./2. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.) - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 135.*(xi + 1.)*(xi + 1.)/(2.*2.)/2.);
                      case 14:
                        return RealGradient(36.*eta - 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 36. - 162.*(eta + 1.)*(eta + 1.)/(2.*2.) + 90.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 15:
                        return RealGradient(-9.*eta + 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 9. + 108.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 90.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 16:
                        return RealGradient(24.*eta - 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 24. - 108.*(eta + 1.)*(eta + 1.)/(2.*2.) + 60.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 17:
                        return RealGradient(-6.*eta + 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 6. + 72.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 60.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 18:
                        return RealGradient(0., -24.*eta - 27.*xi/2. + 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 63./2. + 60.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 45.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 19:
                        return RealGradient(0., 6.*eta + 9.*xi - 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 27./2. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.) - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 45.*(xi + 1.)*(xi + 1.)/(2.*2.)/2.);
                      case 20:
                        return RealGradient(0., 0.);
                      case 21:
                        return RealGradient(0., -9.*xi/2. - 5./2. + 15.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 22:
                        return RealGradient(0., 3.*xi + 5./2. - 15.*(xi + 1.)*(xi + 1.)/(2.*2.)/2.);
                      case 23:
                        return RealGradient(0., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(81.*eta/2. + 81.*xi/2. - 324.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 243./4. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 135.*(xi + 1.)*(xi + 1.)/(2.*2.)/2., 0.);
                      case 1:
                        return sign * RealGradient(-27.*eta/4. - 135.*xi/8. + 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 135.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 81./4. + 45.*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. + 135.*((xi + 1.)*(xi + 1.)/(2.*2.))/4., 0.);
                      case 2:
                        return sign * RealGradient(27.*eta/2. + 27.*xi - 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 135./4. - 45.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 135.*(xi + 1.)*(xi + 1.)/(2.*2.)/2., 0.);
                      case 3:
                        return sign * RealGradient(0., -27.*xi/2. + 45.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 27./2. + 108.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 90.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 4:
                        return sign * RealGradient(0., 45.*xi/8. - 45.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 90.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 75.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 45./8. - 45.*(xi + 1.)*(xi + 1.)/(2.*2.) + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2.);
                      case 5:
                        return sign * RealGradient(0., -9.*xi + 45.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 9. + 72.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 60.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 6:
                        return sign * RealGradient(9.*eta + 9.*xi - 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 63./4. - 45.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 45.*(xi + 1.)*(xi + 1.)/(2.*2.)/2., 0.);
                      case 7:
                        return sign * RealGradient(-9.*eta/2. - 45.*xi/8. + 90.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 90.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 9. + 45.*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. + 45.*((xi + 1.)*(xi + 1.)/(2.*2.))/4., 0.);
                      case 8:
                        return sign * RealGradient(27.*eta + 27.*xi/2. - 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 135./4. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 45.*(xi + 1.)*(xi + 1.)/(2.*2.)/2., 0.);
                      case 9:
                        return sign * RealGradient(0., -15.*eta/2. - 27.*xi + 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 57./2. + 108.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 60.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 10:
                        return sign * RealGradient(0., 15.*eta/4. + 135.*xi/8. - 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 135.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 75.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 135./8. - 135.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2.);
                      case 11:
                        return sign * RealGradient(0., -15.*eta/2. - 81.*xi/2. + 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 39. + 162.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 90.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 12:
                        return RealGradient(0., -36.*xi + 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 36. + 162.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 90.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 13:
                        return RealGradient(0., 9.*xi - 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 9. - 108.*(xi + 1.)*(xi + 1.)/(2.*2.) + 90.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 14:
                        return RealGradient(81.*eta/2. + 36.*xi - 324.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 117./2. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 60.*(xi + 1.)*(xi + 1.)/(2.*2.), 0.);
                      case 15:
                        return RealGradient(-27.*eta - 9.*xi + 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 63./2. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 15.*((xi + 1.)*(xi + 1.)/(2.*2.)), 0.);
                      case 16:
                        return RealGradient(27.*eta/2. + 24.*xi - 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 63./2. - 45.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 60.*(xi + 1.)*(xi + 1.)/(2.*2.), 0.);
                      case 17:
                        return RealGradient(-9.*eta - 6.*xi + 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 27./2. + 45.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 15.*((xi + 1.)*(xi + 1.)/(2.*2.)), 0.);
                      case 18:
                        return RealGradient(0., -24.*xi + 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 24. + 108.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 60.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 19:
                        return RealGradient(0., 6.*xi - 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 6. - 72.*(xi + 1.)*(xi + 1.)/(2.*2.) + 60.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 20:
                        return RealGradient(-9.*eta/2. - 5./2. + 15.*((eta + 1.)*(eta + 1.)/(2.*2.))/2., 0.);
                      case 21:
                        return RealGradient(0., 0.);
                      case 22:
                        return RealGradient(0., 0.);
                      case 23:
                        return RealGradient(3.*eta + 5./2. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.)/2., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-90.*eta*xi + 120.*eta + 60.*xi - 36. - 90.*eta*eta, 180.*eta*xi - 60.*eta - 120.*xi + 18. + 45.*(eta*eta) + 135.*(xi*xi));
                      case 1:
                        return sign * RealGradient(45.*eta*xi - 75.*eta/2. - 30.*xi + 15. + 45.*(eta*eta)/2., -45.*eta*xi + 105.*xi/2. - 21./4. + 45.*(eta*eta)/4. - 135.*xi*xi/2.);
                      case 2:
                        return sign * RealGradient(-90.*eta*xi + 30.*eta + 60.*xi - 24., -90.*xi + 9. + 135.*(xi*xi));
                      case 3:
                        return sign * RealGradient(-90.*eta*xi + 30.*eta, -90.*xi + 9. + 135.*(xi*xi));
                      case 4:
                        return sign * RealGradient(-45.*eta*xi/2. + 45.*eta/2. - 45.*eta*eta, 90.*eta*xi - 45.*eta/2. - 75.*xi/2. + 6. + 45.*(eta*eta)/4. + 135.*(xi*xi)/4.);
                      case 5:
                        return sign * RealGradient(0., -30.*eta + 3. + 45.*(eta*eta));
                      case 6:
                        return sign * RealGradient(0., -30.*eta + 3. + 45.*(eta*eta));
                      case 7:
                        return sign * RealGradient(-45.*eta*xi/2. + 45.*(eta*eta)/2., -45.*eta*xi + 75.*eta/2. - 30.*xi + 9./4. - 45.*eta*eta/2. + 135.*(xi*xi)/4.);
                      case 8:
                        return sign * RealGradient(-90.*eta*xi + 60.*eta - 90.*eta*eta, 180.*eta*xi - 120.*eta - 180.*xi + 54. + 45.*(eta*eta) + 135.*(xi*xi));
                      case 9:
                        return RealGradient(180.*eta*xi - 300.*eta + 360.*(eta*eta), -720.*eta*xi + 300.*eta + 300.*xi - 60. - 270.*eta*eta - 270.*xi*xi);
                      case 10:
                        return RealGradient(-540.*eta*xi + 300.*eta - 360.*eta*eta, 720.*eta*xi - 300.*eta - 900.*xi + 180. + 90.*(eta*eta) + 810.*(xi*xi));
                      case 11:
                        return RealGradient(-360.*eta*xi + 360.*eta - 360.*eta*eta, 720.*eta*xi - 120.*eta - 480.*xi + 60. + 540.*(xi*xi));
                      case 12:
                        return RealGradient(540.*eta*xi - 240.*eta + 180.*(eta*eta), -360.*eta*xi + 60.*eta + 720.*xi - 90. - 810.*xi*xi);
                      case 13:
                        return RealGradient(60.*eta - 180.*eta*eta, 360.*eta*xi - 240.*eta - 60.*xi + 30. + 270.*(eta*eta));
                      case 14:
                        return RealGradient(-120.*eta + 360.*(eta*eta), -720.*eta*xi + 360.*eta + 120.*xi - 60. - 180.*eta*eta);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-180.*eta*xi + 180.*eta + 120.*xi - 54. - 135.*eta*eta - 45.*xi*xi, 90.*eta*xi - 60.*xi + 90.*(xi*xi));
                      case 1:
                        return sign * RealGradient(45.*eta*xi + 30.*eta - 75.*xi/2. - 9./4. - 135.*eta*eta/4. + 45.*(xi*xi)/2., 45.*eta*xi/2. - 45.*xi*xi/2.);
                      case 2:
                        return sign * RealGradient(30.*xi - 3. - 45.*xi*xi, 0.);
                      case 3:
                        return sign * RealGradient(30.*xi - 3. - 45.*xi*xi, 0.);
                      case 4:
                        return sign * RealGradient(-90.*eta*xi + 75.*eta/2. + 45.*xi/2. - 6. - 135.*eta*eta/4. - 45.*xi*xi/4., 45.*eta*xi/2. - 45.*xi/2. + 45.*(xi*xi));
                      case 5:
                        return sign * RealGradient(90.*eta - 9. - 135.*eta*eta, 90.*eta*xi - 30.*xi);
                      case 6:
                        return sign * RealGradient(90.*eta - 9. - 135.*eta*eta, 90.*eta*xi - 60.*eta - 30.*xi + 24.);
                      case 7:
                        return sign * RealGradient(45.*eta*xi - 105.*eta/2. + 21./4. + 135.*(eta*eta)/2. - 45.*xi*xi/4., -45.*eta*xi + 30.*eta + 75.*xi/2. - 15. - 45.*xi*xi/2.);
                      case 8:
                        return sign * RealGradient(-180.*eta*xi + 120.*eta + 60.*xi - 18. - 135.*eta*eta - 45.*xi*xi, 90.*eta*xi - 60.*eta - 120.*xi + 36. + 90.*(xi*xi));
                      case 9:
                        return RealGradient(720.*eta*xi - 900.*eta - 300.*xi + 180. + 810.*(eta*eta) + 90.*(xi*xi), -540.*eta*xi + 300.*xi - 360.*xi*xi);
                      case 10:
                        return RealGradient(-720.*eta*xi + 300.*eta + 300.*xi - 60. - 270.*eta*eta - 270.*xi*xi, 180.*eta*xi - 300.*xi + 360.*(xi*xi));
                      case 11:
                        return RealGradient(-720.*eta*xi + 120.*eta + 360.*xi - 60. - 180.*xi*xi, -120.*xi + 360.*(xi*xi));
                      case 12:
                        return RealGradient(360.*eta*xi - 60.*eta - 240.*xi + 30. + 270.*(xi*xi), 60.*xi - 180.*xi*xi);
                      case 13:
                        return RealGradient(-360.*eta*xi + 720.*eta + 60.*xi - 90. - 810.*eta*eta, 540.*eta*xi - 240.*xi + 180.*(xi*xi));
                      case 14:
                        return RealGradient(720.*eta*xi - 480.*eta - 120.*xi + 60. + 540.*(eta*eta), -360.*eta*xi + 360.*xi - 360.*xi*xi);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          } // end switch (type)
      } // end case THIRD
 
      // quartic Nedelec (first kind) shape function first derivatives
    case FOURTH:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(240.*eta + 60.*xi - 1920.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1680.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 7200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 9600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 270. - 1800.*(eta + 1.)*(eta + 1.)/(2.*2.) - 6300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 105.*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3675.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 2400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1050.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                      case 1:
                        return sign * RealGradient(-760.*eta/9. - 215.*xi/9. + 6880.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. - 6160.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/9. - 8600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. + 34400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 15050.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9. - 880./9. + 1900.*((eta + 1.)*(eta + 1.)/(2.*2.))/3. + 7700.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. + 385.*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 30800.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 13475.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9. - 7600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 3325.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9., 0.);
                      case 2:
                        return sign * RealGradient(400.*eta/9. + 170.*xi/9. - 5440.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. + 6160.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/9. + 6800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. - 27200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 11900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9. + 520./9. - 1000.*(eta + 1.)*(eta + 1.)/(2.*2.)/3. - 7700.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. - 385.*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 30800.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 13475.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9. + 4000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 1750.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9., 0.);
                      case 3:
                        return sign * RealGradient(-120.*eta - 45.*xi + 1440.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1680.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 5400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 7200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 150. + 900.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 6300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 105.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3675.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1200.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 4:
                        return sign * RealGradient(0., 60.*eta + 120.*xi - 1800.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 5400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2100.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 164. - 240.*(eta + 1.)*(eta + 1.)/(2.*2.) - 10800.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 720.*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 140.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 560.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 5:
                        return sign * RealGradient(0., -190.*eta/9. - 170.*xi/9. + 1900.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. - 1900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 13300.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 4300.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. + 7700.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 1012./27. + 860.*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 4300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 30100.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 340.*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 7700.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/3. - 1540.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/27. + 53900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. - 2380.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27.);
                      case 6:
                        return sign * RealGradient(0., 100.*eta/9. + 80.*xi/9. - 1000.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. + 1000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 3400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. - 7700.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 508./27. - 680.*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 3400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 23800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 160.*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 7700.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/3. + 1540.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/27. - 53900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. + 1120.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27.);
                      case 7:
                        return sign * RealGradient(0., -30.*eta - 30.*xi + 900.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 2700.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2700.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 2100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 56. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 8100.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 180.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 140.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 140.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 8:
                        return sign * RealGradient(30.*eta - 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 420.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 2700.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 5400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 30. - 450.*(eta + 1.)*(eta + 1.)/(2.*2.) - 3150.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3675.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 525.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                      case 9:
                        return sign * RealGradient(-100.*eta/9. + 1360.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. - 1540.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/9. - 3400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. + 6800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/3. - 11900.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9. - 100./9. + 500.*((eta + 1.)*(eta + 1.)/(2.*2.))/3. + 3850.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 7700.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/3. + 13475.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9. - 1000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/3. + 1750.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9., 0.);
                      case 10:
                        return sign * RealGradient(190.*eta/9. - 1720.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. + 1540.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/9. + 4300.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. - 8600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/3. + 15050.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/9. + 190./9. - 950.*(eta + 1.)*(eta + 1.)/(2.*2.)/3. - 3850.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 7700.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/3. - 13475.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9. + 1900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/3. - 3325.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/9., 0.);
                      case 11:
                        return sign * RealGradient(-60.*eta + 480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 420.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 3600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 7200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 60. + 900.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 3150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3675.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1800.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 1050.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 12:
                        return sign * RealGradient(0., 120.*eta + 60.*xi - 1800.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2100.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 5400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 4200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 164. - 720.*(eta + 1.)*(eta + 1.)/(2.*2.) - 10800.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 240.*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 560.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 140.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 13:
                        return sign * RealGradient(0., -400.*eta/9. - 160.*xi/9. + 2000.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. - 4000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 7000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 6800.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. + 15400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 1552./27. + 2720.*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 13600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 23800.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 640.*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 30800.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. - 6160.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/27. + 53900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. - 1120.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27.);
                      case 14:
                        return sign * RealGradient(0., 760.*eta/9. + 340.*xi/9. - 3800.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. + 7600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 13300.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 8600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. - 15400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 3028./27. - 3440.*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 17200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 30100.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 1360.*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 30800.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. + 6160.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/27. - 53900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. + 2380.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27.);
                      case 15:
                        return sign * RealGradient(0., -240.*eta - 240.*xi + 3600.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 7200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 7200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 416. + 960.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 14400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 960.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 560.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 560.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 16:
                        return RealGradient(0., -195.*eta - 232.*xi + 3480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 7200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 6960.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 4060.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 375. + 780.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 14400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 960.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 455.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 560.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 17:
                        return RealGradient(0., -45.*eta - 112.*xi + 1680.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 5400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3360.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 1960.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 145. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 10800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 720.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 105.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 560.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 18:
                        return RealGradient(0., -60.*eta - 16.*xi + 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 480.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 280.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 60. + 240.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 140.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.));
                      case 19:
                        return RealGradient(195.*eta - 1560.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1365.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 6960.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 9600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 195. - 1740.*(eta + 1.)*(eta + 1.)/(2.*2.) - 6090.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3675.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 2400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1050.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                      case 20:
                        return RealGradient(45.*eta - 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 315.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 3360.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 7200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 45. - 840.*(eta + 1.)*(eta + 1.)/(2.*2.) - 2940.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3675.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1800.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1050.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                      case 21:
                        return RealGradient(60.*eta - 480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 420.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 480.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 60. - 120.*(eta + 1.)*(eta + 1.)/(2.*2.) - 420.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.), 0.);
                      case 22:
                        return RealGradient(-195.*eta/2. + 1170.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1365.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 5220.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 7200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 195./2. + 870.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 6090.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3675.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1200.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 23:
                        return RealGradient(-45.*eta/2. + 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 315.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 2520.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 5400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 45./2. + 420.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 2940.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3675.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 24:
                        return RealGradient(-30.*eta + 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 420.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 360.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 30. + 60.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 420.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)), 0.);
                      case 25:
                        return RealGradient(0., 195.*eta/2. + 58.*xi - 1740.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2100.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 5220.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 4060.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 285./2. - 585.*(eta + 1.)*(eta + 1.)/(2.*2.) - 10800.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 240.*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 455.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 140.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 26:
                        return RealGradient(0., 45.*eta/2. + 28.*xi - 840.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 2700.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2100.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2520.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 1960.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 95./2. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.) - 8100.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 180.*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 105.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 140.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 27:
                        return RealGradient(0., 30.*eta + 4.*xi - 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 360.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 280.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 30. - 180.*(eta + 1.)*(eta + 1.)/(2.*2.) + 140.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)));
                      case 28:
                        return RealGradient(-9.*eta - 9. + 171.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 120.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 105.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2., 0.);
                      case 29:
                        return RealGradient(9.*eta + 9. - 171.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 120.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 105.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 30:
                        return RealGradient(0., -9.*eta - 57.*xi + 171.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 360.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 210.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 54. + 240.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 140.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 31:
                        return RealGradient(0., 9.*eta + 57.*xi/2. - 171.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 360.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 210.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 63./2. - 120.*(xi + 1.)*(xi + 1.)/(2.*2.) + 70.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 32:
                        return RealGradient(0., -3.*eta/2. - 27.*xi + 81.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 210.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 53./2. + 180.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 140.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 33:
                        return RealGradient(0., 3.*eta/2. + 27.*xi/2. - 81.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 210.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 14. - 90.*(xi + 1.)*(xi + 1.)/(2.*2.) + 70.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 34:
                        return RealGradient(-3.*eta/2. - 3./2. + 81.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 90.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 105.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2., 0.);
                      case 35:
                        return RealGradient(3.*eta/2. + 3./2. - 81.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 90.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 105.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 36:
                        return RealGradient(0., -9.*eta/2. - 6.*xi + 18.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 9./2.);
                      case 37:
                        return RealGradient(9.*eta/2. + 9./2. - 9.*(eta + 1.)*(eta + 1.)/(2.*2.), 0.);
                      case 38:
                        return RealGradient(-9.*eta/2. - 9./2. + 9.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                      case 39:
                        return RealGradient(0., 9.*eta/2. + 3.*xi - 18.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 9./2.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(240.*eta + 240.*xi - 3600.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 7200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 7200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 4200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 416. - 960.*(eta + 1.)*(eta + 1.)/(2.*2.) - 14400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 960.*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 560.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 560.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)), 0.);
                      case 1:
                        return sign * RealGradient(-340.*eta/9. - 760.*xi/9. + 3800.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. - 8600.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 15400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 7600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. + 13300.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 3028./27. + 1360.*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 17200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 30800.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 3440.*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 30100.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. - 2380.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/27. + 53900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. - 6160.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27., 0.);
                      case 2:
                        return sign * RealGradient(160.*eta/9. + 400.*xi/9. - 2000.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. + 6800.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 15400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 4000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. - 7000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 1552./27. - 640.*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 13600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 30800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 2720.*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 23800.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. + 1120.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/27. - 53900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. + 6160.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27., 0.);
                      case 3:
                        return sign * RealGradient(-60.*eta - 120.*xi + 1800.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 5400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 2100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 164. + 240.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 10800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 720.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 140.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 560.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                      case 4:
                        return sign * RealGradient(0., 60.*xi - 480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 420.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 60. - 3150.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 900.*(xi + 1.)*(xi + 1.)/(2.*2.) + 1800.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1050.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 5:
                        return sign * RealGradient(0., -190.*xi/9. + 1720.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. - 4300.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 8600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/3. - 15050.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9. - 1540.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 190./9. + 3850.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 7700.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/3. + 13475.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9. + 950.*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 1900.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/3. + 3325.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9.);
                      case 6:
                        return sign * RealGradient(0., 100.*xi/9. - 1360.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. + 3400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 6800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/3. + 11900.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9. + 1540.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 100./9. - 3850.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 7700.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/3. - 13475.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9. - 500.*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 1000.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/3. - 1750.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9.);
                      case 7:
                        return sign * RealGradient(0., -30.*xi + 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 2700.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 420.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 30. + 3150.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3675.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 450.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 900.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 525.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                      case 8:
                        return sign * RealGradient(30.*eta + 30.*xi - 900.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 2700.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2100.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2700.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2100.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 56. - 180.*(eta + 1.)*(eta + 1.)/(2.*2.) - 8100.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 180.*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 140.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 140.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)), 0.);
                      case 9:
                        return sign * RealGradient(-80.*eta/9. - 100.*xi/9. + 1000.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. - 3400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 7700.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 1000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 7000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 508./27. + 160.*((eta + 1.)*(eta + 1.)/(2.*2.))/3. + 3400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7700.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/3. + 680.*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 23800.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. - 1120.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/27. + 53900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27. - 1540.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27., 0.);
                      case 10:
                        return sign * RealGradient(170.*eta/9. + 190.*xi/9. - 1900.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. + 4300.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 7700.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 1900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 13300.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 1012./27. - 340.*(eta + 1.)*(eta + 1.)/(2.*2.)/3. - 4300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 7700.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/3. - 860.*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 30100.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. + 2380.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/27. - 53900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/27. + 1540.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/27., 0.);
                      case 11:
                        return sign * RealGradient(-120.*eta - 60.*xi + 1800.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 3600.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 164. + 720.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 10800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 240.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 560.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 140.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                      case 12:
                        return sign * RealGradient(0., 45.*eta + 120.*xi - 1440.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 5400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1680.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 150. - 105.*(eta + 1.)*(eta + 1.)/(2.*2.) - 6300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 900.*(xi + 1.)*(xi + 1.)/(2.*2.) + 1200.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 13:
                        return sign * RealGradient(0., -170.*eta/9. - 400.*xi/9. + 5440.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. - 6800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 27200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 11900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9. - 6160.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 520./9. + 385.*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 7700.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 30800.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 13475.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9. + 1000.*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 4000.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 1750.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9.);
                      case 14:
                        return sign * RealGradient(0., 215.*eta/9. + 760.*xi/9. - 6880.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/9. + 8600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 34400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 15050.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/9. + 6160.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 880./9. - 385.*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 7700.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 30800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 13475.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9. - 1900.*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 7600.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 3325.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/9.);
                      case 15:
                        return sign * RealGradient(0., -60.*eta - 240.*xi + 1920.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 7200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 9600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1680.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 270. + 105.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 6300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3675.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1800.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2400.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1050.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                      case 16:
                        return RealGradient(0., -195.*xi + 1560.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 6960.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 9600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1365.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 195. + 6090.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3675.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1740.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2400.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1050.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                      case 17:
                        return RealGradient(0., -45.*xi + 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 3360.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 7200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 315.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 45. + 2940.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3675.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 840.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1800.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1050.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                      case 18:
                        return RealGradient(0., -60.*xi + 480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 480.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 420.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 60. + 420.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 120.*((xi + 1.)*(xi + 1.)/(2.*2.)));
                      case 19:
                        return RealGradient(232.*eta + 195.*xi - 3480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 6960.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4060.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 7200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 4200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 375. - 960.*(eta + 1.)*(eta + 1.)/(2.*2.) - 14400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 780.*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 560.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 455.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)), 0.);
                      case 20:
                        return RealGradient(112.*eta + 45.*xi - 1680.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3360.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1960.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 5400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 4200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 145. - 720.*(eta + 1.)*(eta + 1.)/(2.*2.) - 10800.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 180.*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 560.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4900.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 105.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)), 0.);
                      case 21:
                        return RealGradient(16.*eta + 60.*xi - 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 480.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 280.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 60. - 240.*(xi + 1.)*(xi + 1.)/(2.*2.) + 140.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)), 0.);
                      case 22:
                        return RealGradient(-58.*eta - 195.*xi/2. + 1740.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 5220.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 4060.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 2100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 285./2. + 240.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 10800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 585.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 140.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 455.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                      case 23:
                        return RealGradient(-28.*eta - 45.*xi/2. + 840.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 2520.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 1960.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2700.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 2100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 95./2. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 8100.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 135.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 140.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4900.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 105.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                      case 24:
                        return RealGradient(-4.*eta - 30.*xi + 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 360.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 280.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 30. + 180.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 140.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                      case 25:
                        return RealGradient(0., 195.*xi/2. - 1170.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 5220.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1365.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 195./2. - 6090.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 870.*(xi + 1.)*(xi + 1.)/(2.*2.) + 1200.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 26:
                        return RealGradient(0., 45.*xi/2. - 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 2520.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 5400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 315.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 45./2. - 2940.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 420.*(xi + 1.)*(xi + 1.)/(2.*2.) + 900.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 27:
                        return RealGradient(0., 30.*xi - 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 360.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 420.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 30. - 420.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 60.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      case 28:
                        return RealGradient(-57.*eta - 9.*xi + 171.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 360.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 210.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 54. + 240.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 140.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 29:
                        return RealGradient(57.*eta/2. + 9.*xi - 171.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 360.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 210.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 63./2. - 120.*(eta + 1.)*(eta + 1.)/(2.*2.) + 70.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 30:
                        return RealGradient(0., -9.*xi - 9. + 171.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 120.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 105.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 31:
                        return RealGradient(0., 9.*xi + 9. - 171.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 120.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 105.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2.);
                      case 32:
                        return RealGradient(0., -3.*xi/2. - 3./2. + 81.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 90.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 105.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 33:
                        return RealGradient(0., 3.*xi/2. + 3./2. - 81.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 90.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 105.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2.);
                      case 34:
                        return RealGradient(-27.*eta - 3.*xi/2. + 81.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 210.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 53./2. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 140.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 35:
                        return RealGradient(27.*eta/2. + 3.*xi/2. - 81.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 210.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 14. - 90.*(eta + 1.)*(eta + 1.)/(2.*2.) + 70.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 36:
                        return RealGradient(0., -9.*xi/2. - 9./2. + 9.*((xi + 1.)*(xi + 1.)/(2.*2.)));
                      case 37:
                        return RealGradient(6.*eta + 9.*xi/2. - 18.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 9./2., 0.);
                      case 38:
                        return RealGradient(-3.*eta - 9.*xi/2. + 18.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 9./2., 0.);
                      case 39:
                        return RealGradient(0., 9.*xi/2. + 9./2. - 9.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-1680.*eta*xi + 720.*eta + 672.*eta*(xi*xi) + 480.*xi + 1344.*xi*(eta*eta) - 120. - 1260.*eta*eta - 420.*xi*xi + 672.*(eta*eta*eta), 1680.*eta*xi - 240.*eta - 2016.*eta*xi*xi - 480.*xi - 1344.*xi*eta*eta + 40. + 420.*(eta*eta) + 1260.*(xi*xi) - 224.*eta*eta*eta - 896.*xi*xi*xi);
                      case 1:
                        return sign * RealGradient(5768.*eta*xi/9. - 200.*eta - 2464.*eta*xi*xi/9. - 1720.*xi/9. - 4480.*xi*eta*eta/9. + 380./9. + 784.*(eta*eta)/3. + 1540.*(xi*xi)/9. - 896.*eta*eta*eta/9., -4256.*eta*xi/9. + 176.*eta/9. + 2240.*eta*(xi*xi)/3. + 1600.*xi/9. + 1792.*xi*(eta*eta)/9. - 296./27. + 448.*(eta*eta)/9. - 504.*xi*xi - 1792.*eta*eta*eta/27. + 9856.*(xi*xi*xi)/27.);
                      case 2:
                        return sign * RealGradient(-2240.*eta*xi/9. - 16.*eta + 2464.*eta*(xi*xi)/9. + 1360.*xi/9. + 448.*xi*(eta*eta)/9. - 200./9. + 476.*(eta*eta)/3. - 1540.*xi*xi/9. - 1120.*eta*eta*eta/9., -784.*eta*xi/9. + 112.*eta/9. - 224.*eta*xi*xi/3. - 1024.*xi/9. + 2240.*xi*(eta*eta)/9. + 152./27. - 196.*eta*eta/9. + 420.*(xi*xi) - 224.*eta*eta*eta/27. - 9856.*xi*xi*xi/27.);
                      case 3:
                        return sign * RealGradient(504.*eta*xi - 72.*eta - 672.*eta*xi*xi - 360.*xi + 60. + 420.*(xi*xi), 288.*xi - 16. - 1008.*xi*xi + 896.*(xi*xi*xi));
                      case 4:
                        return sign * RealGradient(504.*eta*xi - 72.*eta - 672.*eta*xi*xi, 288.*xi - 16. - 1008.*xi*xi + 896.*(xi*xi*xi));
                      case 5:
                        return sign * RealGradient(896.*eta*xi/3. - 80.*eta - 1792.*eta*xi*xi/9. - 1792.*xi*eta*eta/3. + 784.*(eta*eta)/3. - 448.*eta*eta*eta/3., -1792.*eta*xi/3. + 56.*eta + 896.*eta*(xi*xi) + 160.*xi + 896.*xi*(eta*eta)/3. - 12. - 140.*eta*eta/3. - 1232.*xi*xi/3. + 224.*(eta*eta*eta)/27. + 7168.*(xi*xi*xi)/27.);
                      case 6:
                        return sign * RealGradient(280.*eta*xi/3. - 56.*eta - 224.*eta*xi*xi/9. - 896.*xi*eta*eta/3. + 896.*(eta*eta)/3. - 896.*eta*eta*eta/3., -1568.*eta*xi/3. + 80.*eta + 448.*eta*(xi*xi) + 64.*xi + 1792.*xi*(eta*eta)/3. - 8. - 448.*eta*eta/3. - 280.*xi*xi/3. + 1792.*(eta*eta*eta)/27. + 896.*(xi*xi*xi)/27.);
                      case 7:
                        return sign * RealGradient(0., 72.*eta - 4. - 252.*eta*eta + 224.*(eta*eta*eta));
                      case 8:
                        return sign * RealGradient(0., 72.*eta - 4. - 252.*eta*eta + 224.*(eta*eta*eta));
                      case 9:
                        return sign * RealGradient(392.*eta*xi/9. - 112.*eta/9. + 224.*eta*(xi*xi)/9. - 2240.*xi*eta*eta/9. + 392.*(eta*eta)/9. + 224.*(eta*eta*eta)/9., -952.*eta*xi/3. + 16.*eta + 1120.*eta*(xi*xi)/3. + 208.*xi/9. - 448.*xi*eta*eta/9. - 112./27. + 1120.*(eta*eta)/9. + 56.*(xi*xi)/9. - 2464.*eta*eta*eta/27. - 896.*xi*xi*xi/27.);
                      case 10:
                        return sign * RealGradient(-896.*eta*xi/9. - 176.*eta/9. + 1792.*eta*(xi*xi)/9. - 1792.*xi*eta*eta/9. + 2128.*(eta*eta)/9. - 2240.*eta*eta*eta/9., -1568.*eta*xi/3. + 200.*eta + 896.*eta*(xi*xi)/3. - 1216.*xi/9. + 4480.*xi*(eta*eta)/9. + 76./27. - 2884.*eta*eta/9. + 3472.*(xi*xi)/9. + 2464.*(eta*eta*eta)/27. - 7168.*xi*xi*xi/27.);
                      case 11:
                        return sign * RealGradient(-840.*eta*xi + 240.*eta + 672.*eta*(xi*xi) + 1344.*xi*(eta*eta) - 840.*eta*eta + 672.*(eta*eta*eta), 2520.*eta*xi - 720.*eta - 2016.*eta*xi*xi - 960.*xi - 1344.*xi*eta*eta + 160. + 840.*(eta*eta) + 1680.*(xi*xi) - 224.*eta*eta*eta - 896.*xi*xi*xi);
                      case 12:
                        return RealGradient(6048.*eta*xi - 3240.*eta - 2016.*eta*xi*xi - 8064.*xi*eta*eta + 9072.*(eta*eta) - 6048.*eta*eta*eta, -12096.*eta*xi + 2160.*eta + 12096.*eta*(xi*xi) + 2160.*xi + 12096.*xi*(eta*eta) - 240. - 4536.*eta*eta - 4536.*xi*xi + 2688.*(eta*eta*eta) + 2688.*(xi*xi*xi));
                      case 13:
                        return RealGradient(-9072.*eta*xi + 2160.*eta + 8064.*eta*(xi*xi) + 12096.*xi*(eta*eta) - 6048.*eta*eta + 4032.*(eta*eta*eta), 18144.*eta*xi - 3240.*eta - 18144.*eta*xi*xi - 8640.*xi - 8064.*xi*eta*eta + 960. + 3024.*(eta*eta) + 18144.*(xi*xi) - 672.*eta*eta*eta - 10752.*xi*xi*xi);
                      case 14:
                        return RealGradient(9072.*eta*xi - 1944.*eta - 6048.*eta*xi*xi - 8064.*xi*eta*eta + 2016.*(eta*eta), -6048.*eta*xi + 432.*eta + 12096.*eta*(xi*xi) + 3456.*xi - 216. - 10584.*xi*xi + 8064.*(xi*xi*xi));
                      case 15:
                        return RealGradient(-7056.*eta*xi + 1152.*eta + 8064.*eta*(xi*xi) + 4032.*xi*(eta*eta) - 1008.*eta*eta, 3024.*eta*xi - 216.*eta - 6048.*eta*xi*xi - 4608.*xi + 288. + 14112.*(xi*xi) - 10752.*xi*xi*xi);
                      case 16:
                        return RealGradient(-216.*eta + 1512.*(eta*eta) - 2016.*eta*eta*eta, -2016.*eta*xi + 1152.*eta + 144.*xi + 4032.*xi*(eta*eta) - 72. - 3528.*eta*eta + 2688.*(eta*eta*eta));
                      case 17:
                        return RealGradient(432.*eta - 3024.*eta*eta + 4032.*(eta*eta*eta), 4032.*eta*xi - 1944.*eta - 288.*xi - 8064.*xi*eta*eta + 144. + 4536.*(eta*eta) - 2016.*eta*eta*eta);
                      case 18:
                        return RealGradient(3276.*eta*xi - 1332.*eta - 1512.*eta*xi*xi - 6048.*xi*eta*eta + 4788.*(eta*eta) - 3528.*eta*eta*eta, -8064.*eta*xi + 1044.*eta + 9072.*eta*(xi*xi) + 1548.*xi + 7056.*xi*(eta*eta) - 144. - 1638.*eta*eta - 3402.*xi*xi + 672.*(eta*eta*eta) + 2016.*(xi*xi*xi));
                      case 19:
                        return RealGradient(-3276.*eta*xi + 1044.*eta + 2016.*eta*(xi*xi) + 7056.*xi*(eta*eta) - 4032.*eta*eta + 3024.*(eta*eta*eta), 9576.*eta*xi - 1332.*eta - 10584.*eta*xi*xi - 2196.*xi - 6048.*xi*eta*eta + 216. + 1638.*(eta*eta) + 4662.*(xi*xi) - 504.*eta*eta*eta - 2688.*xi*xi*xi);
                      case 20:
                        return RealGradient(1008.*eta*xi - 216.*eta - 504.*eta*xi*xi - 756.*eta*eta + 1008.*(eta*eta*eta), 1008.*eta*xi - 360.*eta + 144.*xi - 2016.*xi*eta*eta + 12. + 1008.*(eta*eta) - 756.*xi*xi - 672.*eta*eta*eta + 672.*(xi*xi*xi));
                      case 21:
                        return RealGradient(-756.*eta*xi - 216.*eta + 2016.*eta*(xi*xi) - 3024.*xi*eta*eta + 2268.*(eta*eta) - 2016.*eta*eta*eta, -5544.*eta*xi + 1188.*eta + 4536.*eta*(xi*xi) - 936.*xi + 4032.*xi*(eta*eta) + 6. - 1512.*eta*eta + 3402.*(xi*xi) + 336.*(eta*eta*eta) - 2688.*xi*xi*xi);
                      case 22:
                        return RealGradient(-3024.*eta*xi + 1188.*eta + 1008.*eta*(xi*xi) + 4032.*xi*(eta*eta) - 2772.*eta*eta + 1512.*(eta*eta*eta), 4536.*eta*xi - 216.*eta - 6048.*eta*xi*xi - 972.*xi - 3024.*xi*eta*eta + 66. - 378.*eta*eta + 2268.*(xi*xi) + 672.*(eta*eta*eta) - 1344.*xi*xi*xi);
                      case 23:
                        return RealGradient(2016.*eta*xi - 360.*eta - 2016.*eta*xi*xi - 2016.*xi*eta*eta + 504.*(eta*eta), -1512.*eta*xi - 216.*eta + 3024.*eta*(xi*xi) + 1440.*xi - 48. + 504.*(eta*eta) - 4032.*xi*xi - 168.*eta*eta*eta + 2688.*(xi*xi*xi));
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-2520.*eta*xi + 960.*eta + 1344.*eta*(xi*xi) + 720.*xi + 2016.*xi*(eta*eta) - 160. - 1680.*eta*eta - 840.*xi*xi + 896.*(eta*eta*eta) + 224.*(xi*xi*xi), 840.*eta*xi - 1344.*eta*xi*xi - 240.*xi - 672.*xi*eta*eta + 840.*(xi*xi) - 672.*xi*xi*xi);
                      case 1:
                        return sign * RealGradient(1568.*eta*xi/3. + 1216.*eta/9. - 4480.*eta*xi*xi/9. - 200.*xi - 896.*xi*eta*eta/3. - 76./27. - 3472.*eta*eta/9. + 2884.*(xi*xi)/9. + 7168.*(eta*eta*eta)/27. - 2464.*xi*xi*xi/27., 896.*eta*xi/9. + 1792.*eta*(xi*xi)/9. + 176.*xi/9. - 1792.*xi*eta*eta/9. - 2128.*xi*xi/9. + 2240.*(xi*xi*xi)/9.);
                      case 2:
                        return sign * RealGradient(952.*eta*xi/3. - 208.*eta/9. + 448.*eta*(xi*xi)/9. - 16.*xi - 1120.*xi*eta*eta/3. + 112./27. - 56.*eta*eta/9. - 1120.*xi*xi/9. + 896.*(eta*eta*eta)/27. + 2464.*(xi*xi*xi)/27., -392.*eta*xi/9. + 2240.*eta*(xi*xi)/9. + 112.*xi/9. - 224.*xi*eta*eta/9. - 392.*xi*xi/9. - 224.*xi*xi*xi/9.);
                      case 3:
                        return sign * RealGradient(-72.*xi + 4. + 252.*(xi*xi) - 224.*xi*xi*xi, 0.);
                      case 4:
                        return sign * RealGradient(-72.*xi + 4. + 252.*(xi*xi) - 224.*xi*xi*xi, 0.);
                      case 5:
                        return sign * RealGradient(1568.*eta*xi/3. - 64.*eta - 1792.*eta*xi*xi/3. - 80.*xi - 448.*xi*eta*eta + 8. + 280.*(eta*eta)/3. + 448.*(xi*xi)/3. - 896.*eta*eta*eta/27. - 1792.*xi*xi*xi/27., -280.*eta*xi/3. + 896.*eta*(xi*xi)/3. + 56.*xi + 224.*xi*(eta*eta)/9. - 896.*xi*xi/3. + 896.*(xi*xi*xi)/3.);
                      case 6:
                        return sign * RealGradient(1792.*eta*xi/3. - 160.*eta - 896.*eta*xi*xi/3. - 56.*xi - 896.*xi*eta*eta + 12. + 1232.*(eta*eta)/3. + 140.*(xi*xi)/3. - 7168.*eta*eta*eta/27. - 224.*xi*xi*xi/27., -896.*eta*xi/3. + 1792.*eta*(xi*xi)/3. + 80.*xi + 1792.*xi*(eta*eta)/9. - 784.*xi*xi/3. + 448.*(xi*xi*xi)/3.);
                      case 7:
                        return sign * RealGradient(-288.*eta + 16. + 1008.*(eta*eta) - 896.*eta*eta*eta, -504.*eta*xi + 72.*xi + 672.*xi*(eta*eta));
                      case 8:
                        return sign * RealGradient(-288.*eta + 16. + 1008.*(eta*eta) - 896.*eta*eta*eta, -504.*eta*xi + 360.*eta + 72.*xi + 672.*xi*(eta*eta) - 60. - 420.*eta*eta);
                      case 9:
                        return sign * RealGradient(784.*eta*xi/9. + 1024.*eta/9. - 2240.*eta*xi*xi/9. - 112.*xi/9. + 224.*xi*(eta*eta)/3. - 152./27. - 420.*eta*eta + 196.*(xi*xi)/9. + 9856.*(eta*eta*eta)/27. + 224.*(xi*xi*xi)/27., 2240.*eta*xi/9. - 1360.*eta/9. - 448.*eta*xi*xi/9. + 16.*xi - 2464.*xi*eta*eta/9. + 200./9. + 1540.*(eta*eta)/9. - 476.*xi*xi/3. + 1120.*(xi*xi*xi)/9.);
                      case 10:
                        return sign * RealGradient(4256.*eta*xi/9. - 1600.*eta/9. - 1792.*eta*xi*xi/9. - 176.*xi/9. - 2240.*xi*eta*eta/3. + 296./27. + 504.*(eta*eta) - 448.*xi*xi/9. - 9856.*eta*eta*eta/27. + 1792.*(xi*xi*xi)/27., -5768.*eta*xi/9. + 1720.*eta/9. + 4480.*eta*(xi*xi)/9. + 200.*xi + 2464.*xi*(eta*eta)/9. - 380./9. - 1540.*eta*eta/9. - 784.*xi*xi/3. + 896.*(xi*xi*xi)/9.);
                      case 11:
                        return sign * RealGradient(-1680.*eta*xi + 480.*eta + 1344.*eta*(xi*xi) + 240.*xi + 2016.*xi*(eta*eta) - 40. - 1260.*eta*eta - 420.*xi*xi + 896.*(eta*eta*eta) + 224.*(xi*xi*xi), 1680.*eta*xi - 480.*eta - 1344.*eta*xi*xi - 720.*xi - 672.*xi*eta*eta + 120. + 420.*(eta*eta) + 1260.*(xi*xi) - 672.*xi*xi*xi);
                      case 12:
                        return RealGradient(18144.*eta*xi - 8640.*eta - 8064.*eta*xi*xi - 3240.*xi - 18144.*xi*eta*eta + 960. + 18144.*(eta*eta) + 3024.*(xi*xi) - 10752.*eta*eta*eta - 672.*xi*xi*xi, -9072.*eta*xi + 12096.*eta*(xi*xi) + 2160.*xi + 8064.*xi*(eta*eta) - 6048.*xi*xi + 4032.*(xi*xi*xi));
                      case 13:
                        return RealGradient(-12096.*eta*xi + 2160.*eta + 12096.*eta*(xi*xi) + 2160.*xi + 12096.*xi*(eta*eta) - 240. - 4536.*eta*eta - 4536.*xi*xi + 2688.*(eta*eta*eta) + 2688.*(xi*xi*xi), 6048.*eta*xi - 8064.*eta*xi*xi - 3240.*xi - 2016.*xi*eta*eta + 9072.*(xi*xi) - 6048.*xi*xi*xi);
                      case 14:
                        return RealGradient(4032.*eta*xi - 288.*eta - 8064.*eta*xi*xi - 1944.*xi + 144. + 4536.*(xi*xi) - 2016.*xi*xi*xi, 432.*xi - 3024.*xi*xi + 4032.*(xi*xi*xi));
                      case 15:
                        return RealGradient(-2016.*eta*xi + 144.*eta + 4032.*eta*(xi*xi) + 1152.*xi - 72. - 3528.*xi*xi + 2688.*(xi*xi*xi), -216.*xi + 1512.*(xi*xi) - 2016.*xi*xi*xi);
                      case 16:
                        return RealGradient(3024.*eta*xi - 4608.*eta - 216.*xi - 6048.*xi*eta*eta + 288. + 14112.*(eta*eta) - 10752.*eta*eta*eta, -7056.*eta*xi + 4032.*eta*(xi*xi) + 1152.*xi + 8064.*xi*(eta*eta) - 1008.*xi*xi);
                      case 17:
                        return RealGradient(-6048.*eta*xi + 3456.*eta + 432.*xi + 12096.*xi*(eta*eta) - 216. - 10584.*eta*eta + 8064.*(eta*eta*eta), 9072.*eta*xi - 8064.*eta*xi*xi - 1944.*xi - 6048.*xi*eta*eta + 2016.*(xi*xi));
                      case 18:
                        return RealGradient(9576.*eta*xi - 2196.*eta - 6048.*eta*xi*xi - 1332.*xi - 10584.*xi*eta*eta + 216. + 4662.*(eta*eta) + 1638.*(xi*xi) - 2688.*eta*eta*eta - 504.*xi*xi*xi, -3276.*eta*xi + 7056.*eta*(xi*xi) + 1044.*xi + 2016.*xi*(eta*eta) - 4032.*xi*xi + 3024.*(xi*xi*xi));
                      case 19:
                        return RealGradient(-8064.*eta*xi + 1548.*eta + 7056.*eta*(xi*xi) + 1044.*xi + 9072.*xi*(eta*eta) - 144. - 3402.*eta*eta - 1638.*xi*xi + 2016.*(eta*eta*eta) + 672.*(xi*xi*xi), 3276.*eta*xi - 6048.*eta*xi*xi - 1332.*xi - 1512.*xi*eta*eta + 4788.*(xi*xi) - 3528.*xi*xi*xi);
                      case 20:
                        return RealGradient(-1512.*eta*xi + 1440.*eta - 216.*xi + 3024.*xi*(eta*eta) - 48. - 4032.*eta*eta + 504.*(xi*xi) + 2688.*(eta*eta*eta) - 168.*xi*xi*xi, 2016.*eta*xi - 2016.*eta*xi*xi - 360.*xi - 2016.*xi*eta*eta + 504.*(xi*xi));
                      case 21:
                        return RealGradient(4536.*eta*xi - 972.*eta - 3024.*eta*xi*xi - 216.*xi - 6048.*xi*eta*eta + 66. + 2268.*(eta*eta) - 378.*xi*xi - 1344.*eta*eta*eta + 672.*(xi*xi*xi), -3024.*eta*xi + 4032.*eta*(xi*xi) + 1188.*xi + 1008.*xi*(eta*eta) - 2772.*xi*xi + 1512.*(xi*xi*xi));
                      case 22:
                        return RealGradient(-5544.*eta*xi - 936.*eta + 4032.*eta*(xi*xi) + 1188.*xi + 4536.*xi*(eta*eta) + 6. + 3402.*(eta*eta) - 1512.*xi*xi - 2688.*eta*eta*eta + 336.*(xi*xi*xi), -756.*eta*xi - 3024.*eta*xi*xi - 216.*xi + 2016.*xi*(eta*eta) + 2268.*(xi*xi) - 2016.*xi*xi*xi);
                      case 23:
                        return RealGradient(1008.*eta*xi + 144.*eta - 2016.*eta*xi*xi - 360.*xi + 12. - 756.*eta*eta + 1008.*(xi*xi) + 672.*(eta*eta*eta) - 672.*xi*xi*xi, 1008.*eta*xi - 216.*xi - 504.*xi*eta*eta - 756.*xi*xi + 1008.*(xi*xi*xi));
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          } // end switch (type)
      } // end case FOURTH
 
      // quintic Nedelec (first kind) shape function first derivatives
    case FIFTH:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(1875.*eta/2. + 525.*xi/2. - 13125.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 26250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 15750.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 78750.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 183750.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 183750.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 66150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 1125. - 11250.*(eta + 1.)*(eta + 1.)/(2.*2.) - 157500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 94500.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1050.*(xi + 1.)*(xi + 1.)/(2.*2.) + 367500.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 367500.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 132300.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 26250.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 630.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 220500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 79380.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 26250.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 9450.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                      case 1:
                        return sign * RealGradient(-71625.*eta/256. - 21105.*xi/256. + 527625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/128. - 1021125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 291375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 1582875.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/64. + 3693375.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 3693375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 1329615.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/64. - 10875./32. + 214875.*((eta + 1.)*(eta + 1.)/(2.*2.))/64. + 3063375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 874125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 40845.*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 7147875.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 7147875.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. - 2573235.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/64. - 501375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 2039625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 11655.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. - 2039625.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/32. + 734265.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/32. + 501375.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. - 180495.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/64., 0.);
                      case 2:
                        return sign * RealGradient(2625.*eta/16. + 1155.*xi/16. - 28875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/8. + 70875.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 23625.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 86625.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/4. - 202125.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 202125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 72765.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/4. + 1785./8. - 7875.*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 212625.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 70875.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 2835.*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 496125.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 496125.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. + 178605.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/4. + 18375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 165375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. + 165375.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. - 59535.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/2. - 18375.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. + 6615.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/4., 0.);
                      case 3:
                        return sign * RealGradient(-17625.*eta/256. - 9345.*xi/256. + 233625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/128. - 727125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 291375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 700875.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/64. + 1635375.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 1635375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 588735.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/64. - 3195./32. + 52875.*((eta + 1.)*(eta + 1.)/(2.*2.))/64. + 2181375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 874125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 29085.*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 5089875.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 5089875.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. - 1832355.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/64. - 123375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 2039625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 11655.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. - 2039625.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/32. + 734265.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/32. + 123375.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. - 44415.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/64., 0.);
                      case 4:
                        return sign * RealGradient(375.*eta + 315.*xi/2. - 7875.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 21000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 15750.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 47250.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 110250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 110250.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 39690.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 1005./2. - 4500.*(eta + 1.)*(eta + 1.)/(2.*2.) - 126000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 94500.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 840.*(xi + 1.)*(xi + 1.)/(2.*2.) + 294000.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 294000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 105840.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 10500.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 630.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 220500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 79380.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 10500.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 3780.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                      case 5:
                        return sign * RealGradient(0., -375.*eta/2. - 375.*xi + 9000.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 47250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 84000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 47250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 31500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 42000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 18900.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 2125./4. + 2625.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 165375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 294000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 165375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 7875.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 220500.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 99225.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1750.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 392000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 7000.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 176400.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 7875.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 6:
                        return sign * RealGradient(0., 14325.*eta/256. + 7275.*xi/128. - 42975.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/16. + 902475.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 100275.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 902475.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. + 316575.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/32. - 204225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/16. + 174825.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/32. + 55325./512. - 105525.*(eta + 1.)*(eta + 1.)/(2.*2.)/256. - 6648075.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 738675.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/8. - 6648075.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 152775.*(xi + 1.)*(xi + 1.)/(2.*2.)/256. + 4288725.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 3671325.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. + 68075.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/128. - 476525.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 4288725.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. + 16975.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/16. + 407925.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8. - 58275.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/256. - 3671325.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 152775.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/256.);
                      case 7:
                        return sign * RealGradient(0., -525.*eta/16. - 225.*xi/8. + 1575.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 33075.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 14700.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 33075.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. - 17325.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 14175.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 14175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 1875./32. + 5775.*((eta + 1.)*(eta + 1.)/(2.*2.))/16. + 363825.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 80850.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 363825.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/8. + 4725.*((xi + 1.)*(xi + 1.)/(2.*2.))/16. - 297675.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 297675.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8. - 4725.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/8. + 132300.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 297675.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 66150.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 4725.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/16. + 297675.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/8. + 4725.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/16.);
                      case 8:
                        return sign * RealGradient(0., 3525.*eta/256. + 1275.*xi/128. - 10575.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/16. + 222075.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 24675.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 222075.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. + 140175.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/32. - 145425.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/16. + 174825.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/32. + 11725./512. - 46725.*(eta + 1.)*(eta + 1.)/(2.*2.)/256. - 2943675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 327075.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/8. - 2943675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 26775.*(xi + 1.)*(xi + 1.)/(2.*2.)/256. + 3053925.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 3671325.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. + 48475.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/128. - 339325.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 3053925.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. + 2975.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/16. + 407925.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8. - 58275.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/256. - 3671325.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 26775.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/256.);
                      case 9:
                        return sign * RealGradient(0., -75.*eta - 75.*xi + 3600.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 18900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 33600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 18900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 18900.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 33600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 18900.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 575./4. + 1575.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 99225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 176400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 99225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1575.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 176400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 99225.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 313600.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 176400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1400.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 176400.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 10:
                        return sign * RealGradient(75.*eta - 1575.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 18900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 66150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 88200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 39690.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 75. - 1800.*(eta + 1.)*(eta + 1.)/(2.*2.) - 50400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 37800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 176400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 235200.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 105840.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 6300.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 132300.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 176400.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 79380.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 8400.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 3780.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                      case 11:
                        return sign * RealGradient(-3525.*eta/256. + 46725.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/128. - 145425.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 58275.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 140175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/32. + 981225.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 327075.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/16. + 588735.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/64. - 3525./256. + 10575.*((eta + 1.)*(eta + 1.)/(2.*2.))/32. + 436275.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/32. - 174825.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. - 3053925.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 1017975.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/16. - 1832355.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/64. - 74025.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 1223775.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 407925.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/8. + 734265.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/32. + 24675.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/16. - 44415.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/64., 0.);
                      case 12:
                        return sign * RealGradient(525.*eta/16. - 5775.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/8. + 14175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 4725.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 17325.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 121275.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 40425.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 72765.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/4. + 525./16. - 1575.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 42525.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 14175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 297675.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 99225.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 178605.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/4. + 11025.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 66150.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 59535.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/2. - 3675.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 6615.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/4., 0.);
                      case 13:
                        return sign * RealGradient(-14325.*eta/256. + 105525.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/128. - 204225.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 58275.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 316575.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/32. + 2216025.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 738675.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/16. + 1329615.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/64. - 14325./256. + 42975.*((eta + 1.)*(eta + 1.)/(2.*2.))/32. + 612675.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/32. - 174825.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. - 4288725.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 1429575.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/16. - 2573235.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/64. - 300825.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 1223775.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 407925.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/8. + 734265.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/32. + 100275.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/16. - 180495.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/64., 0.);
                      case 14:
                        return sign * RealGradient(375.*eta/2. - 2625.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 5250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 31500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 110250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 147000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 66150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 375./2. - 4500.*(eta + 1.)*(eta + 1.)/(2.*2.) - 63000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 37800.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 220500.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 294000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 132300.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 15750.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 132300.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 176400.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 79380.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 21000.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 9450.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                      case 15:
                        return sign * RealGradient(0., -375.*eta - 375.*xi/2. + 9000.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 31500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 42000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 18900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 47250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 84000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 47250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 2125./4. + 7875.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 165375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 99225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 2625.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 294000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 165375.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 7000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 392000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 176400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1750.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 220500.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 7875.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 16:
                        return sign * RealGradient(0., 17625.*eta/256. + 6375.*xi/256. - 52875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/32. + 370125.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 123375.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. + 222075.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. + 700875.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/64. - 727125.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/32. + 874125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. + 45875./512. - 233625.*(eta + 1.)*(eta + 1.)/(2.*2.)/256. - 4906125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 1635375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 2943675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 44625.*(xi + 1.)*(xi + 1.)/(2.*2.)/256. + 5089875.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 6118875.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. + 242375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/128. - 1696625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. + 3053925.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. + 14875.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. + 2039625.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/32. - 291375.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/256. - 3671325.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 26775.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/256.);
                      case 17:
                        return sign * RealGradient(0., -2625.*eta/16. - 1125.*xi/16. + 7875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 55125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 18375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 33075.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. - 86625.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/4. + 70875.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 70875.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. - 7125./32. + 28875.*((eta + 1.)*(eta + 1.)/(2.*2.))/16. + 606375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 202125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 363825.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/8. + 7875.*((xi + 1.)*(xi + 1.)/(2.*2.))/16. - 496125.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 496125.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8. - 23625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/8. + 165375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 297675.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. - 2625.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. - 165375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. + 23625.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/16. + 297675.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/8. + 4725.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/16.);
                      case 18:
                        return sign * RealGradient(0., 71625.*eta/256. + 36375.*xi/256. - 214875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/32. + 1504125.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 501375.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. + 902475.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. + 1582875.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/64. - 1021125.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/32. + 874125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. + 203875./512. - 527625.*(eta + 1.)*(eta + 1.)/(2.*2.)/256. - 11080125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 3693375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 6648075.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 254625.*(xi + 1.)*(xi + 1.)/(2.*2.)/256. + 7147875.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 6118875.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. + 340375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/128. - 2382625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. + 4288725.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. + 84875.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. + 2039625.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/32. - 291375.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/256. - 3671325.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 152775.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/256.);
                      case 19:
                        return sign * RealGradient(0., -1875.*eta/2. - 1875.*xi/2. + 22500.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 78750.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 105000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 47250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 78750.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 105000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 47250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 6875./4. + 13125.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 275625.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 367500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 165375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 13125.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 367500.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 165375.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 8750.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 490000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 8750.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 220500.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 7875.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 7875.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 20:
                        return RealGradient(0., -2925.*eta/4. - 3525.*xi/4. + 21150.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 155475.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 105000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 47250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 74025.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 98700.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 44415.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 11925./8. + 20475.*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 1088325.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 367500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 165375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 51825.*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 362775.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 652995.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 6825.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 490000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 8750.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 220500.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 12285.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 7875.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 21:
                        return RealGradient(0., 150.*eta + 2775.*xi/8. - 8325.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 92475.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 84000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 47250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 58275.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 38850.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 34965.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 3775./8. - 1050.*(eta + 1.)*(eta + 1.)/(2.*2.) - 647325.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 294000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 165375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 30825.*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 215775.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 388395.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. + 1400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 392000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 220500.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 7000.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 176400.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 630.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 7875.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2.);
                      case 22:
                        return RealGradient(0., -675.*eta/2. - 1125.*xi/8. + 3375.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 6075.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. - 23625.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 15750.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 14175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 3375./8. + 4725.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 42525.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. + 2025.*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 14175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 25515.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 3150.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2835.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2.);
                      case 23:
                        return RealGradient(0., 675.*eta/4. + 225.*xi/2. - 2700.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 6075.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. + 9450.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 12600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 5670.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 2025./8. - 4725.*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 42525.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. - 2025.*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 14175.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 25515.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2835.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4.);
                      case 24:
                        return RealGradient(2925.*eta/4. - 20475.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 20475.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 12285.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 74025.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 362775.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 183750.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 66150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 2925./4. - 10575.*(eta + 1.)*(eta + 1.)/(2.*2.) - 148050.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 88830.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 362775.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 367500.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 132300.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 51825.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 217665.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 220500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 79380.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 26250.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 9450.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                      case 25:
                        return RealGradient(-150.*eta + 2100.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 4200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2520.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 58275.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 215775.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 147000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 66150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 150. + 8325.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 58275.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 34965.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 215775.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 294000.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 132300.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 30825.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 129465.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 176400.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 79380.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 21000.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 9450.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                      case 26:
                        return RealGradient(675.*eta/2. - 4725.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 9450.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 5670.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 23625.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 14175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 675./2. - 3375.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 23625.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 14175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 14175.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 2025.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 8505.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                      case 27:
                        return RealGradient(-675.*eta/4. + 4725.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 4725.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2835.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 9450.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 14175.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 675./4. + 1350.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 18900.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 11340.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 14175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 2025.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 8505.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)), 0.);
                      case 28:
                        return RealGradient(585.*eta/2. - 12285.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 16380.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 12285.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 44415.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 217665.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 110250.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 39690.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 585./2. - 4230.*(eta + 1.)*(eta + 1.)/(2.*2.) - 118440.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 88830.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 290220.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 294000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 105840.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 10365.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 217665.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 220500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 79380.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 10500.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 3780.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                      case 29:
                        return RealGradient(-60.*eta + 1260.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 3360.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2520.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 34965.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 129465.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 88200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 39690.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 60. + 1665.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 46620.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 34965.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 172620.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 235200.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 105840.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) - 6165.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 129465.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 176400.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 79380.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) + 8400.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 3780.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                      case 30:
                        return RealGradient(135.*eta - 2835.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 7560.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 5670.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 14175.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 8505.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 135. - 675.*(eta + 1.)*(eta + 1.)/(2.*2.) - 18900.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 14175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 11340.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 405.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 8505.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                      case 31:
                        return RealGradient(-135.*eta/2. + 2835.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 3780.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 2835.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5670.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 8505.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 135./2. + 540.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 15120.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 11340.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 11340.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 405.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 8505.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)), 0.);
                      case 32:
                        return RealGradient(0., -585.*eta/2. - 705.*xi/4. + 8460.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 31095.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 42000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 18900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 44415.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 78960.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 44415.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 3555./8. + 12285.*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 652995.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 220500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 99225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 10365.*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 290220.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 652995.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 5460.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 392000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 176400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1750.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 220500.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 12285.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 33:
                        return RealGradient(0., 60.*eta + 555.*xi/8. - 3330.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 18495.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 33600.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 18900.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 34965.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 31080.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 34965.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 995./8. - 630.*(eta + 1.)*(eta + 1.)/(2.*2.) - 388395.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 176400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 99225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 6165.*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 172620.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 388395.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. + 1120.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 313600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 176400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1400.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 176400.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 630.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2.);
                      case 34:
                        return RealGradient(0., -135.*eta - 225.*xi/8. + 1350.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1215.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 14175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 12600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 14175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 1215./8. + 2835.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 25515.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. + 405.*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 11340.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 25515.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 2520.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2835.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2.);
                      case 35:
                        return RealGradient(0., 135.*eta/2. + 45.*xi/2. - 1080.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1215.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 5670.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 10080.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 5670.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 675./8. - 2835.*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 25515.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. - 405.*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 11340.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 25515.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. + 1260.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2835.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4.);
                      case 36:
                        return RealGradient(-72.*eta + 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1980.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 5100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1890.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 72. + 1188.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 3060.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3150.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1134.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                      case 37:
                        return RealGradient(-48.*eta + 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1980.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 5100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1890.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 48. + 792.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2040.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2100.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 756.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.), 0.);
                      case 38:
                        return RealGradient(30.*eta - 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 990.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2550.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2625.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 945.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 30. - 495.*(eta + 1.)*(eta + 1.)/(2.*2.) + 1275.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2625.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. + 945.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.))/2., 0.);
                      case 39:
                        return RealGradient(0., -72.*eta - 297.*xi + 2376.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 9180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 12600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5670.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1980.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 333. + 120.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 7650.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 10500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4725.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 2295.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3150.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2835.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 40:
                        return RealGradient(0., -48.*eta - 99.*xi + 1584.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 6120.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3780.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1980.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 135. + 120.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 7650.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 10500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4725.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 765.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1050.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2.);
                      case 41:
                        return RealGradient(0., 30.*eta + 99.*xi/2. - 990.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3825.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 5250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4725.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 990.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 147./2. - 60.*(eta + 1.)*(eta + 1.)/(2.*2.) - 3825.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5250.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. - 765.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 525.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 945.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4.);
                      case 42:
                        return RealGradient(0., 9.*eta + 108.*xi - 864.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 5400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 10080.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 5670.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 720.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 225./2. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.) - 4500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1350.*(xi + 1.)*(xi + 1.)/(2.*2.) + 2520.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2835.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2.);
                      case 43:
                        return RealGradient(0., 6.*eta + 36.*xi - 576.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6720.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3780.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 720.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 81./2. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.) - 4500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 450.*(xi + 1.)*(xi + 1.)/(2.*2.) + 840.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 945.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2.);
                      case 44:
                        return RealGradient(0., -15.*eta/4. - 18.*xi + 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 2250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. - 360.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 21. + 15.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 2250.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4725.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 225.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 420.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4.);
                      case 45:
                        return RealGradient(9.*eta - 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 720.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 3000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1890.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 9. - 432.*(eta + 1.)*(eta + 1.)/(2.*2.) + 1800.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2520.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1134.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                      case 46:
                        return RealGradient(6.*eta - 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 720.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 3000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1890.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.) + 6. - 288.*(eta + 1.)*(eta + 1.)/(2.*2.) + 1200.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1680.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 756.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)), 0.);
                      case 47:
                        return RealGradient(-15.*eta/4. + 15.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 360.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 1500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2100.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 945.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)) - 15./4. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 750.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 1050.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.*2.)/2., 0.);
                      case 48:
                        return RealGradient(0., -36.*eta - 81.*xi/2. + 324.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 117./2. + 60.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 135.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 49:
                        return RealGradient(0., 9.*eta + 27.*xi - 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 63./2. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.) - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 135.*(xi + 1.)*(xi + 1.)/(2.*2.)/2.);
                      case 50:
                        return RealGradient(36.*eta - 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 36. - 162.*(eta + 1.)*(eta + 1.)/(2.*2.) + 90.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 51:
                        return RealGradient(-9.*eta + 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 9. + 108.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 90.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 52:
                        return RealGradient(24.*eta - 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 24. - 108.*(eta + 1.)*(eta + 1.)/(2.*2.) + 60.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 53:
                        return RealGradient(-6.*eta + 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 6. + 72.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 60.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 54:
                        return RealGradient(0., -24.*eta - 27.*xi/2. + 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 63./2. + 60.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 45.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 55:
                        return RealGradient(0., 6.*eta + 9.*xi - 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 27./2. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.) - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 45.*(xi + 1.)*(xi + 1.)/(2.*2.)/2.);
                      case 56:
                        return RealGradient(0., 0.);
                      case 57:
                        return RealGradient(0., -9.*xi/2. - 5./2. + 15.*((xi + 1.)*(xi + 1.)/(2.*2.))/2.);
                      case 58:
                        return RealGradient(0., 3.*xi + 5./2. - 15.*(xi + 1.)*(xi + 1.)/(2.*2.)/2.);
                      case 59:
                        return RealGradient(0., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(1875.*eta/2. + 1875.*xi/2. - 22500.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 78750.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 105000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 47250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 78750.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 105000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 47250.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 6875./4. - 13125.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 275625.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 367500.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 165375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 13125.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 367500.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 165375.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 8750.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 490000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 220500.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 8750.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 220500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 7875.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 7875.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 1:
                        return sign * RealGradient(-36375.*eta/256. - 71625.*xi/256. + 214875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/32. - 1582875.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/64. + 1021125.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 874125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. - 1504125.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/64. + 501375.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/16. - 902475.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. - 203875./512. + 254625.*((eta + 1.)*(eta + 1.)/(2.*2.))/256. + 11080125.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 7147875.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 6118875.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 527625.*((xi + 1.)*(xi + 1.)/(2.*2.))/256. - 3693375.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/32. + 6648075.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/128. - 84875.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 2382625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/16. - 2039625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/32. - 340375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/128. - 4288725.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 152775.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/256. + 3671325.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 291375.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/256., 0.);
                      case 2:
                        return sign * RealGradient(1125.*eta/16. + 2625.*xi/16. - 7875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 86625.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 70875.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 70875.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. + 55125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/4. - 18375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 33075.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. + 7125./32. - 7875.*(eta + 1.)*(eta + 1.)/(2.*2.)/16. - 606375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 496125.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 496125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. - 28875.*(xi + 1.)*(xi + 1.)/(2.*2.)/16. + 202125.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 363825.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/8. + 2625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 165375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 165375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 23625.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/8. + 297675.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 4725.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/16. - 297675.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. - 23625.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/16., 0.);
                      case 3:
                        return sign * RealGradient(-6375.*eta/256. - 17625.*xi/256. + 52875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/32. - 700875.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/64. + 727125.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 874125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. - 370125.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/64. + 123375.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/16. - 222075.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. - 45875./512. + 44625.*((eta + 1.)*(eta + 1.)/(2.*2.))/256. + 4906125.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 5089875.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 6118875.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 233625.*((xi + 1.)*(xi + 1.)/(2.*2.))/256. - 1635375.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/32. + 2943675.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/128. - 14875.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 1696625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/16. - 2039625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/32. - 242375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/128. - 3053925.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 26775.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/256. + 3671325.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 291375.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/256., 0.);
                      case 4:
                        return sign * RealGradient(375.*eta/2. + 375.*xi - 9000.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 47250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 84000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 47250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 31500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 42000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 18900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 2125./4. - 2625.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 165375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 294000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 165375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 7875.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 220500.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 99225.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1750.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 392000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 220500.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 7000.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 176400.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 7875.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 5:
                        return sign * RealGradient(0., -375.*xi/2. + 2625.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 31500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 110250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 147000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 66150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 5250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 3150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 375./2. + 63000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 294000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 132300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 4500.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 37800.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 132300.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 176400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 79380.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 15750.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 21000.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 9450.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                      case 6:
                        return sign * RealGradient(0., 14325.*xi/256. - 105525.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/128. + 316575.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/32. - 2216025.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 738675.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/16. - 1329615.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 204225.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/128. - 58275.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 14325./256. - 612675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/32. + 4288725.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 1429575.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/16. + 2573235.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/64. - 42975.*(xi + 1.)*(xi + 1.)/(2.*2.)/32. + 174825.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/16. - 1223775.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 407925.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/8. - 734265.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/32. + 300825.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 100275.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/16. + 180495.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/64.);
                      case 7:
                        return sign * RealGradient(0., -525.*xi/16. + 5775.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/8. - 17325.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 121275.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 40425.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 72765.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/4. - 14175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/8. + 4725.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 525./16. + 42525.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 297675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 99225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 178605.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/4. + 1575.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 14175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 66150.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 59535.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/2. - 11025.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 3675.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 6615.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/4.);
                      case 8:
                        return sign * RealGradient(0., 3525.*xi/256. - 46725.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/128. + 140175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/32. - 981225.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 327075.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/16. - 588735.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 145425.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/128. - 58275.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 3525./256. - 436275.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/32. + 3053925.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 1017975.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/16. + 1832355.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/64. - 10575.*(xi + 1.)*(xi + 1.)/(2.*2.)/32. + 174825.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/16. - 1223775.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 407925.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/8. - 734265.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/32. + 74025.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 24675.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/16. + 44415.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/64.);
                      case 9:
                        return sign * RealGradient(0., -75.*xi + 1575.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 18900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 66150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 88200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 4200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 3150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 75. + 50400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 176400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 235200.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 105840.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 1800.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 37800.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 132300.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 176400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 79380.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 6300.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 8400.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 3780.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                      case 10:
                        return sign * RealGradient(75.*eta + 75.*xi - 3600.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 18900.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 33600.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 18900.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 18900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 33600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 18900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 575./4. - 1575.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 99225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 176400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 99225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1575.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 176400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 99225.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 313600.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 176400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1400.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 176400.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 11:
                        return sign * RealGradient(-1275.*eta/128. - 3525.*xi/256. + 10575.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/16. - 140175.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/32. + 145425.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/16. - 174825.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/32. - 222075.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/64. + 24675.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 222075.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. - 11725./512. + 26775.*((eta + 1.)*(eta + 1.)/(2.*2.))/256. + 2943675.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 3053925.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 3671325.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 46725.*((xi + 1.)*(xi + 1.)/(2.*2.))/256. - 327075.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/8. + 2943675.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/128. - 2975.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/16. + 339325.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 407925.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. - 48475.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/128. - 3053925.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 26775.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/256. + 3671325.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 58275.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/256., 0.);
                      case 12:
                        return sign * RealGradient(225.*eta/8. + 525.*xi/16. - 1575.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 17325.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 14175.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 14175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 33075.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/4. - 14700.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 33075.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. + 1875./32. - 4725.*(eta + 1.)*(eta + 1.)/(2.*2.)/16. - 363825.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 297675.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 297675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. - 5775.*(xi + 1.)*(xi + 1.)/(2.*2.)/16. + 80850.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 363825.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/8. + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 132300.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 66150.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 4725.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/8. + 297675.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4. - 4725.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/16. - 297675.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. - 4725.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/16., 0.);
                      case 13:
                        return sign * RealGradient(-7275.*eta/128. - 14325.*xi/256. + 42975.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/16. - 316575.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/32. + 204225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/16. - 174825.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/32. - 902475.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/64. + 100275.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 902475.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. - 55325./512. + 152775.*((eta + 1.)*(eta + 1.)/(2.*2.))/256. + 6648075.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 4288725.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 3671325.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 105525.*((xi + 1.)*(xi + 1.)/(2.*2.))/256. - 738675.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/8. + 6648075.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/128. - 16975.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/16. + 476525.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 407925.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. - 68075.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/128. - 4288725.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/64. + 152775.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/256. + 3671325.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 58275.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/256., 0.);
                      case 14:
                        return sign * RealGradient(375.*eta + 375.*xi/2. - 9000.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 31500.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 42000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 18900.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 47250.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 84000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 47250.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 2125./4. - 7875.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 165375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 220500.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 99225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 2625.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 294000.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 165375.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 7000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 392000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 176400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 1750.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 220500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 7875.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 15:
                        return sign * RealGradient(0., -315.*eta/2. - 375.*xi + 7875.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 47250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 110250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 110250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 21000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 15750.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1005./2. + 840.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 126000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 294000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 294000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 105840.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 4500.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 94500.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 630.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 220500.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 79380.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 10500.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 10500.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 3780.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                      case 16:
                        return sign * RealGradient(0., 9345.*eta/256. + 17625.*xi/256. - 233625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/128. + 700875.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 1635375.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 1635375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. - 588735.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 727125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/128. - 291375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 3195./32. - 29085.*(eta + 1.)*(eta + 1.)/(2.*2.)/128. - 2181375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/64. + 5089875.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 5089875.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. + 1832355.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/64. - 52875.*(xi + 1.)*(xi + 1.)/(2.*2.)/64. + 874125.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/32. + 11655.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 2039625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 2039625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/32. - 734265.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/32. + 123375.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 123375.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. + 44415.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/64.);
                      case 17:
                        return sign * RealGradient(0., -1155.*eta/16. - 2625.*xi/16. + 28875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/8. - 86625.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 202125.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 202125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. + 72765.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/4. - 70875.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/8. + 23625.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. - 1785./8. + 2835.*((eta + 1.)*(eta + 1.)/(2.*2.))/8. + 212625.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 496125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 496125.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. - 178605.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/4. + 7875.*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 70875.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/4. + 165375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 165375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. + 59535.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/2. - 18375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 18375.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. - 6615.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/4.);
                      case 18:
                        return sign * RealGradient(0., 21105.*eta/256. + 71625.*xi/256. - 527625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/128. + 1582875.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 3693375.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/64. + 3693375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/64. - 1329615.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/64. + 1021125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/128. - 291375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. + 10875./32. - 40845.*(eta + 1.)*(eta + 1.)/(2.*2.)/128. - 3063375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/64. + 7147875.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 7147875.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. + 2573235.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/64. - 214875.*(xi + 1.)*(xi + 1.)/(2.*2.)/64. + 874125.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/32. + 11655.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/64. - 2039625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 2039625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/32. - 734265.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/32. + 501375.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 501375.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. + 180495.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/64.);
                      case 19:
                        return sign * RealGradient(0., -525.*eta/2. - 1875.*xi/2. + 13125.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 78750.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 183750.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 183750.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 66150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 26250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 15750.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1125. + 1050.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 157500.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 367500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 367500.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 132300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 11250.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 94500.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 630.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 220500.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 79380.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 26250.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 26250.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 9450.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                      case 20:
                        return RealGradient(0., -2925.*xi/4. + 20475.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 74025.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 362775.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 183750.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 66150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 20475.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 12285.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2925./4. + 148050.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 362775.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 367500.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 132300.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 10575.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 88830.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 217665.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 79380.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 51825.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 26250.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 9450.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                      case 21:
                        return RealGradient(0., 150.*xi - 2100.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 58275.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 215775.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 147000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 66150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2520.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 150. - 58275.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 215775.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 294000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 132300.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 8325.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 34965.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 129465.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 176400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 79380.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 30825.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 21000.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 9450.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                      case 22:
                        return RealGradient(0., -675.*xi/2. + 4725.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 23625.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 14175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 9450.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 5670.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 675./2. + 23625.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 14175.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3375.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 14175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 8505.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2025.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2.);
                      case 23:
                        return RealGradient(0., 675.*xi/4. - 4725.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 9450.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 14175.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 4725.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2835.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 675./4. - 18900.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 14175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1350.*(xi + 1.)*(xi + 1.)/(2.*2.) + 11340.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 8505.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2025.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2.);
                      case 24:
                        return RealGradient(3525.*eta/4. + 2925.*xi/4. - 21150.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 74025.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 98700.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 44415.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 155475.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 105000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 47250.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 11925./8. - 51825.*(eta + 1.)*(eta + 1.)/(2.*2.)/8. - 1088325.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 362775.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 652995.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. - 20475.*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 367500.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 165375.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 8750.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 490000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 220500.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 6825.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 220500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 7875.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 12285.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4., 0.);
                      case 25:
                        return RealGradient(-2775.*eta/8. - 150.*xi + 8325.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 58275.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 38850.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 34965.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. - 92475.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. + 84000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 47250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 3775./8. + 30825.*((eta + 1.)*(eta + 1.)/(2.*2.))/8. + 647325.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 215775.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 388395.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. + 1050.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 294000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 165375.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 7000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 392000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 176400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1400.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 220500.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 7875.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 630.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)), 0.);
                      case 26:
                        return RealGradient(1125.*eta/8. + 675.*xi/2. - 3375.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 23625.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 15750.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 14175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 6075.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 3375./8. - 2025.*(eta + 1.)*(eta + 1.)/(2.*2.)/8. - 42525.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 14175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 25515.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. - 4725.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 3150.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2835.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 27:
                        return RealGradient(-225.*eta/2. - 675.*xi/4. + 2700.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 9450.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 12600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5670.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 6075.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 2025./8. + 2025.*((eta + 1.)*(eta + 1.)/(2.*2.))/8. + 42525.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 14175.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 25515.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. + 4725.*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2835.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4., 0.);
                      case 28:
                        return RealGradient(705.*eta/4. + 585.*xi/2. - 8460.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 44415.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 78960.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 44415.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 31095.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 42000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 18900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 3555./8. - 10365.*(eta + 1.)*(eta + 1.)/(2.*2.)/8. - 652995.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 290220.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 652995.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. - 12285.*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 220500.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 99225.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1750.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 392000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 220500.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 5460.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 176400.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 12285.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4., 0.);
                      case 29:
                        return RealGradient(-555.*eta/8. - 60.*xi + 3330.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 34965.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 31080.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 34965.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. - 18495.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 33600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 18900.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 995./8. + 6165.*((eta + 1.)*(eta + 1.)/(2.*2.))/8. + 388395.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 172620.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 388395.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. + 630.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 176400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 99225.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 313600.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 176400.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1120.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 176400.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 630.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)), 0.);
                      case 30:
                        return RealGradient(225.*eta/8. + 135.*xi - 1350.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 14175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 12600.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 14175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 1215.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 1215./8. - 405.*(eta + 1.)*(eta + 1.)/(2.*2.)/8. - 25515.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 11340.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 25515.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4. - 2835.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 2520.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2835.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 31:
                        return RealGradient(-45.*eta/2. - 135.*xi/2. + 1080.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 5670.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 10080.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5670.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 1215.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 675./8. + 405.*((eta + 1.)*(eta + 1.)/(2.*2.))/8. + 25515.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 11340.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 25515.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. + 2835.*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 1260.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2835.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4., 0.);
                      case 32:
                        return RealGradient(0., -585.*xi/2. + 12285.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 44415.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 217665.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 110250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 39690.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 16380.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 12285.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 585./2. + 118440.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 290220.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 294000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 105840.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 4230.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 88830.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 217665.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 220500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 79380.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 10365.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 10500.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 3780.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                      case 33:
                        return RealGradient(0., 60.*xi - 1260.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 34965.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 129465.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 88200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 39690.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 3360.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2520.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 60. - 46620.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 172620.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 235200.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 105840.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 1665.*(xi + 1.)*(xi + 1.)/(2.*2.) + 34965.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 129465.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 176400.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 79380.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 6165.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 8400.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 3780.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                      case 34:
                        return RealGradient(0., -135.*xi + 2835.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 14175.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 8505.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 7560.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 5670.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 135. + 18900.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 11340.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 675.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 14175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 8505.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 405.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 35:
                        return RealGradient(0., 135.*xi/2. - 2835.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 5670.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8505.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 3780.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 2835.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 135./2. - 15120.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 11340.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 540.*(xi + 1.)*(xi + 1.)/(2.*2.) + 11340.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 8505.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 405.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 36:
                        return RealGradient(-297.*eta - 72.*xi + 2376.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1980.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 9180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 12600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 5670.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 333. + 2295.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 7650.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 120.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 10500.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4725.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 3150.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2835.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2., 0.);
                      case 37:
                        return RealGradient(-99.*eta - 48.*xi + 1584.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1980.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 6120.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 8400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 3780.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 135. + 765.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 7650.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 120.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 10500.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4725.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 1050.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 945.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2., 0.);
                      case 38:
                        return RealGradient(99.*eta/2. + 30.*xi - 990.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 990.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 3825.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 5250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4725.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 147./2. - 765.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 3825.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 60.*(xi + 1.)*(xi + 1.)/(2.*2.) + 5250.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4725.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4., 0.);
                      case 39:
                        return RealGradient(0., -72.*xi + 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1980.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 1890.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 72. + 1188.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3060.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3150.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 1134.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                      case 40:
                        return RealGradient(0., -48.*xi + 240.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 1980.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 5250.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 1890.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 48. + 792.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2040.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2100.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 756.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.));
                      case 41:
                        return RealGradient(0., 30.*xi - 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 990.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2550.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2625.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 945.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 30. - 495.*(xi + 1.)*(xi + 1.)/(2.*2.) + 1275.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2625.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.))/2.);
                      case 42:
                        return RealGradient(0., 9.*xi - 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 720.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 1890.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 9. - 432.*(xi + 1.)*(xi + 1.)/(2.*2.) + 1800.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2520.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 1134.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                      case 43:
                        return RealGradient(0., 6.*xi - 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 720.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4200.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 1890.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.) + 6. - 288.*(xi + 1.)*(xi + 1.)/(2.*2.) + 1200.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1680.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 756.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)));
                      case 44:
                        return RealGradient(0., -15.*xi/4. + 15.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 360.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 1500.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2100.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) + 945.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)) - 15./4. + 180.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 750.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1050.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) - 945.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.*2.)/2.);
                      case 45:
                        return RealGradient(108.*eta + 9.*xi - 864.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 720.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 5400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 10080.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 5670.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 225./2. - 1350.*(eta + 1.)*(eta + 1.)/(2.*2.) - 4500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 15.*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4725.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 2520.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2835.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 46:
                        return RealGradient(36.*eta + 6.*xi - 576.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 720.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 3600.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 6720.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3780.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 81./2. - 450.*(eta + 1.)*(eta + 1.)/(2.*2.) - 4500.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 15.*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4725.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 840.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2., 0.);
                      case 47:
                        return RealGradient(-18.*eta - 15.*xi/4. + 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 360.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 2250.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 4200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4725.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 21. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 2250.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 15.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 4200.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4725.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. - 420.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 945.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4., 0.);
                      case 48:
                        return RealGradient(0., -36.*xi + 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 36. + 162.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 90.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 49:
                        return RealGradient(0., 9.*xi - 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 9. - 108.*(xi + 1.)*(xi + 1.)/(2.*2.) + 90.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 50:
                        return RealGradient(81.*eta/2. + 36.*xi - 324.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 270.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 117./2. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 60.*(xi + 1.)*(xi + 1.)/(2.*2.), 0.);
                      case 51:
                        return RealGradient(-27.*eta - 9.*xi + 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 270.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 63./2. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 15.*((xi + 1.)*(xi + 1.)/(2.*2.)), 0.);
                      case 52:
                        return RealGradient(27.*eta/2. + 24.*xi - 216.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 270.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 180.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 63./2. - 45.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 60.*(xi + 1.)*(xi + 1.)/(2.*2.), 0.);
                      case 53:
                        return RealGradient(-9.*eta - 6.*xi + 144.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 180.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 180.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 27./2. + 45.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 225.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 15.*((xi + 1.)*(xi + 1.)/(2.*2.)), 0.);
                      case 54:
                        return RealGradient(0., -24.*xi + 120.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 270.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 24. + 108.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 60.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 55:
                        return RealGradient(0., 6.*xi - 30.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 180.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 6. - 72.*(xi + 1.)*(xi + 1.)/(2.*2.) + 60.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 56:
                        return RealGradient(-9.*eta/2. - 5./2. + 15.*((eta + 1.)*(eta + 1.)/(2.*2.))/2., 0.);
                      case 57:
                        return RealGradient(0., 0.);
                      case 58:
                        return RealGradient(0., 0.);
                      case 59:
                        return RealGradient(3.*eta + 5./2. - 15.*(eta + 1.)*(eta + 1.)/(2.*2.)/2., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-12600.*eta*xi + 2800.*eta + 15120.*eta*(xi*xi) - 4200.*eta*xi*xi*xi + 2100.*xi + 22680.*xi*(eta*eta) - 12600.*xi*eta*eta*eta - 300. - 8400.*eta*eta - 12600.*eta*eta*xi*xi - 4200.*xi*xi + 10080.*(eta*eta*eta) + 2520.*(xi*xi*xi) - 4200.*eta*eta*eta*eta, 8400.*eta*xi - 700.*eta - 22680.*eta*xi*xi + 16800.*eta*(xi*xi*xi) - 1400.*xi - 15120.*xi*eta*eta + 8400.*xi*(eta*eta*eta) + 75. + 2100.*(eta*eta) + 18900.*(eta*eta)*(xi*xi) + 6300.*(xi*xi) - 2520.*eta*eta*eta - 10080.*xi*xi*xi + 1050.*(eta*eta*eta*eta) + 5250.*(xi*xi*xi*xi));
                      case 1:
                        return sign * RealGradient(136185.*eta*xi/32. - 12145.*eta/16. - 20475.*eta*xi*xi/4. + 19425.*eta*(xi*xi*xi)/16. - 21105.*xi/32. - 240975.*xi*eta*eta/32. + 127575.*xi*(eta*eta*eta)/32. + 2865./32. + 7245.*(eta*eta)/4. + 146475.*(eta*eta)*(xi*xi)/32. + 40845.*(xi*xi)/32. - 25515.*eta*eta*eta/16. - 11655.*xi*xi*xi/16. + 14175.*(eta*eta*eta*eta)/32., -39375.*eta*xi/16. + 3045.*eta/32. + 252315.*eta*(xi*xi)/32. - 48825.*eta*xi*xi*xi/8. + 1715.*xi/4. + 25515.*xi*(eta*eta)/8. - 14175.*xi*eta*eta*eta/16. - 2395./128. + 2835.*(eta*eta)/64. - 382725.*eta*eta*xi*xi/64. - 125265.*xi*xi/64. - 14175.*eta*eta*eta/32. + 48615.*(xi*xi*xi)/16. + 42525.*(eta*eta*eta*eta)/128. - 97125.*xi*xi*xi*xi/64.);
                      case 2:
                        return sign * RealGradient(-3255.*eta*xi/2. + 3780.*eta*(xi*xi) - 1575.*eta*xi*xi*xi + 1155.*xi/2. + 945.*xi*(eta*eta)/2. + 1575.*xi*(eta*eta*eta)/2. - 105./2. + 840.*(eta*eta) - 4725.*eta*eta*xi*xi/2. - 2835.*xi*xi/2. - 1575.*eta*eta*eta + 945.*(xi*xi*xi) + 1575.*(eta*eta*eta*eta)/2., 105.*eta*xi + 35.*eta/2. - 4725.*eta*xi*xi/2. + 3150.*eta*(xi*xi*xi) - 315.*xi + 1890.*xi*(eta*eta) - 1575.*xi*eta*eta*eta + 85./8. - 525.*eta*eta/4. - 4725.*eta*eta*xi*xi/4. + 7455.*(xi*xi)/4. + 105.*(eta*eta*eta)/2. - 3465.*xi*xi*xi + 525.*(eta*eta*eta*eta)/8. + 7875.*(xi*xi*xi*xi)/4.);
                      case 3:
                        return sign * RealGradient(-16695.*eta*xi/32. + 1855.*eta/16. - 2835.*eta*xi*xi/4. + 19425.*eta*(xi*xi*xi)/16. - 9345.*xi/32. + 76545.*xi*(eta*eta)/32. - 48825.*xi*eta*eta*eta/32. + 705./32. - 1155.*eta*eta/4. - 29925.*eta*eta*xi*xi/32. + 29085.*(xi*xi)/32. - 315.*eta*eta*eta/16. - 11655.*xi*xi*xi/16. + 5775.*(eta*eta*eta*eta)/32., 9345.*eta*xi/16. - 875.*eta/32. - 65205.*eta*xi*xi/32. + 9975.*eta*(xi*xi*xi)/8. + 595.*xi/4. - 4725.*xi*eta*eta/8. - 5775.*xi*eta*eta*eta/16. - 555./128. + 1155.*(eta*eta)/64. + 146475.*(eta*eta)*(xi*xi)/64. - 66465.*xi*xi/64. + 945.*(eta*eta*eta)/32. + 36855.*(xi*xi*xi)/16. + 525.*(eta*eta*eta*eta)/128. - 97125.*xi*xi*xi*xi/64.);
                      case 4:
                        return sign * RealGradient(-1680.*eta*xi + 140.*eta + 5040.*eta*(xi*xi) - 4200.*eta*xi*xi*xi + 1260.*xi - 120. - 3360.*xi*xi + 2520.*(xi*xi*xi), -700.*xi + 25. + 4200.*(xi*xi) - 8400.*xi*xi*xi + 5250.*(xi*xi*xi*xi));
                      case 5:
                        return sign * RealGradient(-1680.*eta*xi + 140.*eta + 5040.*eta*(xi*xi) - 4200.*eta*xi*xi*xi, -700.*xi + 25. + 4200.*(xi*xi) - 8400.*xi*xi*xi + 5250.*(xi*xi*xi*xi));
                      case 6:
                        return sign * RealGradient(-2835.*eta*xi/2. + 735.*eta/4. + 42525.*eta*(xi*xi)/16. - 42525.*eta*xi*xi*xi/32. + 76545.*xi*(eta*eta)/16. - 42525.*xi*eta*eta*eta/16. - 1575.*eta*eta/2. - 42525.*eta*eta*xi*xi/8. + 12285.*(eta*eta*eta)/16. - 1575.*eta*eta*eta*eta/8., 2205.*eta*xi - 455.*eta/4. - 127575.*eta*xi*xi/16. + 14175.*eta*(xi*xi*xi)/2. - 1785.*xi/4. - 31185.*xi*eta*eta/16. + 1575.*xi*(eta*eta*eta)/4. + 20. + 525.*(eta*eta)/4. + 127575.*(eta*eta)*(xi*xi)/32. + 8505.*(xi*xi)/4. - 735.*eta*eta*eta/16. - 53865.*xi*xi*xi/16. + 525.*(eta*eta*eta*eta)/128. + 212625.*(xi*xi*xi*xi)/128.);
                      case 7:
                        return sign * RealGradient(-840.*eta*xi + 175.*eta + 945.*eta*(xi*xi) - 525.*eta*xi*xi*xi/2. + 4725.*xi*(eta*eta) - 4725.*xi*eta*eta*eta - 1260.*eta*eta - 3150.*eta*eta*xi*xi + 2205.*(eta*eta*eta) - 1050.*eta*eta*eta*eta, 2520.*eta*xi - 175.*eta - 6615.*eta*xi*xi + 4200.*eta*(xi*xi*xi) - 245.*xi - 4725.*xi*eta*eta + 2100.*xi*(eta*eta*eta) + 15. + 420.*(eta*eta) + 14175.*(eta*eta)*(xi*xi)/2. + 840.*(xi*xi) - 315.*eta*eta*eta - 945.*xi*xi*xi + 525.*(eta*eta*eta*eta)/8. + 2625.*(xi*xi*xi*xi)/8.);
                      case 8:
                        return sign * RealGradient(-525.*eta*xi/2. + 455.*eta/4. + 2205.*eta*(xi*xi)/16. - 525.*eta*xi*xi*xi/32. + 31185.*xi*(eta*eta)/16. - 42525.*xi*eta*eta*eta/16. - 2205.*eta*eta/2. - 4725.*eta*eta*xi*xi/8. + 42525.*(eta*eta*eta)/16. - 14175.*eta*eta*eta*eta/8., 1575.*eta*xi - 735.*eta/4. - 36855.*eta*xi*xi/16. + 1575.*eta*(xi*xi*xi)/2. - 385.*xi/4. - 76545.*xi*eta*eta/16. + 14175.*xi*(eta*eta*eta)/4. + 10. + 2835.*(eta*eta)/4. + 127575.*(eta*eta)*(xi*xi)/32. + 735.*(xi*xi)/4. - 14175.*eta*eta*eta/16. - 1785.*xi*xi*xi/16. + 42525.*(eta*eta*eta*eta)/128. + 2625.*(xi*xi*xi*xi)/128.);
                      case 9:
                        return sign * RealGradient(0., -140.*eta + 5. + 840.*(eta*eta) - 1680.*eta*eta*eta + 1050.*(eta*eta*eta*eta));
                      case 10:
                        return sign * RealGradient(0., -140.*eta + 5. + 840.*(eta*eta) - 1680.*eta*eta*eta + 1050.*(eta*eta*eta*eta));
                      case 11:
                        return sign * RealGradient(-1155.*eta*xi/32. + 875.*eta/32. - 2835.*eta*xi*xi/32. - 525.*eta*xi*xi*xi/32. + 4725.*xi*(eta*eta)/8. - 48825.*xi*eta*eta*eta/32. - 9345.*eta*eta/32. + 17325.*(eta*eta)*(xi*xi)/32. + 21735.*(eta*eta*eta)/32. - 9975.*eta*eta*eta*eta/32., 1155.*eta*xi/2. - 1855.*eta/16. + 945.*eta*(xi*xi)/16. - 5775.*eta*xi*xi*xi/8. - 595.*xi/32. - 76545.*xi*eta*eta/32. + 9975.*xi*(eta*eta*eta)/16. + 825./128. + 16695.*(eta*eta)/64. + 146475.*(eta*eta)*(xi*xi)/64. - 1785.*xi*xi/64. + 945.*(eta*eta*eta)/4. + 945.*(xi*xi*xi)/32. - 19425.*eta*eta*eta*eta/64. + 2625.*(xi*xi*xi*xi)/128.);
                      case 12:
                        return sign * RealGradient(525.*eta*xi/2. - 35.*eta/2. - 315.*eta*xi*xi/2. - 525.*eta*xi*xi*xi/2. - 1890.*xi*eta*eta + 1575.*xi*(eta*eta*eta)/2. - 105.*eta*eta/2. + 4725.*(eta*eta)*(xi*xi)/2. + 1575.*(eta*eta*eta)/2. - 1575.*eta*eta*eta*eta/2., -1680.*eta*xi + 4725.*eta*(xi*xi) - 3150.*eta*xi*xi*xi + 175.*xi/2. - 945.*xi*eta*eta/2. + 1575.*xi*(eta*eta*eta) - 55./8. + 3255.*(eta*eta)/4. - 4725.*eta*eta*xi*xi/4. - 105.*xi*xi/4. - 1260.*eta*eta*eta - 735.*xi*xi*xi/2. + 1575.*(eta*eta*eta*eta)/4. + 2625.*(xi*xi*xi*xi)/8.);
                      case 13:
                        return sign * RealGradient(-2835.*eta*xi/32. - 3045.*eta/32. + 42525.*eta*(xi*xi)/32. - 42525.*eta*xi*xi*xi/32. - 25515.*xi*eta*eta/8. + 127575.*xi*(eta*eta*eta)/32. + 39375.*(eta*eta)/32. + 42525.*(eta*eta)*(xi*xi)/32. - 84105.*eta*eta*eta/32. + 48825.*(eta*eta*eta*eta)/32., -7245.*eta*xi/2. + 12145.*eta/16. + 76545.*eta*(xi*xi)/16. - 14175.*eta*xi*xi*xi/8. - 11235.*xi/32. + 240975.*xi*(eta*eta)/32. - 48825.*xi*eta*eta*eta/16. - 695./128. - 136185.*eta*eta/64. - 382725.*eta*eta*xi*xi/64. + 127575.*(xi*xi)/64. + 6825.*(eta*eta*eta)/4. - 104895.*xi*xi*xi/32. - 19425.*eta*eta*eta*eta/64. + 212625.*(xi*xi*xi*xi)/128.);
                      case 14:
                        return sign * RealGradient(-4200.*eta*xi + 700.*eta + 7560.*eta*(xi*xi) - 4200.*eta*xi*xi*xi + 15120.*xi*(eta*eta) - 12600.*xi*eta*eta*eta - 4200.*eta*eta - 12600.*eta*eta*xi*xi + 7560.*(eta*eta*eta) - 4200.*eta*eta*eta*eta, 16800.*eta*xi - 2800.*eta - 30240.*eta*xi*xi + 16800.*eta*(xi*xi*xi) - 3500.*xi - 22680.*xi*eta*eta + 8400.*xi*(eta*eta*eta) + 375. + 6300.*(eta*eta) + 18900.*(eta*eta)*(xi*xi) + 10500.*(xi*xi) - 5040.*eta*eta*eta - 12600.*xi*xi*xi + 1050.*(eta*eta*eta*eta) + 5250.*(xi*xi*xi*xi));
                      case 15:
                        return RealGradient(70560.*eta*xi - 19600.*eta - 70560.*eta*xi*xi + 16800.*eta*(xi*xi*xi) - 211680.*xi*eta*eta + 151200.*xi*(eta*eta*eta) + 94080.*(eta*eta) + 100800.*(eta*eta)*(xi*xi) - 141120.*eta*eta*eta + 67200.*(eta*eta*eta*eta), -94080.*eta*xi + 9800.*eta + 211680.*eta*(xi*xi) - 134400.*eta*xi*xi*xi + 9800.*xi + 211680.*xi*(eta*eta) - 134400.*xi*eta*eta*eta - 700. - 35280.*eta*eta - 226800.*eta*eta*xi*xi - 35280.*xi*xi + 47040.*(eta*eta*eta) + 47040.*(xi*xi*xi) - 21000.*eta*eta*eta*eta - 21000.*xi*xi*xi*xi);
                      case 16:
                        return RealGradient(-70560.*eta*xi + 9800.*eta + 141120.*eta*(xi*xi) - 84000.*eta*xi*xi*xi + 211680.*xi*(eta*eta) - 151200.*xi*eta*eta*eta - 47040.*eta*eta - 201600.*eta*eta*xi*xi + 70560.*(eta*eta*eta) - 33600.*eta*eta*eta*eta, 188160.*eta*xi - 19600.*eta - 423360.*eta*xi*xi + 268800.*eta*(xi*xi*xi) - 49000.*xi - 211680.*xi*eta*eta + 67200.*xi*(eta*eta*eta) + 3500. + 35280.*(eta*eta) + 226800.*(eta*eta)*(xi*xi) + 176400.*(xi*xi) - 23520.*eta*eta*eta - 235200.*xi*xi*xi + 4200.*(eta*eta*eta*eta) + 105000.*(xi*xi*xi*xi));
                      case 17:
                        return RealGradient(-60480.*eta*xi + 6440.*eta + 131040.*eta*(xi*xi) - 67200.*eta*xi*xi*xi + 60480.*xi*(eta*eta) - 6720.*eta*eta - 100800.*eta*eta*xi*xi, 26880.*eta*xi - 1120.*eta - 120960.*eta*xi*xi + 134400.*eta*(xi*xi*xi) - 14560.*xi + 560. + 80640.*(xi*xi) - 147840.*xi*xi*xi + 84000.*(xi*xi*xi*xi));
                      case 18:
                        return RealGradient(40320.*eta*xi - 3640.*eta - 110880.*eta*xi*xi + 84000.*eta*(xi*xi*xi) - 30240.*xi*eta*eta + 3360.*(eta*eta) + 50400.*(eta*eta)*(xi*xi), -13440.*eta*xi + 560.*eta + 60480.*eta*(xi*xi) - 67200.*eta*xi*xi*xi + 18200.*xi - 700. - 100800.*xi*xi + 184800.*(xi*xi*xi) - 105000.*xi*xi*xi*xi);
                      case 19:
                        return RealGradient(560.*eta - 6720.*eta*eta + 20160.*(eta*eta*eta) - 16800.*eta*eta*eta*eta, 6720.*eta*xi - 3640.*eta - 280.*xi - 30240.*xi*eta*eta + 33600.*xi*(eta*eta*eta) + 140. + 20160.*(eta*eta) - 36960.*eta*eta*eta + 21000.*(eta*eta*eta*eta));
                      case 20:
                        return RealGradient(-1120.*eta + 13440.*(eta*eta) - 40320.*eta*eta*eta + 33600.*(eta*eta*eta*eta), -13440.*eta*xi + 6440.*eta + 560.*xi + 60480.*xi*(eta*eta) - 67200.*xi*eta*eta*eta - 280. - 30240.*eta*eta + 43680.*(eta*eta*eta) - 16800.*eta*eta*eta*eta);
                      case 21:
                        return RealGradient(-35840.*eta*xi + 17920.*eta/3. + 156800.*eta*(xi*xi)/3. - 179200.*eta*xi*xi*xi/9. + 125440.*xi*(eta*eta) - 89600.*xi*eta*eta*eta - 29120.*eta*eta - 291200.*eta*eta*xi*xi/3. + 116480.*(eta*eta*eta)/3. - 140000.*eta*eta*eta*eta/9., 56000.*eta*xi - 10360.*eta/3. - 170240.*eta*xi*xi + 1164800.*eta*(xi*xi*xi)/9. - 24920.*xi/3. - 81760.*xi*eta*eta + 280000.*xi*(eta*eta*eta)/9. + 420. + 6720.*(eta*eta) + 134400.*(eta*eta)*(xi*xi) + 35840.*(xi*xi) - 39200.*eta*eta*eta/9. - 474880.*xi*xi*xi/9. + 7000.*(eta*eta*eta*eta)/9. + 224000.*(xi*xi*xi*xi)/9.);
                      case 22:
                        return RealGradient(29120.*eta*xi - 12880.*eta/3. - 152320.*eta*xi*xi/3. + 224000.*eta*(xi*xi*xi)/9. - 109760.*xi*eta*eta + 78400.*xi*(eta*eta*eta) + 22400.*(eta*eta) + 313600.*(eta*eta)*(xi*xi)/3. - 91840.*eta*eta*eta/3. + 112000.*(eta*eta*eta*eta)/9., -62720.*eta*xi + 12040.*eta/3. + 185920.*eta*(xi*xi) - 1254400.*eta*xi*xi*xi/9. + 32480.*xi/3. + 76160.*xi*(eta*eta) - 224000.*xi*eta*eta*eta/9. - 560. - 6720.*eta*eta - 117600.*eta*eta*xi*xi - 45920.*xi*xi + 34720.*(eta*eta*eta)/9. + 600320.*(xi*xi*xi)/9. - 5600.*eta*eta*eta*eta/9. - 280000.*xi*xi*xi*xi/9.);
                      case 23:
                        return RealGradient(-13440.*eta*xi + 12040.*eta/3. + 34720.*eta*(xi*xi)/3. - 22400.*eta*xi*xi*xi/9. + 76160.*xi*(eta*eta) - 78400.*xi*eta*eta*eta - 31360.*eta*eta - 112000.*eta*eta*xi*xi/3. + 185920.*(eta*eta*eta)/3. - 313600.*eta*eta*eta*eta/9., 44800.*eta*xi - 12880.*eta/3. - 91840.*eta*xi*xi + 448000.*eta*(xi*xi*xi)/9. - 10640.*xi/3. - 109760.*xi*eta*eta + 627200.*xi*(eta*eta*eta)/9. + 280. + 14560.*(eta*eta) + 117600.*(eta*eta)*(xi*xi) + 10080.*(xi*xi) - 152320.*eta*eta*eta/9. - 89600.*xi*xi*xi/9. + 56000.*(eta*eta*eta*eta)/9. + 28000.*(xi*xi*xi*xi)/9.);
                      case 24:
                        return RealGradient(13440.*eta*xi - 10360.*eta/3. - 39200.*eta*xi*xi/3. + 28000.*eta*(xi*xi*xi)/9. - 81760.*xi*eta*eta + 89600.*xi*(eta*eta*eta) + 28000.*(eta*eta) + 140000.*(eta*eta)*(xi*xi)/3. - 170240.*eta*eta*eta/3. + 291200.*(eta*eta*eta*eta)/9., -58240.*eta*xi + 17920.*eta/3. + 116480.*eta*(xi*xi) - 560000.*eta*xi*xi*xi/9. + 14840.*xi/3. + 125440.*xi*(eta*eta) - 582400.*xi*eta*eta*eta/9. - 420. - 17920.*eta*eta - 134400.*eta*eta*xi*xi - 13440.*xi*xi + 156800.*(eta*eta*eta)/9. + 115360.*(xi*xi*xi)/9. - 44800.*eta*eta*eta*eta/9. - 35000.*xi*xi*xi*xi/9.);
                      case 25:
                        return RealGradient(11200.*eta*xi - 12880.*eta/9. - 49280.*eta*xi*xi/3. + 44800.*eta*(xi*xi*xi)/9. - 2240.*xi*eta*eta - 11200.*xi*eta*eta*eta - 15680.*eta*eta/3. + 22400.*(eta*eta)*(xi*xi)/3. + 51520.*(eta*eta*eta)/3. - 95200.*eta*eta*eta*eta/9., 15680.*eta*xi/3. - 10360.*eta/9. + 2240.*eta*(xi*xi) - 89600.*eta*xi*xi*xi/9. + 6440.*xi/9. - 25760.*xi*eta*eta + 190400.*xi*(eta*eta*eta)/9. + 140./9. + 5600.*(eta*eta) + 16800.*(eta*eta)*(xi*xi) - 5600.*xi*xi - 75040.*eta*eta*eta/9. + 98560.*(xi*xi*xi)/9. + 35000.*(eta*eta*eta*eta)/9. - 56000.*xi*xi*xi*xi/9.);
                      case 26:
                        return RealGradient(-2240.*eta*xi - 9520.*eta/9. + 71680.*eta*(xi*xi)/3. - 224000.*eta*xi*xi*xi/9. - 51520.*xi*eta*eta + 56000.*xi*(eta*eta*eta) + 44800.*(eta*eta)/3. + 89600.*(eta*eta)*(xi*xi)/3. - 82880.*eta*eta*eta/3. + 123200.*(eta*eta*eta*eta)/9., -138880.*eta*xi/3. + 51800.*eta/9. + 82880.*eta*(xi*xi) - 358400.*eta*xi*xi*xi/9. - 48160.*xi/9. + 80640.*xi*(eta*eta) - 246400.*xi*eta*eta*eta/9. + 560./9. - 13440.*eta*eta - 84000.*eta*eta*xi*xi + 32480.*(xi*xi) + 79520.*(eta*eta*eta)/9. - 519680.*xi*xi*xi/9. - 11200.*eta*eta*eta*eta/9. + 280000.*(xi*xi*xi*xi)/9.);
                      case 27:
                        return RealGradient(-1120.*eta*xi + 2800.*eta/9. - 1120.*eta*xi*xi/3. + 5600.*eta*(xi*xi*xi)/9. + 12320.*xi*(eta*eta) - 5600.*xi*eta*eta*eta - 4480.*eta*eta/3. - 22400.*eta*eta*xi*xi/3. - 11200.*eta*eta*eta/3. + 44800.*(eta*eta*eta*eta)/9., 4480.*eta*xi/3. + 5320.*eta/9. - 12320.*eta*xi*xi + 89600.*eta*(xi*xi*xi)/9. - 1400.*xi/9. + 5600.*xi*(eta*eta) - 89600.*xi*eta*eta*eta/9. - 140./9. - 3920.*eta*eta + 8400.*(eta*eta)*(xi*xi) + 560.*(xi*xi) + 64960.*(eta*eta*eta)/9. + 2240.*(xi*xi*xi)/9. - 35000.*eta*eta*eta*eta/9. - 7000.*xi*xi*xi*xi/9.);
                      case 28:
                        return RealGradient(3360.*eta*xi + 280.*eta/9. - 11200.*eta*xi*xi/3. - 28000.*eta*xi*xi*xi/9. - 19040.*xi*eta*eta - 5600.*xi*eta*eta*eta - 11200.*eta*eta/3. + 112000.*(eta*eta)*(xi*xi)/3. + 52640.*(eta*eta*eta)/3. - 123200.*eta*eta*eta*eta/9., -35840.*eta*xi/3. - 8960.*eta/9. + 58240.*eta*(xi*xi) - 448000.*eta*xi*xi*xi/9. + 8680.*xi/9. - 30240.*xi*eta*eta + 246400.*xi*(eta*eta*eta)/9. - 140./9. + 9520.*(eta*eta) + 8400.*(eta*eta)*(xi*xi) - 1680.*xi*xi - 99680.*eta*eta*eta/9. - 24640.*xi*xi*xi/9. + 23800.*(eta*eta*eta*eta)/9. + 35000.*(xi*xi*xi*xi)/9.);
                      case 29:
                        return RealGradient(-26880.*eta*xi + 51800.*eta/9. + 79520.*eta*(xi*xi)/3. - 44800.*eta*xi*xi*xi/9. + 80640.*xi*(eta*eta) - 56000.*xi*eta*eta*eta - 69440.*eta*eta/3. - 123200.*eta*eta*xi*xi/3. + 82880.*(eta*eta*eta)/3. - 89600.*eta*eta*eta*eta/9., 89600.*eta*xi/3. - 9520.*eta/9. - 82880.*eta*xi*xi + 492800.*eta*(xi*xi*xi)/9. - 29680.*xi/9. - 51520.*xi*eta*eta + 179200.*xi*(eta*eta*eta)/9. + 1400./9. - 1120.*eta*eta + 84000.*(eta*eta)*(xi*xi) + 12320.*(xi*xi) + 71680.*(eta*eta*eta)/9. - 138880.*xi*xi*xi/9. - 56000.*eta*eta*eta*eta/9. + 56000.*(xi*xi*xi*xi)/9.);
                      case 30:
                        return RealGradient(11200.*eta*xi - 10360.*eta/9. - 75040.*eta*xi*xi/3. + 140000.*eta*(xi*xi*xi)/9. - 25760.*xi*eta*eta + 11200.*xi*(eta*eta*eta) + 7840.*(eta*eta)/3. + 95200.*(eta*eta)*(xi*xi)/3. + 2240.*(eta*eta*eta)/3. - 22400.*eta*eta*eta*eta/9., -31360.*eta*xi/3. - 12880.*eta/9. + 51520.*eta*(xi*xi) - 380800.*eta*xi*xi*xi/9. + 51800.*xi/9. - 2240.*xi*eta*eta + 44800.*xi*(eta*eta*eta)/9. - 700./9. + 5600.*(eta*eta) - 16800.*eta*eta*xi*xi - 28000.*xi*xi - 49280.*eta*eta*eta/9. + 375200.*(xi*xi*xi)/9. + 11200.*(eta*eta*eta*eta)/9. - 175000.*xi*xi*xi*xi/9.);
                      case 31:
                        return RealGradient(19040.*eta*xi - 8960.*eta/9. - 99680.*eta*xi*xi/3. + 95200.*eta*(xi*xi*xi)/9. - 30240.*xi*eta*eta + 5600.*xi*(eta*eta*eta) - 17920.*eta*eta/3. + 123200.*(eta*eta)*(xi*xi)/3. + 58240.*(eta*eta*eta)/3. - 112000.*eta*eta*eta*eta/9., -22400.*eta*xi/3. + 280.*eta/9. + 52640.*eta*(xi*xi) - 492800.*eta*xi*xi*xi/9. + 27160.*xi/9. - 19040.*xi*eta*eta + 224000.*xi*(eta*eta*eta)/9. - 980./9. + 1680.*(eta*eta) - 8400.*eta*eta*xi*xi - 16240.*xi*xi - 11200.*eta*eta*eta/9. + 239680.*(xi*xi*xi)/9. - 7000.*eta*eta*eta*eta/9. - 119000.*xi*xi*xi*xi/9.);
                      case 32:
                        return RealGradient(-7840.*eta*xi + 5320.*eta/9. + 64960.*eta*(xi*xi)/3. - 140000.*eta*xi*xi*xi/9. + 5600.*xi*(eta*eta) + 5600.*xi*(eta*eta*eta) + 2240.*(eta*eta)/3. - 44800.*eta*eta*xi*xi/3. - 12320.*eta*eta*eta/3. + 22400.*(eta*eta*eta*eta)/9., -8960.*eta*xi/3. + 2800.*eta/9. - 11200.*eta*xi*xi + 179200.*eta*(xi*xi*xi)/9. - 26600.*xi/9. + 12320.*xi*(eta*eta) - 44800.*xi*eta*eta*eta/9. + 700./9. - 560.*eta*eta - 8400.*eta*eta*xi*xi + 19600.*(xi*xi) - 1120.*eta*eta*eta/9. - 324800.*xi*xi*xi/9. + 1400.*(eta*eta*eta*eta)/9. + 175000.*(xi*xi*xi*xi)/9.);
                      case 33:
                        return RealGradient(3360.*eta*xi - 6440.*eta/9. - 4480.*eta*xi*xi + 5600.*eta*(xi*xi*xi)/3. - 19040.*xi*eta*eta + 16800.*xi*(eta*eta*eta) + 19040.*(eta*eta)/3. + 11200.*(eta*eta)*(xi*xi) - 11200.*eta*eta*eta + 5600.*(eta*eta*eta*eta), -29120.*eta*xi/3. + 6160.*eta/9. + 23520.*eta*(xi*xi) - 44800.*eta*xi*xi*xi/3. + 9520.*xi/9. + 20160.*xi*(eta*eta) - 11200.*xi*eta*eta*eta - 560./9. - 1680.*eta*eta - 25200.*eta*eta*xi*xi - 3920.*xi*xi + 1120.*(eta*eta*eta) + 15680.*(xi*xi*xi)/3. - 7000.*xi*xi*xi*xi/3.);
                      case 34:
                        return RealGradient(-3360.*eta*xi + 6160.*eta/9. + 3360.*eta*(xi*xi) + 20160.*xi*(eta*eta) - 16800.*xi*eta*eta*eta - 14560.*eta*eta/3. - 16800.*eta*eta*xi*xi + 7840.*(eta*eta*eta) - 11200.*eta*eta*eta*eta/3., 38080.*eta*xi/3. - 6440.*eta/9. - 33600.*eta*xi*xi + 22400.*eta*(xi*xi*xi) - 5600.*xi/9. - 19040.*xi*eta*eta + 22400.*xi*(eta*eta*eta)/3. + 280./9. + 1680.*(eta*eta) + 25200.*(eta*eta)*(xi*xi) + 1680.*(xi*xi) - 4480.*eta*eta*eta/3. - 1120.*xi*xi*xi + 1400.*(eta*eta*eta*eta)/3.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-16800.*eta*xi + 3500.*eta + 22680.*eta*(xi*xi) - 8400.*eta*xi*xi*xi + 2800.*xi + 30240.*xi*(eta*eta) - 16800.*xi*eta*eta*eta - 375. - 10500.*eta*eta - 18900.*eta*eta*xi*xi - 6300.*xi*xi + 12600.*(eta*eta*eta) + 5040.*(xi*xi*xi) - 5250.*eta*eta*eta*eta - 1050.*xi*xi*xi*xi, 4200.*eta*xi - 15120.*eta*xi*xi + 12600.*eta*(xi*xi*xi) - 700.*xi - 7560.*xi*eta*eta + 4200.*xi*(eta*eta*eta) + 12600.*(eta*eta)*(xi*xi) + 4200.*(xi*xi) - 7560.*xi*xi*xi + 4200.*(xi*xi*xi*xi));
                      case 1:
                        return sign * RealGradient(7245.*eta*xi/2. + 11235.*eta/32. - 240975.*eta*xi*xi/32. + 48825.*eta*(xi*xi*xi)/16. - 12145.*xi/16. - 76545.*xi*eta*eta/16. + 14175.*xi*(eta*eta*eta)/8. + 695./128. - 127575.*eta*eta/64. + 382725.*(eta*eta)*(xi*xi)/64. + 136185.*(xi*xi)/64. + 104895.*(eta*eta*eta)/32. - 6825.*xi*xi*xi/4. - 212625.*eta*eta*eta*eta/128. + 19425.*(xi*xi*xi*xi)/64., 2835.*eta*xi/32. + 25515.*eta*(xi*xi)/8. - 127575.*eta*xi*xi*xi/32. + 3045.*xi/32. - 42525.*xi*eta*eta/32. + 42525.*xi*(eta*eta*eta)/32. - 42525.*eta*eta*xi*xi/32. - 39375.*xi*xi/32. + 84105.*(xi*xi*xi)/32. - 48825.*xi*xi*xi*xi/32.);
                      case 2:
                        return sign * RealGradient(1680.*eta*xi - 175.*eta/2. + 945.*eta*(xi*xi)/2. - 1575.*eta*xi*xi*xi - 4725.*xi*eta*eta + 3150.*xi*(eta*eta*eta) + 55./8. + 105.*(eta*eta)/4. + 4725.*(eta*eta)*(xi*xi)/4. - 3255.*xi*xi/4. + 735.*(eta*eta*eta)/2. + 1260.*(xi*xi*xi) - 2625.*eta*eta*eta*eta/8. - 1575.*xi*xi*xi*xi/4., -525.*eta*xi/2. + 1890.*eta*(xi*xi) - 1575.*eta*xi*xi*xi/2. + 35.*xi/2. + 315.*xi*(eta*eta)/2. + 525.*xi*(eta*eta*eta)/2. - 4725.*eta*eta*xi*xi/2. + 105.*(xi*xi)/2. - 1575.*xi*xi*xi/2. + 1575.*(xi*xi*xi*xi)/2.);
                      case 3:
                        return sign * RealGradient(-1155.*eta*xi/2. + 595.*eta/32. + 76545.*eta*(xi*xi)/32. - 9975.*eta*xi*xi*xi/16. + 1855.*xi/16. - 945.*xi*eta*eta/16. + 5775.*xi*(eta*eta*eta)/8. - 825./128. + 1785.*(eta*eta)/64. - 146475.*eta*eta*xi*xi/64. - 16695.*xi*xi/64. - 945.*eta*eta*eta/32. - 945.*xi*xi*xi/4. - 2625.*eta*eta*eta*eta/128. + 19425.*(xi*xi*xi*xi)/64., 1155.*eta*xi/32. - 4725.*eta*xi*xi/8. + 48825.*eta*(xi*xi*xi)/32. - 875.*xi/32. + 2835.*xi*(eta*eta)/32. + 525.*xi*(eta*eta*eta)/32. - 17325.*eta*eta*xi*xi/32. + 9345.*(xi*xi)/32. - 21735.*xi*xi*xi/32. + 9975.*(xi*xi*xi*xi)/32.);
                      case 4:
                        return sign * RealGradient(140.*xi - 5. - 840.*xi*xi + 1680.*(xi*xi*xi) - 1050.*xi*xi*xi*xi, 0.);
                      case 5:
                        return sign * RealGradient(140.*xi - 5. - 840.*xi*xi + 1680.*(xi*xi*xi) - 1050.*xi*xi*xi*xi, 0.);
                      case 6:
                        return sign * RealGradient(-1575.*eta*xi + 385.*eta/4. + 76545.*eta*(xi*xi)/16. - 14175.*eta*xi*xi*xi/4. + 735.*xi/4. + 36855.*xi*(eta*eta)/16. - 1575.*xi*eta*eta*eta/2. - 10. - 735.*eta*eta/4. - 127575.*eta*eta*xi*xi/32. - 2835.*xi*xi/4. + 1785.*(eta*eta*eta)/16. + 14175.*(xi*xi*xi)/16. - 2625.*eta*eta*eta*eta/128. - 42525.*xi*xi*xi*xi/128., 525.*eta*xi/2. - 31185.*eta*xi*xi/16. + 42525.*eta*(xi*xi*xi)/16. - 455.*xi/4. - 2205.*xi*eta*eta/16. + 525.*xi*(eta*eta*eta)/32. + 4725.*(eta*eta)*(xi*xi)/8. + 2205.*(xi*xi)/2. - 42525.*xi*xi*xi/16. + 14175.*(xi*xi*xi*xi)/8.);
                      case 7:
                        return sign * RealGradient(-2520.*eta*xi + 245.*eta + 4725.*eta*(xi*xi) - 2100.*eta*xi*xi*xi + 175.*xi + 6615.*xi*(eta*eta) - 4200.*xi*eta*eta*eta - 15. - 840.*eta*eta - 14175.*eta*eta*xi*xi/2. - 420.*xi*xi + 945.*(eta*eta*eta) + 315.*(xi*xi*xi) - 2625.*eta*eta*eta*eta/8. - 525.*xi*xi*xi*xi/8., 840.*eta*xi - 4725.*eta*xi*xi + 4725.*eta*(xi*xi*xi) - 175.*xi - 945.*xi*eta*eta + 525.*xi*(eta*eta*eta)/2. + 3150.*(eta*eta)*(xi*xi) + 1260.*(xi*xi) - 2205.*xi*xi*xi + 1050.*(xi*xi*xi*xi));
                      case 8:
                        return sign * RealGradient(-2205.*eta*xi + 1785.*eta/4. + 31185.*eta*(xi*xi)/16. - 1575.*eta*xi*xi*xi/4. + 455.*xi/4. + 127575.*xi*(eta*eta)/16. - 14175.*xi*eta*eta*eta/2. - 20. - 8505.*eta*eta/4. - 127575.*eta*eta*xi*xi/32. - 525.*xi*xi/4. + 53865.*(eta*eta*eta)/16. + 735.*(xi*xi*xi)/16. - 212625.*eta*eta*eta*eta/128. - 525.*xi*xi*xi*xi/128., 2835.*eta*xi/2. - 76545.*eta*xi*xi/16. + 42525.*eta*(xi*xi*xi)/16. - 735.*xi/4. - 42525.*xi*eta*eta/16. + 42525.*xi*(eta*eta*eta)/32. + 42525.*(eta*eta)*(xi*xi)/8. + 1575.*(xi*xi)/2. - 12285.*xi*xi*xi/16. + 1575.*(xi*xi*xi*xi)/8.);
                      case 9:
                        return sign * RealGradient(700.*eta - 25. - 4200.*eta*eta + 8400.*(eta*eta*eta) - 5250.*eta*eta*eta*eta, 1680.*eta*xi - 140.*xi - 5040.*xi*eta*eta + 4200.*xi*(eta*eta*eta));
                      case 10:
                        return sign * RealGradient(700.*eta - 25. - 4200.*eta*eta + 8400.*(eta*eta*eta) - 5250.*eta*eta*eta*eta, 1680.*eta*xi - 1260.*eta - 140.*xi - 5040.*xi*eta*eta + 4200.*xi*(eta*eta*eta) + 120. + 3360.*(eta*eta) - 2520.*eta*eta*eta);
                      case 11:
                        return sign * RealGradient(-9345.*eta*xi/16. - 595.*eta/4. + 4725.*eta*(xi*xi)/8. + 5775.*eta*(xi*xi*xi)/16. + 875.*xi/32. + 65205.*xi*(eta*eta)/32. - 9975.*xi*eta*eta*eta/8. + 555./128. + 66465.*(eta*eta)/64. - 146475.*eta*eta*xi*xi/64. - 1155.*xi*xi/64. - 36855.*eta*eta*eta/16. - 945.*xi*xi*xi/32. + 97125.*(eta*eta*eta*eta)/64. - 525.*xi*xi*xi*xi/128., 16695.*eta*xi/32. + 9345.*eta/32. - 76545.*eta*xi*xi/32. + 48825.*eta*(xi*xi*xi)/32. - 1855.*xi/16. + 2835.*xi*(eta*eta)/4. - 19425.*xi*eta*eta*eta/16. - 705./32. - 29085.*eta*eta/32. + 29925.*(eta*eta)*(xi*xi)/32. + 1155.*(xi*xi)/4. + 11655.*(eta*eta*eta)/16. + 315.*(xi*xi*xi)/16. - 5775.*xi*xi*xi*xi/32.);
                      case 12:
                        return sign * RealGradient(-105.*eta*xi + 315.*eta - 1890.*eta*xi*xi + 1575.*eta*(xi*xi*xi) - 35.*xi/2. + 4725.*xi*(eta*eta)/2. - 3150.*xi*eta*eta*eta - 85./8. - 7455.*eta*eta/4. + 4725.*(eta*eta)*(xi*xi)/4. + 525.*(xi*xi)/4. + 3465.*(eta*eta*eta) - 105.*xi*xi*xi/2. - 7875.*eta*eta*eta*eta/4. - 525.*xi*xi*xi*xi/8., 3255.*eta*xi/2. - 1155.*eta/2. - 945.*eta*xi*xi/2. - 1575.*eta*xi*xi*xi/2. - 3780.*xi*eta*eta + 1575.*xi*(eta*eta*eta) + 105./2. + 2835.*(eta*eta)/2. + 4725.*(eta*eta)*(xi*xi)/2. - 840.*xi*xi - 945.*eta*eta*eta + 1575.*(xi*xi*xi) - 1575.*xi*xi*xi*xi/2.);
                      case 13:
                        return sign * RealGradient(39375.*eta*xi/16. - 1715.*eta/4. - 25515.*eta*xi*xi/8. + 14175.*eta*(xi*xi*xi)/16. - 3045.*xi/32. - 252315.*xi*eta*eta/32. + 48825.*xi*(eta*eta*eta)/8. + 2395./128. + 125265.*(eta*eta)/64. + 382725.*(eta*eta)*(xi*xi)/64. - 2835.*xi*xi/64. - 48615.*eta*eta*eta/16. + 14175.*(xi*xi*xi)/32. + 97125.*(eta*eta*eta*eta)/64. - 42525.*xi*xi*xi*xi/128., -136185.*eta*xi/32. + 21105.*eta/32. + 240975.*eta*(xi*xi)/32. - 127575.*eta*xi*xi*xi/32. + 12145.*xi/16. + 20475.*xi*(eta*eta)/4. - 19425.*xi*eta*eta*eta/16. - 2865./32. - 40845.*eta*eta/32. - 146475.*eta*eta*xi*xi/32. - 7245.*xi*xi/4. + 11655.*(eta*eta*eta)/16. + 25515.*(xi*xi*xi)/16. - 14175.*xi*xi*xi*xi/32.);
                      case 14:
                        return sign * RealGradient(-8400.*eta*xi + 1400.*eta + 15120.*eta*(xi*xi) - 8400.*eta*xi*xi*xi + 700.*xi + 22680.*xi*(eta*eta) - 16800.*xi*eta*eta*eta - 75. - 6300.*eta*eta - 18900.*eta*eta*xi*xi - 2100.*xi*xi + 10080.*(eta*eta*eta) + 2520.*(xi*xi*xi) - 5250.*eta*eta*eta*eta - 1050.*xi*xi*xi*xi, 12600.*eta*xi - 2100.*eta - 22680.*eta*xi*xi + 12600.*eta*(xi*xi*xi) - 2800.*xi - 15120.*xi*eta*eta + 4200.*xi*(eta*eta*eta) + 300. + 4200.*(eta*eta) + 12600.*(eta*eta)*(xi*xi) + 8400.*(xi*xi) - 2520.*eta*eta*eta - 10080.*xi*xi*xi + 4200.*(xi*xi*xi*xi));
                      case 15:
                        return RealGradient(188160.*eta*xi - 49000.*eta - 211680.*eta*xi*xi + 67200.*eta*(xi*xi*xi) - 19600.*xi - 423360.*xi*eta*eta + 268800.*xi*(eta*eta*eta) + 3500. + 176400.*(eta*eta) + 226800.*(eta*eta)*(xi*xi) + 35280.*(xi*xi) - 235200.*eta*eta*eta - 23520.*xi*xi*xi + 105000.*(eta*eta*eta*eta) + 4200.*(xi*xi*xi*xi), -70560.*eta*xi + 211680.*eta*(xi*xi) - 151200.*eta*xi*xi*xi + 9800.*xi + 141120.*xi*(eta*eta) - 84000.*xi*eta*eta*eta - 201600.*eta*eta*xi*xi - 47040.*xi*xi + 70560.*(xi*xi*xi) - 33600.*xi*xi*xi*xi);
                      case 16:
                        return RealGradient(-94080.*eta*xi + 9800.*eta + 211680.*eta*(xi*xi) - 134400.*eta*xi*xi*xi + 9800.*xi + 211680.*xi*(eta*eta) - 134400.*xi*eta*eta*eta - 700. - 35280.*eta*eta - 226800.*eta*eta*xi*xi - 35280.*xi*xi + 47040.*(eta*eta*eta) + 47040.*(xi*xi*xi) - 21000.*eta*eta*eta*eta - 21000.*xi*xi*xi*xi, 70560.*eta*xi - 211680.*eta*xi*xi + 151200.*eta*(xi*xi*xi) - 19600.*xi - 70560.*xi*eta*eta + 16800.*xi*(eta*eta*eta) + 100800.*(eta*eta)*(xi*xi) + 94080.*(xi*xi) - 141120.*xi*xi*xi + 67200.*(xi*xi*xi*xi));
                      case 17:
                        return RealGradient(-13440.*eta*xi + 560.*eta + 60480.*eta*(xi*xi) - 67200.*eta*xi*xi*xi + 6440.*xi - 280. - 30240.*xi*xi + 43680.*(xi*xi*xi) - 16800.*xi*xi*xi*xi, -1120.*xi + 13440.*(xi*xi) - 40320.*xi*xi*xi + 33600.*(xi*xi*xi*xi));
                      case 18:
                        return RealGradient(6720.*eta*xi - 280.*eta - 30240.*eta*xi*xi + 33600.*eta*(xi*xi*xi) - 3640.*xi + 140. + 20160.*(xi*xi) - 36960.*xi*xi*xi + 21000.*(xi*xi*xi*xi), 560.*xi - 6720.*xi*xi + 20160.*(xi*xi*xi) - 16800.*xi*xi*xi*xi);
                      case 19:
                        return RealGradient(-13440.*eta*xi + 18200.*eta + 560.*xi + 60480.*xi*(eta*eta) - 67200.*xi*eta*eta*eta - 700. - 100800.*eta*eta + 184800.*(eta*eta*eta) - 105000.*eta*eta*eta*eta, 40320.*eta*xi - 30240.*eta*xi*xi - 3640.*xi - 110880.*xi*eta*eta + 84000.*xi*(eta*eta*eta) + 50400.*(eta*eta)*(xi*xi) + 3360.*(xi*xi));
                      case 20:
                        return RealGradient(26880.*eta*xi - 14560.*eta - 1120.*xi - 120960.*xi*eta*eta + 134400.*xi*(eta*eta*eta) + 560. + 80640.*(eta*eta) - 147840.*eta*eta*eta + 84000.*(eta*eta*eta*eta), -60480.*eta*xi + 60480.*eta*(xi*xi) + 6440.*xi + 131040.*xi*(eta*eta) - 67200.*xi*eta*eta*eta - 100800.*eta*eta*xi*xi - 6720.*xi*xi);
                      case 21:
                        return RealGradient(-58240.*eta*xi + 14840.*eta/3. + 125440.*eta*(xi*xi) - 582400.*eta*xi*xi*xi/9. + 17920.*xi/3. + 116480.*xi*(eta*eta) - 560000.*xi*eta*eta*eta/9. - 420. - 13440.*eta*eta - 134400.*eta*eta*xi*xi - 17920.*xi*xi + 115360.*(eta*eta*eta)/9. + 156800.*(xi*xi*xi)/9. - 35000.*eta*eta*eta*eta/9. - 44800.*xi*xi*xi*xi/9., 13440.*eta*xi - 81760.*eta*xi*xi + 89600.*eta*(xi*xi*xi) - 10360.*xi/3. - 39200.*xi*eta*eta/3. + 28000.*xi*(eta*eta*eta)/9. + 140000.*(eta*eta)*(xi*xi)/3. + 28000.*(xi*xi) - 170240.*xi*xi*xi/3. + 291200.*(xi*xi*xi*xi)/9.);
                      case 22:
                        return RealGradient(44800.*eta*xi - 10640.*eta/3. - 109760.*eta*xi*xi + 627200.*eta*(xi*xi*xi)/9. - 12880.*xi/3. - 91840.*xi*eta*eta + 448000.*xi*(eta*eta*eta)/9. + 280. + 10080.*(eta*eta) + 117600.*(eta*eta)*(xi*xi) + 14560.*(xi*xi) - 89600.*eta*eta*eta/9. - 152320.*xi*xi*xi/9. + 28000.*(eta*eta*eta*eta)/9. + 56000.*(xi*xi*xi*xi)/9., -13440.*eta*xi + 76160.*eta*(xi*xi) - 78400.*eta*xi*xi*xi + 12040.*xi/3. + 34720.*xi*(eta*eta)/3. - 22400.*xi*eta*eta*eta/9. - 112000.*eta*eta*xi*xi/3. - 31360.*xi*xi + 185920.*(xi*xi*xi)/3. - 313600.*xi*xi*xi*xi/9.);
                      case 23:
                        return RealGradient(-62720.*eta*xi + 32480.*eta/3. + 76160.*eta*(xi*xi) - 224000.*eta*xi*xi*xi/9. + 12040.*xi/3. + 185920.*xi*(eta*eta) - 1254400.*xi*eta*eta*eta/9. - 560. - 45920.*eta*eta - 117600.*eta*eta*xi*xi - 6720.*xi*xi + 600320.*(eta*eta*eta)/9. + 34720.*(xi*xi*xi)/9. - 280000.*eta*eta*eta*eta/9. - 5600.*xi*xi*xi*xi/9., 29120.*eta*xi - 109760.*eta*xi*xi + 78400.*eta*(xi*xi*xi) - 12880.*xi/3. - 152320.*xi*eta*eta/3. + 224000.*xi*(eta*eta*eta)/9. + 313600.*(eta*eta)*(xi*xi)/3. + 22400.*(xi*xi) - 91840.*xi*xi*xi/3. + 112000.*(xi*xi*xi*xi)/9.);
                      case 24:
                        return RealGradient(56000.*eta*xi - 24920.*eta/3. - 81760.*eta*xi*xi + 280000.*eta*(xi*xi*xi)/9. - 10360.*xi/3. - 170240.*xi*eta*eta + 1164800.*xi*(eta*eta*eta)/9. + 420. + 35840.*(eta*eta) + 134400.*(eta*eta)*(xi*xi) + 6720.*(xi*xi) - 474880.*eta*eta*eta/9. - 39200.*xi*xi*xi/9. + 224000.*(eta*eta*eta*eta)/9. + 7000.*(xi*xi*xi*xi)/9., -35840.*eta*xi + 125440.*eta*(xi*xi) - 89600.*eta*xi*xi*xi + 17920.*xi/3. + 156800.*xi*(eta*eta)/3. - 179200.*xi*eta*eta*eta/9. - 291200.*eta*eta*xi*xi/3. - 29120.*xi*xi + 116480.*(xi*xi*xi)/3. - 140000.*xi*xi*xi*xi/9.);
                      case 25:
                        return RealGradient(-31360.*eta*xi/3. + 51800.*eta/9. - 2240.*eta*xi*xi + 44800.*eta*(xi*xi*xi)/9. - 12880.*xi/9. + 51520.*xi*(eta*eta) - 380800.*xi*eta*eta*eta/9. - 700./9. - 28000.*eta*eta - 16800.*eta*eta*xi*xi + 5600.*(xi*xi) + 375200.*(eta*eta*eta)/9. - 49280.*xi*xi*xi/9. - 175000.*eta*eta*eta*eta/9. + 11200.*(xi*xi*xi*xi)/9., 11200.*eta*xi - 25760.*eta*xi*xi + 11200.*eta*(xi*xi*xi) - 10360.*xi/9. - 75040.*xi*eta*eta/3. + 140000.*xi*(eta*eta*eta)/9. + 95200.*(eta*eta)*(xi*xi)/3. + 7840.*(xi*xi)/3. + 2240.*(xi*xi*xi)/3. - 22400.*xi*xi*xi*xi/9.);
                      case 26:
                        return RealGradient(89600.*eta*xi/3. - 29680.*eta/9. - 51520.*eta*xi*xi + 179200.*eta*(xi*xi*xi)/9. - 9520.*xi/9. - 82880.*xi*eta*eta + 492800.*xi*(eta*eta*eta)/9. + 1400./9. + 12320.*(eta*eta) + 84000.*(eta*eta)*(xi*xi) - 1120.*xi*xi - 138880.*eta*eta*eta/9. + 71680.*(xi*xi*xi)/9. + 56000.*(eta*eta*eta*eta)/9. - 56000.*xi*xi*xi*xi/9., -26880.*eta*xi + 80640.*eta*(xi*xi) - 56000.*eta*xi*xi*xi + 51800.*xi/9. + 79520.*xi*(eta*eta)/3. - 44800.*xi*eta*eta*eta/9. - 123200.*eta*eta*xi*xi/3. - 69440.*xi*xi/3. + 82880.*(xi*xi*xi)/3. - 89600.*xi*xi*xi*xi/9.);
                      case 27:
                        return RealGradient(-8960.*eta*xi/3. - 26600.*eta/9. + 12320.*eta*(xi*xi) - 44800.*eta*xi*xi*xi/9. + 2800.*xi/9. - 11200.*xi*eta*eta + 179200.*xi*(eta*eta*eta)/9. + 700./9. + 19600.*(eta*eta) - 8400.*eta*eta*xi*xi - 560.*xi*xi - 324800.*eta*eta*eta/9. - 1120.*xi*xi*xi/9. + 175000.*(eta*eta*eta*eta)/9. + 1400.*(xi*xi*xi*xi)/9., -7840.*eta*xi + 5600.*eta*(xi*xi) + 5600.*eta*(xi*xi*xi) + 5320.*xi/9. + 64960.*xi*(eta*eta)/3. - 140000.*xi*eta*eta*eta/9. - 44800.*eta*eta*xi*xi/3. + 2240.*(xi*xi)/3. - 12320.*xi*xi*xi/3. + 22400.*(xi*xi*xi*xi)/9.);
                      case 28:
                        return RealGradient(-22400.*eta*xi/3. + 27160.*eta/9. - 19040.*eta*xi*xi + 224000.*eta*(xi*xi*xi)/9. + 280.*xi/9. + 52640.*xi*(eta*eta) - 492800.*xi*eta*eta*eta/9. - 980./9. - 16240.*eta*eta - 8400.*eta*eta*xi*xi + 1680.*(xi*xi) + 239680.*(eta*eta*eta)/9. - 11200.*xi*xi*xi/9. - 119000.*eta*eta*eta*eta/9. - 7000.*xi*xi*xi*xi/9., 19040.*eta*xi - 30240.*eta*xi*xi + 5600.*eta*(xi*xi*xi) - 8960.*xi/9. - 99680.*xi*eta*eta/3. + 95200.*xi*(eta*eta*eta)/9. + 123200.*(eta*eta)*(xi*xi)/3. - 17920.*xi*xi/3. + 58240.*(xi*xi*xi)/3. - 112000.*xi*xi*xi*xi/9.);
                      case 29:
                        return RealGradient(-138880.*eta*xi/3. - 48160.*eta/9. + 80640.*eta*(xi*xi) - 246400.*eta*xi*xi*xi/9. + 51800.*xi/9. + 82880.*xi*(eta*eta) - 358400.*xi*eta*eta*eta/9. + 560./9. + 32480.*(eta*eta) - 84000.*eta*eta*xi*xi - 13440.*xi*xi - 519680.*eta*eta*eta/9. + 79520.*(xi*xi*xi)/9. + 280000.*(eta*eta*eta*eta)/9. - 11200.*xi*xi*xi*xi/9., -2240.*eta*xi - 51520.*eta*xi*xi + 56000.*eta*(xi*xi*xi) - 9520.*xi/9. + 71680.*xi*(eta*eta)/3. - 224000.*xi*eta*eta*eta/9. + 89600.*(eta*eta)*(xi*xi)/3. + 44800.*(xi*xi)/3. - 82880.*xi*xi*xi/3. + 123200.*(xi*xi*xi*xi)/9.);
                      case 30:
                        return RealGradient(15680.*eta*xi/3. + 6440.*eta/9. - 25760.*eta*xi*xi + 190400.*eta*(xi*xi*xi)/9. - 10360.*xi/9. + 2240.*xi*(eta*eta) - 89600.*xi*eta*eta*eta/9. + 140./9. - 5600.*eta*eta + 16800.*(eta*eta)*(xi*xi) + 5600.*(xi*xi) + 98560.*(eta*eta*eta)/9. - 75040.*xi*xi*xi/9. - 56000.*eta*eta*eta*eta/9. + 35000.*(xi*xi*xi*xi)/9., 11200.*eta*xi - 2240.*eta*xi*xi - 11200.*eta*xi*xi*xi - 12880.*xi/9. - 49280.*xi*eta*eta/3. + 44800.*xi*(eta*eta*eta)/9. + 22400.*(eta*eta)*(xi*xi)/3. - 15680.*xi*xi/3. + 51520.*(xi*xi*xi)/3. - 95200.*xi*xi*xi*xi/9.);
                      case 31:
                        return RealGradient(-35840.*eta*xi/3. + 8680.*eta/9. - 30240.*eta*xi*xi + 246400.*eta*(xi*xi*xi)/9. - 8960.*xi/9. + 58240.*xi*(eta*eta) - 448000.*xi*eta*eta*eta/9. - 140./9. - 1680.*eta*eta + 8400.*(eta*eta)*(xi*xi) + 9520.*(xi*xi) - 24640.*eta*eta*eta/9. - 99680.*xi*xi*xi/9. + 35000.*(eta*eta*eta*eta)/9. + 23800.*(xi*xi*xi*xi)/9., 3360.*eta*xi - 19040.*eta*xi*xi - 5600.*eta*xi*xi*xi + 280.*xi/9. - 11200.*xi*eta*eta/3. - 28000.*xi*eta*eta*eta/9. + 112000.*(eta*eta)*(xi*xi)/3. - 11200.*xi*xi/3. + 52640.*(xi*xi*xi)/3. - 123200.*xi*xi*xi*xi/9.);
                      case 32:
                        return RealGradient(4480.*eta*xi/3. - 1400.*eta/9. + 5600.*eta*(xi*xi) - 89600.*eta*xi*xi*xi/9. + 5320.*xi/9. - 12320.*xi*eta*eta + 89600.*xi*(eta*eta*eta)/9. - 140./9. + 560.*(eta*eta) + 8400.*(eta*eta)*(xi*xi) - 3920.*xi*xi + 2240.*(eta*eta*eta)/9. + 64960.*(xi*xi*xi)/9. - 7000.*eta*eta*eta*eta/9. - 35000.*xi*xi*xi*xi/9., -1120.*eta*xi + 12320.*eta*(xi*xi) - 5600.*eta*xi*xi*xi + 2800.*xi/9. - 1120.*xi*eta*eta/3. + 5600.*xi*(eta*eta*eta)/9. - 22400.*eta*eta*xi*xi/3. - 4480.*xi*xi/3. - 11200.*xi*xi*xi/3. + 44800.*(xi*xi*xi*xi)/9.);
                      case 33:
                        return RealGradient(38080.*eta*xi/3. - 5600.*eta/9. - 19040.*eta*xi*xi + 22400.*eta*(xi*xi*xi)/3. - 6440.*xi/9. - 33600.*xi*eta*eta + 22400.*xi*(eta*eta*eta) + 280./9. + 1680.*(eta*eta) + 25200.*(eta*eta)*(xi*xi) + 1680.*(xi*xi) - 1120.*eta*eta*eta - 4480.*xi*xi*xi/3. + 1400.*(xi*xi*xi*xi)/3., -3360.*eta*xi + 20160.*eta*(xi*xi) - 16800.*eta*xi*xi*xi + 6160.*xi/9. + 3360.*xi*(eta*eta) - 16800.*eta*eta*xi*xi - 14560.*xi*xi/3. + 7840.*(xi*xi*xi) - 11200.*xi*xi*xi*xi/3.);
                      case 34:
                        return RealGradient(-29120.*eta*xi/3. + 9520.*eta/9. + 20160.*eta*(xi*xi) - 11200.*eta*xi*xi*xi + 6160.*xi/9. + 23520.*xi*(eta*eta) - 44800.*xi*eta*eta*eta/3. - 560./9. - 3920.*eta*eta - 25200.*eta*eta*xi*xi - 1680.*xi*xi + 15680.*(eta*eta*eta)/3. + 1120.*(xi*xi*xi) - 7000.*eta*eta*eta*eta/3., 3360.*eta*xi - 19040.*eta*xi*xi + 16800.*eta*(xi*xi*xi) - 6440.*xi/9. - 4480.*xi*eta*eta + 5600.*xi*(eta*eta*eta)/3. + 11200.*(eta*eta)*(xi*xi) + 19040.*(xi*xi)/3. - 11200.*xi*xi*xi + 5600.*(xi*xi*xi*xi));
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          } // end switch (type)
      } // end case FIFTH
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 2D FE order!: " << totalorder);
    }
#else // LIBMESH_DIM > 1
  libmesh_ignore(elem, order, i, j, add_p_level);
  libmesh_not_implemented();
#endif
}

shape_deriv() [77/233]

RealGradient libMesh::FE< 3, NEDELEC_ONE >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 158 of file fe_nedelec_one_shape_3D.C.

{
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
  libmesh_assert_less (j, 3);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = elem->positive_edge_orientation(i) ? 1 : -1;
 
  const Real xi   = p(0);
  const Real eta  = p(1);
  const Real zeta = p(2);
 
  switch (totalorder)
    {
      // linear Nedelec (first kind) shape function first derivatives
    case FIRST:
      {
        switch (elem->type())
          {
          case HEX20:
          case HEX27:
            {
              // Even with a loose inverse_map tolerance we ought to
              // be nearly on the element interior in master
              // coordinates
              libmesh_assert_less_equal ( std::fabs(xi),   1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(eta),  1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(zeta), 1.0+10*TOLERANCE );
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(i)
                      {
                      case 0:
                      case 2:
                      case 8:
                      case 10:
                        return RealGradient();
                      case 1:
                        return sign * RealGradient( 0.0, -0.125*(1.0-zeta) );
                      case 3:
                        return sign * RealGradient( 0.0, -0.125*(-1.0+zeta) );
                      case 4:
                        return sign * RealGradient( 0.0, 0.0, -0.125*(-1.0+eta) );
                      case 5:
                        return sign * RealGradient( 0.0, 0.0, -0.125*(1.0-eta) );
                      case 6:
                        return sign * RealGradient( 0.0, 0.0, -0.125*(1.0+eta) );
                      case 7:
                        return sign * RealGradient( 0.0, 0.0, -0.125*(-1.0-eta) );
                      case 9:
                        return sign * RealGradient( 0.0, -0.125*(1.0+zeta), 0.0 );
                      case 11:
                        return sign * RealGradient( 0.0, -0.125*(-1.0-zeta), 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(i)
                      {
                      case 1:
                      case 3:
                      case 9:
                      case 11:
                        return RealGradient();
                      case 0:
                        return sign * RealGradient( -0.125*(-1.0+zeta), 0.0, 0.0 );
                      case 2:
                        return sign * RealGradient( 0.125*(1.0-zeta), 0.0, 0.0 );
                      case 4:
                        return sign * RealGradient( 0.0, 0.0, -0.125*(-1.0+xi) );
                      case 5:
                        return sign * RealGradient( 0.0, 0.0, -0.125*(-1.0-xi) );
                      case 6:
                        return sign * RealGradient( 0.0, 0.0, -0.125*(1.0+xi) );
                      case 7:
                        return sign * RealGradient( 0.0, 0.0, -0.125*(1.0-xi) );
                      case 8:
                        return sign * RealGradient( -0.125*(-1.0-zeta), 0.0, 0.0 );
                      case 10:
                        return sign * RealGradient( 0.125*(1.0+zeta), 0.0, 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 1
 
                  // d()/dzeta
                case 2:
                  {
                    switch(i)
                      {
                      case 4:
                      case 5:
                      case 6:
                      case 7:
                        return RealGradient();
                      case 0:
                        return sign * RealGradient( -0.125*(-1.0+eta), 0.0, 0.0 );
                      case 1:
                        return sign * RealGradient( 0.0, -0.125*(-1.0-xi), 0.0 );
                      case 2:
                        return sign * RealGradient( 0.125*(-1.0-eta), 0.0, 0.0 );
                      case 3:
                        return sign * RealGradient( 0.0, -0.125*(-1.0+xi), 0.0 );
                      case 8:
                        return sign * RealGradient( -0.125*(1.0-eta), 0.0, 0.0 );
                      case 9:
                        return sign * RealGradient( 0.0, -0.125*(1.0+xi), 0.0 );
                      case 10:
                        return sign * RealGradient( 0.125*(1.0+eta), 0.0, 0.0 );
                      case 11:
                        return sign * RealGradient( 0.0, -0.125*(1.0-xi), 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TET10:
          case TET14:
            {
              switch (j)
                {
                  // d()/dxi
                case 0:
                  {
                    switch(i)
                      {
                      case 0:
                        return sign * RealGradient( 0.0, -1.0, -1.0 );
                      case 1:
                        return sign * RealGradient( 0.0, -1.0, 0.0 );
                      case 2:
                        return sign * RealGradient( 0.0, 1.0, 0.0 );
                      case 3:
                        return sign * RealGradient( 0.0, 0.0, 1.0 );
                      case 4:
                        return sign * RealGradient( 0.0, 0.0, -1.0 );
                      case 5:
                        return RealGradient();
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 0
 
                  // d()/deta
                case 1:
                  {
                    switch(i)
                      {
                      case 0:
                      case 1:
                        return sign * RealGradient( 1.0, 0.0, 0.0 );
                      case 2:
                        return sign * RealGradient( -1.0, 0.0, -1.0 );
                      case 3:
                        return sign * RealGradient( 0.0, 0.0, 1.0 );
                      case 4:
                        return RealGradient();
                      case 5:
                        return sign * RealGradient( 0.0, 0.0, -1.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 1
 
                  // d()/dzeta
                case 2:
                  {
                    switch(i)
                      {
                        case 0:
                          return sign * RealGradient( 1.0, 0.0, 0.0 );
                        case 1:
                          return RealGradient();
                        case 2:
                        case 5:
                          return sign * RealGradient( 0.0, 1.0, 0.0 );
                        case 3:
                          return sign * RealGradient( -1.0, -1.0, 0.0 );
                        case 4:
                          return sign * RealGradient( 1.0, 0.0, 0.0 );
 
                        default:
                          libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
          }
      }
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, j, p, add_p_level);
  libmesh_not_implemented();
#endif
}

shape_deriv() [78/233]

Real libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 84 of file fe_rational_shape_1D.C.

{
  libmesh_assert(elem);
 
  FEType underlying_fe_type(order, _underlying_fe_family);
 
  return rational_fe_shape_deriv(*elem, underlying_fe_type, i, j, p,
                                 add_p_level);
}

shape_deriv() [79/233]

Real libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 83 of file fe_rational_shape_2D.C.

{
  libmesh_assert(elem);
 
  FEType underlying_fe_type(order, _underlying_fe_family);
 
  return rational_fe_shape_deriv(*elem, underlying_fe_type, i, j, p,
                                 add_p_level);
}

shape_deriv() [80/233]

Real libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 81 of file fe_rational_shape_3D.C.

{
  libmesh_assert(elem);
 
  FEType underlying_fe_type(order, _underlying_fe_family);
 
  return rational_fe_shape_deriv(*elem, underlying_fe_type, i, j, p,
                                 add_p_level);
}

shape_deriv() [81/233]

RealGradient libMesh::FE< 2, RAVIART_THOMAS >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 91 of file fe_raviart_shape_2D.C.

{
  RealGradient ND1 = FE<2,NEDELEC_ONE>::shape_deriv(elem, order, i, j, p, add_p_level);
  return RealGradient(-ND1(1), ND1(0));
}

shape_deriv() [82/233]

RealGradient libMesh::FE< 2, L2_RAVIART_THOMAS >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 103 of file fe_raviart_shape_2D.C.

{
  return FE<2,RAVIART_THOMAS>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [83/233]

RealGradient libMesh::FE< 3, L2_RAVIART_THOMAS >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 342 of file fe_raviart_shape_3D.C.

{
  return FE<3,RAVIART_THOMAS>::shape_deriv(elem, order, i, j, p, add_p_level);
}

shape_deriv() [84/233]

Real libMesh::FE< 2, SUBDIVISION >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 789 of file fe_subdivision_2D.C.

{
  libmesh_assert(elem);
  const Order totalorder = order + add_p_level*elem->p_level();
  return FE<2,SUBDIVISION>::shape_deriv(elem->type(), totalorder, i, j, p);
}

shape_deriv() [85/233]

Real libMesh::FE< 1, SZABAB >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 156 of file fe_szabab_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape_deriv(elem->type(),
                                   order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [86/233]

Real libMesh::FE< 2, SZABAB >::shape_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 670 of file fe_szabab_shape_2D.C.

{
  libmesh_assert(elem);
 
  const ElemType type = elem->type();
 
  const Order totalorder = order + add_p_level*elem->p_level();
 
  switch (totalorder)
    {
 
      // 1st & 2nd-order Szabo-Babuska.
    case FIRST:
    case SECOND:
      {
        switch (type)
          {
 
            // Szabo-Babuska shape functions on the triangle.
          case TRI3:
          case TRI6:
          case TRI7:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<2,SZABAB>::shape);
            }
 
 
            // Szabo-Babuska shape functions on the quadrilateral.
          case QUAD4:
          case QUAD8:
          case QUAD9:
            {
              // Compute quad shape functions as a tensor-product
              const Real xi  = p(0);
              const Real eta = p(1);
 
              libmesh_assert_less (i, 9);
 
              //                                0  1  2  3  4  5  6  7  8
              static const unsigned int i0[] = {0, 1, 1, 0, 2, 1, 2, 0, 2};
              static const unsigned int i1[] = {0, 0, 1, 1, 0, 2, 1, 2, 2};
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return (FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi)*
                          FE<1,SZABAB>::shape      (EDGE3, totalorder, i1[i],    eta));
 
                  // d()/deta
                case 1:
                  return (FE<1,SZABAB>::shape      (EDGE3, totalorder, i0[i],    xi)*
                          FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta));
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
 
 
      // 3rd-order Szabo-Babuska.
    case THIRD:
      {
        switch (type)
          {
            // Szabo-Babuska shape functions on the triangle.
          case TRI6:
          case TRI7:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<2,SZABAB>::shape);
            }
 
 
            // Szabo-Babuska shape functions on the quadrilateral.
          case QUAD8:
          case QUAD9:
            {
              // Compute quad shape functions as a tensor-product
              const Real xi  = p(0);
              const Real eta = p(1);
 
              libmesh_assert_less (i, 16);
 
              //                                0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
              static const unsigned int i0[] = {0,  1,  1,  0,  2,  3,  1,  1,  2,  3,  0,  0,  2,  3,  2,  3};
              static const unsigned int i1[] = {0,  0,  1,  1,  0,  0,  2,  3,  1,  1,  2,  3,  2,  2,  3,  3};
 
              const Real f = quad_flip(elem, totalorder, i);
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return f*(FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi)*
                            FE<1,SZABAB>::shape      (EDGE3, totalorder, i1[i],    eta));
 
                  // d()/deta
                case 1:
                  return f*(FE<1,SZABAB>::shape      (EDGE3, totalorder, i0[i],    xi)*
                            FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta));
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
 
 
 
      // 4th-order Szabo-Babuska.
    case FOURTH:
      {
        switch (type)
          {
 
            // Szabo-Babuska shape functions on the triangle.
          case TRI6:
          case TRI7:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<2,SZABAB>::shape);
            }
 
 
            // Szabo-Babuska shape functions on the quadrilateral.
          case QUAD8:
          case QUAD9:
            {
              // Compute quad shape functions as a tensor-product
              const Real xi  = p(0);
              const Real eta = p(1);
 
              libmesh_assert_less (i, 25);
 
              //                                0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
              static const unsigned int i0[] = {0, 1, 1, 0, 2, 3, 4, 1, 1, 1, 2, 3, 4, 0, 0, 0, 2, 3, 4, 2, 3, 4, 2, 3, 4};
              static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 0, 2, 3, 4, 1, 1, 1, 2, 3, 4, 2, 2, 2, 3, 3, 3, 4, 4, 4};
 
              const Real f = quad_flip(elem, totalorder, i);
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return f*(FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi)*
                            FE<1,SZABAB>::shape      (EDGE3, totalorder, i1[i],    eta));
 
                  // d()/deta
                case 1:
                  return f*(FE<1,SZABAB>::shape      (EDGE3, totalorder, i0[i],    xi)*
                            FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta));
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
 
 
 
      // 5th-order Szabo-Babuska.
    case FIFTH:
      {
        // Szabo-Babuska shape functions on the quadrilateral.
        switch (type)
          {
 
            // Szabo-Babuska shape functions on the triangle.
          case TRI6:
          case TRI7:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<2,SZABAB>::shape);
            }
 
 
          case QUAD8:
          case QUAD9:
            {
              // Compute quad shape functions as a tensor-product
              const Real xi  = p(0);
              const Real eta = p(1);
 
              libmesh_assert_less (i, 36);
 
              //                                0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
              static const unsigned int i0[] = {0, 1, 1, 0, 2, 3, 4, 5, 1, 1, 1, 1, 2, 3, 4, 5, 0, 0, 0, 0, 2, 3, 4, 5, 2, 3, 4, 5, 2, 3, 4, 5, 2, 3, 4, 5};
              static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 0, 0, 2, 3, 4, 5, 1, 1, 1, 1, 2, 3, 4, 5, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5};
 
              const Real f = quad_flip(elem, totalorder, i);
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return f*(FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi)*
                            FE<1,SZABAB>::shape      (EDGE3, totalorder, i1[i],    eta));
 
                  // d()/deta
                case 1:
                  return f*(FE<1,SZABAB>::shape      (EDGE3, totalorder, i0[i],    xi)*
                            FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta));
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
 
      // 6th-order Szabo-Babuska.
    case SIXTH:
      {
        // Szabo-Babuska shape functions on the quadrilateral.
        switch (type)
          {
 
            // Szabo-Babuska shape functions on the triangle.
          case TRI6:
          case TRI7:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<2,SZABAB>::shape);
            }
 
 
          case QUAD8:
          case QUAD9:
            {
              // Compute quad shape functions as a tensor-product
              const Real xi  = p(0);
              const Real eta = p(1);
 
              libmesh_assert_less (i, 49);
 
              //                                0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
              static const unsigned int i0[] = {0, 1, 1, 0, 2, 3, 4, 5, 6, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 0, 0, 0, 0, 0, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6};
              static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 3, 4, 5, 6, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6};
 
              const Real f = quad_flip(elem, totalorder, i);
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return f*(FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi)*
                            FE<1,SZABAB>::shape      (EDGE3, totalorder, i1[i],    eta));
 
                  // d()/deta
                case 1:
                  return f*(FE<1,SZABAB>::shape      (EDGE3, totalorder, i0[i],    xi)*
                            FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta));
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
 
      // 7th-order Szabo-Babuska.
    case SEVENTH:
      {
        // Szabo-Babuska shape functions on the quadrilateral.
        switch (type)
          {
 
            // Szabo-Babuska shape functions on the triangle.
          case TRI6:
          case TRI7:
            {
              return fe_fdm_deriv(elem, order, i, j, p, add_p_level, FE<2,SZABAB>::shape);
            }
 
 
          case QUAD8:
          case QUAD9:
            {
              // Compute quad shape functions as a tensor-product
              const Real xi  = p(0);
              const Real eta = p(1);
 
              libmesh_assert_less (i, 64);
 
              //                                0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
              static const unsigned int i0[] = {0, 1, 1, 0, 2, 3, 4, 5, 6, 7, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 0, 0, 0, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7};
              static const unsigned int i1[] = {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2, 3, 4, 5, 6, 7, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7};
 
              const Real f = quad_flip(elem, totalorder, i);
 
              switch (j)
                {
                  // d()/dxi
                case 0:
                  return f*(FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i0[i], 0, xi)*
                            FE<1,SZABAB>::shape      (EDGE3, totalorder, i1[i],    eta));
 
                  // d()/deta
                case 1:
                  return f*(FE<1,SZABAB>::shape      (EDGE3, totalorder, i0[i],    xi)*
                            FE<1,SZABAB>::shape_deriv(EDGE3, totalorder, i1[i], 0, eta));
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
          }
      }
 
 
 
      // by default throw an error;call the orientation-independent shape functions
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order!");
    }
}

shape_deriv() [87/233]

Real libMesh::FE< 3, CLOUGH >::shape_deriv ( const Elem *  libmesh_dbg_varelem, const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 90 of file fe_clough_shape_3D.C.

{
  libmesh_assert(elem);
  libmesh_not_implemented();
  return 0.;
}

shape_deriv() [88/233]

Real libMesh::FE< 1, HIERARCHIC >::shape_deriv ( const ElemType  elem_type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 178 of file fe_hierarchic_shape_1D.C.

{
  return fe_hierarchic_1D_shape_deriv(elem_type, order, i, j, p);
}

shape_deriv() [89/233]

Real libMesh::FE< 1, L2_HIERARCHIC >::shape_deriv ( const ElemType  elem_type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 190 of file fe_hierarchic_shape_1D.C.

{
  return fe_hierarchic_1D_shape_deriv(elem_type, order, i, j, p);
}

shape_deriv() [90/233]

static OutputShape libMesh::FE< Dim, T >::shape_deriv ( const ElemType  t, const Order  o, const unsigned int  i, const unsigned int  j, const Point &  p  )

staticinherited

Returns

The \( j^{th} \) derivative of the \( i^{th} \) shape function at point p. This method allows you to specify the dimension, element type, and order directly.

On a p-refined element, o should be the total order of the element.

shape_deriv() [91/233]

RealGradient libMesh::FE< 0, HIERARCHIC_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 136 of file fe_hierarchic_vec.C.

{
  Real value = FE<0,HIERARCHIC>::shape_deriv( type, order, i, j, p );
  return libMesh::RealGradient( value );
}

shape_deriv() [92/233]

RealGradient libMesh::FE< 0, L2_HIERARCHIC_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 160 of file fe_hierarchic_vec.C.

{
  return FE<0,HIERARCHIC_VEC>::shape_deriv(type, order, i, j, p);
}

shape_deriv() [93/233]

RealGradient libMesh::FE< 1, HIERARCHIC_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 184 of file fe_hierarchic_vec.C.

{
  Real value = FE<1,HIERARCHIC>::shape_deriv( type, order, i, j, p );
  return libMesh::RealGradient( value );
}

shape_deriv() [94/233]

RealGradient libMesh::FE< 1, L2_HIERARCHIC_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 207 of file fe_hierarchic_vec.C.

{
  return FE<1,HIERARCHIC_VEC>::shape_deriv(type, order, i, j, p);
}

shape_deriv() [95/233]

RealGradient libMesh::FE< 2, HIERARCHIC_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 245 of file fe_hierarchic_vec.C.

{
  Real value = FE<2,HIERARCHIC>::shape_deriv( type, order, i/2, j, p );
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_deriv() [96/233]

RealGradient libMesh::FE< 2, L2_HIERARCHIC_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 298 of file fe_hierarchic_vec.C.

{
  return FE<2,HIERARCHIC_VEC>::shape_deriv(type, order, i, j, p);
}

shape_deriv() [97/233]

RealGradient libMesh::FE< 3, HIERARCHIC_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 339 of file fe_hierarchic_vec.C.

{
  Real value = FE<3,HIERARCHIC>::shape_deriv( type, order, i/3, j, p );
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_deriv() [98/233]

RealGradient libMesh::FE< 3, L2_HIERARCHIC_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 399 of file fe_hierarchic_vec.C.

{
  return FE<3,HIERARCHIC_VEC>::shape_deriv(type, order, i, j, p);
}

shape_deriv() [99/233]

Real libMesh::FE< 2, LAGRANGE >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 148 of file fe_lagrange_shape_2D.C.

{
  return fe_lagrange_2D_shape_deriv<LAGRANGE>(type, nullptr, order, i, j, p);
}

shape_deriv() [100/233]

Real libMesh::FE< 2, L2_LAGRANGE >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 160 of file fe_lagrange_shape_2D.C.

{
  return fe_lagrange_2D_shape_deriv<L2_LAGRANGE>(type, nullptr, order, i, j, p);
}

shape_deriv() [101/233]

Real libMesh::FE< 3, LAGRANGE >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 495 of file fe_lagrange_shape_3D.C.

{
  return fe_lagrange_3D_shape_deriv<LAGRANGE>(type, order, nullptr, i, j, p);
}

shape_deriv() [102/233]

Real libMesh::FE< 3, L2_LAGRANGE >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 507 of file fe_lagrange_shape_3D.C.

{
  return fe_lagrange_3D_shape_deriv<L2_LAGRANGE>(type, order, nullptr, i, j, p);
}

shape_deriv() [103/233]

RealGradient libMesh::FE< 0, LAGRANGE_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 676 of file fe_lagrange_vec.C.

{
  Real value = FE<0,LAGRANGE>::shape_deriv( type, order, i, j, p );
  return libMesh::RealGradient( value );
}

shape_deriv() [104/233]

RealGradient libMesh::FE< 0, L2_LAGRANGE_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 700 of file fe_lagrange_vec.C.

{
  return FE<0,LAGRANGE_VEC>::shape_deriv(type, order, i, j, p);
}

shape_deriv() [105/233]

RealGradient libMesh::FE< 1, LAGRANGE_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 724 of file fe_lagrange_vec.C.

{
  Real value = FE<1,LAGRANGE>::shape_deriv( type, order, i, j, p );
  return libMesh::RealGradient( value );
}

shape_deriv() [106/233]

RealGradient libMesh::FE< 1, L2_LAGRANGE_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 747 of file fe_lagrange_vec.C.

{
  return FE<1,LAGRANGE_VEC>::shape_deriv(type, order, i, j, p);
}

shape_deriv() [107/233]

RealGradient libMesh::FE< 2, LAGRANGE_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 785 of file fe_lagrange_vec.C.

{
  Real value = FE<2,LAGRANGE>::shape_deriv( type, order, i/2, j, p );
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_deriv() [108/233]

RealGradient libMesh::FE< 2, L2_LAGRANGE_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 838 of file fe_lagrange_vec.C.

{
  return FE<2,LAGRANGE_VEC>::shape_deriv(type, order, i, j, p);
}

shape_deriv() [109/233]

RealGradient libMesh::FE< 3, LAGRANGE_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 879 of file fe_lagrange_vec.C.

{
  Real value = FE<3,LAGRANGE>::shape_deriv( type, order, i/3, j, p );
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_deriv() [110/233]

RealGradient libMesh::FE< 3, L2_LAGRANGE_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 939 of file fe_lagrange_vec.C.

{
  return FE<3,LAGRANGE_VEC>::shape_deriv(type, order, i, j, p);
}

shape_deriv() [111/233]

RealVectorValue libMesh::FE< 0, MONOMIAL_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 158 of file fe_monomial_vec.C.

{
  Real value = FE<0, MONOMIAL>::shape_deriv(type, order, i, j, p);
  return libMesh::RealVectorValue(value);
}

shape_deriv() [112/233]

RealVectorValue libMesh::FE< 1, MONOMIAL_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 196 of file fe_monomial_vec.C.

{
  Real value = FE<1, MONOMIAL>::shape_deriv(type, order, i, j, p);
  return libMesh::RealVectorValue(value);
}

shape_deriv() [113/233]

RealVectorValue libMesh::FE< 2, MONOMIAL_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 247 of file fe_monomial_vec.C.

{
  Real value = FE<2, MONOMIAL>::shape_deriv(type, order, i / 2, j, p);
 
  switch (i % 2)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape_deriv() [114/233]

RealVectorValue libMesh::FE< 3, MONOMIAL_VEC >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 330 of file fe_monomial_vec.C.

{
  Real value = FE<3, MONOMIAL>::shape_deriv(type, order, i / 3, j, p);
 
  switch (i % 3)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    case 2:
      return libMesh::RealVectorValue(Real(0), Real(0), value);
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape_deriv() [115/233]

Real libMesh::FE< 2, SUBDIVISION >::shape_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 762 of file fe_subdivision_2D.C.

{
  switch (order)
    {
    case FOURTH:
      {
        switch (type)
          {
          case TRI3SUBDIVISION:
            libmesh_assert_less(i, 12);
            return FESubdivision::regular_shape_deriv(i,j,p(0),p(1));
          default:
            libmesh_error_msg("ERROR: Unsupported element type == " << Utility::enum_to_string(type));
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order == " << order);
    }
}

shape_deriv() [116/233]

Real libMesh::FE< 2, MONOMIAL >::shape_deriv ( const ElemType  , const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 150 of file fe_monomial_shape_2D.C.

{
#if LIBMESH_DIM > 1
 
 
  libmesh_assert_less (j, 2);
 
  libmesh_assert_less (i, (static_cast<unsigned int>(order)+1)*
                       (static_cast<unsigned int>(order)+2)/2);
 
  const Real xi  = p(0);
  const Real eta = p(1);
 
  // monomials. since they are hierarchic we only need one case block.
 
  switch (j)
    {
      // d()/dxi
    case 0:
      {
        switch (i)
          {
            // constants
          case 0:
            return 0.;
 
            // linears
          case 1:
            return 1.;
 
          case 2:
            return 0.;
 
            // quadratics
          case 3:
            return 2.*xi;
 
          case 4:
            return eta;
 
          case 5:
            return 0.;
 
            // cubics
          case 6:
            return 3.*xi*xi;
 
          case 7:
            return 2.*xi*eta;
 
          case 8:
            return eta*eta;
 
          case 9:
            return 0.;
 
            // quartics
          case 10:
            return 4.*xi*xi*xi;
 
          case 11:
            return 3.*xi*xi*eta;
 
          case 12:
            return 2.*xi*eta*eta;
 
          case 13:
            return eta*eta*eta;
 
          case 14:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            const int ny = i - (o*(o+1)/2);
            const int nx = o - ny;
            Real val = nx;
            for (int index=1; index < nx; index++)
              val *= xi;
            for (int index=0; index != ny; index++)
              val *= eta;
            return val;
          }
      }
 
 
      // d()/deta
    case 1:
      {
        switch (i)
          {
            // constants
          case 0:
            return 0.;
 
            // linears
          case 1:
            return 0.;
 
          case 2:
            return 1.;
 
            // quadratics
          case 3:
            return 0.;
 
          case 4:
            return xi;
 
          case 5:
            return 2.*eta;
 
            // cubics
          case 6:
            return 0.;
 
          case 7:
            return xi*xi;
 
          case 8:
            return 2.*xi*eta;
 
          case 9:
            return 3.*eta*eta;
 
            // quartics
          case 10:
            return 0.;
 
          case 11:
            return xi*xi*xi;
 
          case 12:
            return 2.*xi*xi*eta;
 
          case 13:
            return 3.*xi*eta*eta;
 
          case 14:
            return 4.*eta*eta*eta;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            const int ny = i - (o*(o+1)/2);
            const int nx = o - ny;
            Real val = ny;
            for (int index=0; index != nx; index++)
              val *= xi;
            for (int index=1; index < ny; index++)
              val *= eta;
            return val;
          }
      }
 
    default:
      libmesh_error_msg("Invalid shape function derivative j = " << j);
    }
 
#else // LIBMESH_DIM == 1
  libmesh_ignore(i, j, p);
  libmesh_assert(order);
  libmesh_not_implemented();
#endif
}

shape_deriv() [117/233]

Real libMesh::FE< 3, MONOMIAL >::shape_deriv ( const ElemType  , const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 219 of file fe_monomial_shape_3D.C.

{
#if LIBMESH_DIM == 3
 
  libmesh_assert_less (j, 3);
 
  libmesh_assert_less (i, (static_cast<unsigned int>(order)+1)*
                       (static_cast<unsigned int>(order)+2)*
                       (static_cast<unsigned int>(order)+3)/6);
 
 
  const Real xi   = p(0);
  const Real eta  = p(1);
  const Real zeta = p(2);
 
  // monomials. since they are hierarchic we only need one case block.
  switch (j)
    {
      // d()/dxi
    case 0:
      {
        switch (i)
          {
            // constant
          case 0:
            return 0.;
 
            // linear
          case 1:
            return 1.;
 
          case 2:
            return 0.;
 
          case 3:
            return 0.;
 
            // quadratic
          case 4:
            return 2.*xi;
 
          case 5:
            return eta;
 
          case 6:
            return 0.;
 
          case 7:
            return zeta;
 
          case 8:
            return 0.;
 
          case 9:
            return 0.;
 
            // cubic
          case 10:
            return 3.*xi*xi;
 
          case 11:
            return 2.*xi*eta;
 
          case 12:
            return eta*eta;
 
          case 13:
            return 0.;
 
          case 14:
            return 2.*xi*zeta;
 
          case 15:
            return eta*zeta;
 
          case 16:
            return 0.;
 
          case 17:
            return zeta*zeta;
 
          case 18:
            return 0.;
 
          case 19:
            return 0.;
 
            // quartics
          case 20:
            return 4.*xi*xi*xi;
 
          case 21:
            return 3.*xi*xi*eta;
 
          case 22:
            return 2.*xi*eta*eta;
 
          case 23:
            return eta*eta*eta;
 
          case 24:
            return 0.;
 
          case 25:
            return 3.*xi*xi*zeta;
 
          case 26:
            return 2.*xi*eta*zeta;
 
          case 27:
            return eta*eta*zeta;
 
          case 28:
            return 0.;
 
          case 29:
            return 2.*xi*zeta*zeta;
 
          case 30:
            return eta*zeta*zeta;
 
          case 31:
            return 0.;
 
          case 32:
            return zeta*zeta*zeta;
 
          case 33:
            return 0.;
 
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            const int i2 = i - (o*(o+1)*(o+2)/6);
            int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const int nx = block - i2;
            const int ny = o - nx - nz;
            Real val = nx;
            for (int index=1; index < nx; index++)
              val *= xi;
            for (int index=0; index != ny; index++)
              val *= eta;
            for (int index=0; index != nz; index++)
              val *= zeta;
            return val;
          }
      }
 
 
      // d()/deta
    case 1:
      {
        switch (i)
          {
            // constant
          case 0:
            return 0.;
 
            // linear
          case 1:
            return 0.;
 
          case 2:
            return 1.;
 
          case 3:
            return 0.;
 
            // quadratic
          case 4:
            return 0.;
 
          case 5:
            return xi;
 
          case 6:
            return 2.*eta;
 
          case 7:
            return 0.;
 
          case 8:
            return zeta;
 
          case 9:
            return 0.;
 
            // cubic
          case 10:
            return 0.;
 
          case 11:
            return xi*xi;
 
          case 12:
            return 2.*xi*eta;
 
          case 13:
            return 3.*eta*eta;
 
          case 14:
            return 0.;
 
          case 15:
            return xi*zeta;
 
          case 16:
            return 2.*eta*zeta;
 
          case 17:
            return 0.;
 
          case 18:
            return zeta*zeta;
 
          case 19:
            return 0.;
 
            // quartics
          case 20:
            return 0.;
 
          case 21:
            return xi*xi*xi;
 
          case 22:
            return 2.*xi*xi*eta;
 
          case 23:
            return 3.*xi*eta*eta;
 
          case 24:
            return 4.*eta*eta*eta;
 
          case 25:
            return 0.;
 
          case 26:
            return xi*xi*zeta;
 
          case 27:
            return 2.*xi*eta*zeta;
 
          case 28:
            return 3.*eta*eta*zeta;
 
          case 29:
            return 0.;
 
          case 30:
            return xi*zeta*zeta;
 
          case 31:
            return 2.*eta*zeta*zeta;
 
          case 32:
            return 0.;
 
          case 33:
            return zeta*zeta*zeta;
 
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            const int i2 = i - (o*(o+1)*(o+2)/6);
            int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const int nx = block - i2;
            const int ny = o - nx - nz;
            Real val = ny;
            for (int index=0; index != nx; index++)
              val *= xi;
            for (int index=1; index < ny; index++)
              val *= eta;
            for (int index=0; index != nz; index++)
              val *= zeta;
            return val;
          }
      }
 
 
      // d()/dzeta
    case 2:
      {
        switch (i)
          {
            // constant
          case 0:
            return 0.;
 
            // linear
          case 1:
            return 0.;
 
          case 2:
            return 0.;
 
          case 3:
            return 1.;
 
            // quadratic
          case 4:
            return 0.;
 
          case 5:
            return 0.;
 
          case 6:
            return 0.;
 
          case 7:
            return xi;
 
          case 8:
            return eta;
 
          case 9:
            return 2.*zeta;
 
            // cubic
          case 10:
            return 0.;
 
          case 11:
            return 0.;
 
          case 12:
            return 0.;
 
          case 13:
            return 0.;
 
          case 14:
            return xi*xi;
 
          case 15:
            return xi*eta;
 
          case 16:
            return eta*eta;
 
          case 17:
            return 2.*xi*zeta;
 
          case 18:
            return 2.*eta*zeta;
 
          case 19:
            return 3.*zeta*zeta;
 
            // quartics
          case 20:
            return 0.;
 
          case 21:
            return 0.;
 
          case 22:
            return 0.;
 
          case 23:
            return 0.;
 
          case 24:
            return 0.;
 
          case 25:
            return xi*xi*xi;
 
          case 26:
            return xi*xi*eta;
 
          case 27:
            return xi*eta*eta;
 
          case 28:
            return eta*eta*eta;
 
          case 29:
            return 2.*xi*xi*zeta;
 
          case 30:
            return 2.*xi*eta*zeta;
 
          case 31:
            return 2.*eta*eta*zeta;
 
          case 32:
            return 3.*xi*zeta*zeta;
 
          case 33:
            return 3.*eta*zeta*zeta;
 
          case 34:
            return 4.*zeta*zeta*zeta;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            const int i2 = i - (o*(o+1)*(o+2)/6);
            int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const int nx = block - i2;
            const int ny = o - nx - nz;
            Real val = nz;
            for (int index=0; index != nx; index++)
              val *= xi;
            for (int index=0; index != ny; index++)
              val *= eta;
            for (int index=1; index < nz; index++)
              val *= zeta;
            return val;
          }
      }
 
    default:
      libmesh_error_msg("Invalid shape function derivative j = " << j);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_assert(order);
  libmesh_ignore(i, j, p);
  libmesh_not_implemented();
#endif
}

shape_deriv() [118/233]

Real libMesh::FE< 1, MONOMIAL >::shape_deriv ( const ElemType  , const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  libmesh_dbg_varj, const Point &  p  )

inherited

Definition at line 97 of file fe_monomial_shape_1D.C.

{
  // only d()/dxi in 1D!
 
  libmesh_assert_equal_to (j, 0);
 
  const Real xi = p(0);
 
  libmesh_assert_less_equal (i, static_cast<unsigned int>(order));
 
  // monomials. since they are hierarchic we only need one case block.
  switch (i)
    {
    case 0:
      return 0.;
 
    case 1:
      return 1.;
 
    case 2:
      return 2.*xi;
 
    case 3:
      return 3.*xi*xi;
 
    case 4:
      return 4.*xi*xi*xi;
 
    default:
      Real val = i;
      for (unsigned int index = 1; index != i; ++index)
        val *= xi;
      return val;
    }
}

shape_deriv() [119/233]

Real libMesh::FE< 1, SZABAB >::shape_deriv ( const ElemType  , const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  libmesh_dbg_varj, const Point &  p  )

inherited

Definition at line 110 of file fe_szabab_shape_1D.C.

{
  // only d()/dxi in 1D!
  libmesh_assert_equal_to (j, 0);
 
  const Real xi  = p(0);
  const Real xi2 = xi*xi;
 
  // Use this libmesh_assert rather than a switch with a single entry...
  // It will go away in optimized mode, essentially has the same effect.
  libmesh_assert_less_equal (order, SEVENTH);
 
  //   switch (order)
  //     {
  //     case FIRST:
  //     case SECOND:
  //     case THIRD:
  //     case FOURTH:
  //     case FIFTH:
  //     case SIXTH:
  //     case SEVENTH:
 
  switch(i)
    {
    case 0:return -1./2.;
    case 1:return 1./2.;
    case 2:return 1./2.*2.4494897427831780982*xi;
    case 3:return -1./4.*3.1622776601683793320+3./4.*3.1622776601683793320*xi2;
    case 4:return 1./16.*3.7416573867739413856*(-12.+20*xi2)*xi;
    case 5:return 9./16.*1.4142135623730950488+(-45./8.*1.4142135623730950488+105./16.*1.4142135623730950488*xi2)*xi2;
    case 6:return 1./32.*4.6904157598234295546*(30.+(-140.+126.*xi2)*xi2)*xi;
    case 7:return -5./32.*5.0990195135927848300+(105./32.*5.0990195135927848300+(-315./32.*5.0990195135927848300+231./32.*5.0990195135927848300*xi2)*xi2)*xi2;
    case 8:return 1./256.*5.4772255750516611346*(-280.+(2520.+(-5544.+3432.*xi2)*xi2)*xi2)*xi;
 
    default:
      libmesh_error_msg("Invalid shape function index!");
    }
}

shape_deriv() [120/233]

Real libMesh::FE< 1, LAGRANGE >::shape_deriv ( const ElemType  , const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 103 of file fe_lagrange_shape_1D.C.

{
  return fe_lagrange_1D_shape_deriv(order, i, j, p(0));
}

shape_deriv() [121/233]

Real libMesh::FE< 1, L2_LAGRANGE >::shape_deriv ( const ElemType  , const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 115 of file fe_lagrange_shape_1D.C.

{
  return fe_lagrange_1D_shape_deriv(order, i, j, p(0));
}

shape_deriv() [122/233]

Real libMesh::FE< 1, BERNSTEIN >::shape_deriv ( const ElemType  , const Order  order, const unsigned int  i, const unsigned int  libmesh_dbg_varj, const Point &  p  )

inherited

Definition at line 222 of file fe_bernstein_shape_1D.C.

{
  // only d()/dxi in 1D!
 
  libmesh_assert_equal_to (j, 0);
 
  const Real xi = p(0);
 
  using Utility::pow;
 
  switch (order)
    {
    case FIRST:
 
      switch(i)
        {
        case 0:
          return -.5;
        case 1:
          return .5;
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case SECOND:
 
      switch(i)
        {
        case 0:
          return (xi-1.)*.5;
        case 1:
          return (xi+1.)*.5;
        case 2:
          return -xi;
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case THIRD:
 
      switch(i)
        {
        case 0:
          return -0.375*pow<2>(1.-xi);
        case 1:
          return  0.375*pow<2>(1.+xi);
        case 2:
          return -0.375 -.75*xi +1.125*pow<2>(xi);
        case 3:
          return  0.375 -.75*xi -1.125*pow<2>(xi);
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case FOURTH:
 
      switch(i)
        {
        case 0:
          return -0.25*pow<3>(1.-xi);
        case 1:
          return  0.25*pow<3>(1.+xi);
        case 2:
          return -0.5 +1.5*pow<2>(xi)-pow<3>(xi);
        case 3:
          return  1.5*(pow<3>(xi)-xi);
        case 4:
          return  0.5 -1.5*pow<2>(xi)-pow<3>(xi);
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case FIFTH:
 
      switch(i)
        {
        case 0:
          return -(5./32.)*pow<4>(xi-1.);
        case 1:
          return  (5./32.)*pow<4>(xi+1.);
        case 2:
          return  (5./32.)*pow<4>(1.-xi)         -(5./8.)*(1.+xi)*pow<3>(1.-xi);
        case 3:
          return  (5./ 8.)*(1.+xi)*pow<3>(1.-xi) -(15./16.)*pow<2>(1.+xi)*pow<2>(1.-xi);
        case 4:
          return -(5./ 8.)*pow<3>(1.+xi)*(1.-xi) +(15./16.)*pow<2>(1.+xi)*pow<2>(1.-xi);
        case 5:
          return  (5./ 8.)*pow<3>(1.+xi)*(1.-xi) -(5./32.)*pow<4>(1.+xi);
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case SIXTH:
 
      switch(i)
        {
        case 0:
          return -( 3./32.)*pow<5>(1.-xi);
        case 1:
          return  ( 3./32.)*pow<5>(1.+xi);
        case 2:
          return  ( 3./32.)*pow<5>(1.-xi)-(15./32.)*(1.+xi)*pow<4>(1.-xi);
        case 3:
          return  (15./32.)*(1.+xi)*pow<4>(1.-xi)-(15./16.)*pow<2>(1.+xi)*pow<3>(1.-xi);
        case 4:
          return -(15./ 8.)*xi +(15./4.)*pow<3>(xi)-(15./8.)*pow<5>(xi);
        case 5:
          return -(15./32.)*(1.-xi)*pow<4>(1.+xi)+(15./16.)*pow<2>(1.-xi)*pow<3>(1.+xi);
        case 6:
          return  (15./32.)*pow<4>(1.+xi)*(1.-xi)-(3./32.)*pow<5>(1.+xi);
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
 
    default:
      {
        libmesh_assert (order>6);
 
        // Use this for arbitrary orders
        const int p_order = static_cast<int>(order);
        const int m       = p_order-(i-1);
        const int n       = (i-1);
 
        Real binomial_p_i = 1;
 
        // the binomial coefficient (p choose n)
        // Using an unsigned long here will work for any of the orders we support.
        // Explicitly construct a Real to prevent conversion warnings
        if (i>1)
          binomial_p_i = Real(Utility::binomial(static_cast<unsigned long>(p_order),
                                                static_cast<unsigned long>(n)));
 
        switch(i)
          {
          case 0:
            return binomial_p_i * (-1./2.) * p_order * std::pow((1-xi)/2, p_order-1);
          case 1:
            return binomial_p_i * ( 1./2.) * p_order * std::pow((1+xi)/2, p_order-1);
 
          default:
            {
              return binomial_p_i * (1./2. * n * std::pow((1+xi)/2,n-1) * std::pow((1-xi)/2,m)
                                     - 1./2. * m * std::pow((1+xi)/2,n)   * std::pow((1-xi)/2,m-1));
            }
          }
      }
 
    }
}

shape_deriv() [123/233]

Real libMesh::FE< 0, BERNSTEIN >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 70 of file fe_bernstein_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [124/233]

Real libMesh::FE< 2, BERNSTEIN >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 515 of file fe_bernstein_shape_2D.C.

{
  libmesh_error_msg("Bernstein polynomials require the element type \nbecause edge orientation is needed.");
  return 0.;
}

shape_deriv() [125/233]

Real libMesh::FE< 3, BERNSTEIN >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 2315 of file fe_bernstein_shape_3D.C.

{
  libmesh_error_msg("Bernstein polynomials require the element type \nbecause edge and face orientation is needed.");
  return 0.;
}

shape_deriv() [126/233]

Real libMesh::FE< 0, CLOUGH >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 71 of file fe_clough_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [127/233]

Real libMesh::FE< 1, CLOUGH >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 304 of file fe_clough_shape_1D.C.

{
  libmesh_error_msg("Clough-Tocher elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_deriv() [128/233]

Real libMesh::FE< 2, CLOUGH >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 2155 of file fe_clough_shape_2D.C.

{
  libmesh_error_msg("Clough-Tocher elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_deriv() [129/233]

Real libMesh::FE< 3, CLOUGH >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 77 of file fe_clough_shape_3D.C.

{
  libmesh_error_msg("Clough-Tocher elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_deriv() [130/233]

Real libMesh::FE< 0, HERMITE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 71 of file fe_hermite_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [131/233]

Real libMesh::FE< 1, HERMITE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 308 of file fe_hermite_shape_1D.C.

{
  libmesh_error_msg("Hermite elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_deriv() [132/233]

Real libMesh::FE< 2, HERMITE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 335 of file fe_hermite_shape_2D.C.

{
  libmesh_error_msg("Hermite elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_deriv() [133/233]

Real libMesh::FE< 3, HERMITE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 547 of file fe_hermite_shape_3D.C.

{
  libmesh_error_msg("Hermite elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_deriv() [134/233]

Real libMesh::FE< 0, HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 149 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [135/233]

Real libMesh::FE< 0, L2_HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 190 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [136/233]

Real libMesh::FE< 0, SIDE_HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 230 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [137/233]

Real libMesh::FE< 1, SIDE_HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 202 of file fe_hierarchic_shape_1D.C.

{
  return 0;
}

shape_deriv() [138/233]

Real libMesh::FE< 2, HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 402 of file fe_hierarchic_shape_2D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge orientation.");
  return 0.;
}

shape_deriv() [139/233]

Real libMesh::FE< 2, L2_HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 415 of file fe_hierarchic_shape_2D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge orientation.");
  return 0.;
}

shape_deriv() [140/233]

Real libMesh::FE< 2, SIDE_HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 428 of file fe_hierarchic_shape_2D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge orientation.");
  return 0.;
}

shape_deriv() [141/233]

Real libMesh::FE< 3, HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1509 of file fe_hierarchic_shape_3D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge/face orientation.");
  return 0.;
}

shape_deriv() [142/233]

Real libMesh::FE< 3, L2_HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1522 of file fe_hierarchic_shape_3D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge/face orientation.");
  return 0.;
}

shape_deriv() [143/233]

Real libMesh::FE< 3, SIDE_HIERARCHIC >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1535 of file fe_hierarchic_shape_3D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge/face orientation.");
  return 0.;
}

shape_deriv() [144/233]

Real libMesh::FE< 0, L2_LAGRANGE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 105 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [145/233]

Real libMesh::FE< 0, LAGRANGE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 132 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [146/233]

Real libMesh::FE< 0, MONOMIAL >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 72 of file fe_monomial_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [147/233]

RealGradient libMesh::FE< 0, NEDELEC_ONE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 463 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape_deriv() [148/233]

RealGradient libMesh::FE< 1, NEDELEC_ONE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 490 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape_deriv() [149/233]

RealGradient libMesh::FE< 2, NEDELEC_ONE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1978 of file fe_nedelec_one_shape_2D.C.

{
  libmesh_error_msg("Nedelec elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape_deriv() [150/233]

RealGradient libMesh::FE< 3, NEDELEC_ONE >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 398 of file fe_nedelec_one_shape_3D.C.

{
  libmesh_error_msg("Nedelec elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape_deriv() [151/233]

Real libMesh::FE< 0, RATIONAL_BERNSTEIN >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 69 of file fe_rational_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [152/233]

Real libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 101 of file fe_rational_shape_1D.C.

{
  libmesh_error_msg("Rational bases require the real element \nto query nodal weighting.");
  return 0.;
}

shape_deriv() [153/233]

Real libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 100 of file fe_rational_shape_2D.C.

{
  libmesh_error_msg("Rational bases require the real element \nto query nodal weighting.");
  return 0.;
}

shape_deriv() [154/233]

Real libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 98 of file fe_rational_shape_3D.C.

{
  libmesh_error_msg("Rational bases require the real element \nto query nodal weighting.");
  return 0.;
}

shape_deriv() [155/233]

RealGradient libMesh::FE< 0, RAVIART_THOMAS >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 561 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_deriv() [156/233]

RealGradient libMesh::FE< 0, L2_RAVIART_THOMAS >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 569 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_deriv() [157/233]

RealGradient libMesh::FE< 1, RAVIART_THOMAS >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 610 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_deriv() [158/233]

RealGradient libMesh::FE< 1, L2_RAVIART_THOMAS >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 618 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_deriv() [159/233]

RealGradient libMesh::FE< 2, RAVIART_THOMAS >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 114 of file fe_raviart_shape_2D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape_deriv() [160/233]

RealGradient libMesh::FE< 2, L2_RAVIART_THOMAS >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 125 of file fe_raviart_shape_2D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape_deriv() [161/233]

RealGradient libMesh::FE< 3, RAVIART_THOMAS >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 354 of file fe_raviart_shape_3D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}

shape_deriv() [162/233]

RealGradient libMesh::FE< 3, L2_RAVIART_THOMAS >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 366 of file fe_raviart_shape_3D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}

shape_deriv() [163/233]

Real libMesh::FE< 0, SCALAR >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 63 of file fe_scalar_shape_0D.C.

{
  return 0.;
}

shape_deriv() [164/233]

Real libMesh::FE< 1, SCALAR >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 66 of file fe_scalar_shape_1D.C.

{
  return 0.;
}

shape_deriv() [165/233]

Real libMesh::FE< 2, SCALAR >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 65 of file fe_scalar_shape_2D.C.

{
  return 0.;
}

shape_deriv() [166/233]

Real libMesh::FE< 3, SCALAR >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 64 of file fe_scalar_shape_3D.C.

{
  return 0.;
}

shape_deriv() [167/233]

Real libMesh::FE< 0, SZABAB >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 72 of file fe_szabab_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [168/233]

Real libMesh::FE< 2, SZABAB >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1021 of file fe_szabab_shape_2D.C.

{
  libmesh_error_msg("Szabo-Babuska polynomials require the element type \nbecause edge orientation is needed.");
  return 0.;
}

shape_deriv() [169/233]

Real libMesh::FE< 3, SZABAB >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 72 of file fe_szabab_shape_3D.C.

{
  libmesh_error_msg("Szabo-Babuska polynomials are not defined in 3D");
  return 0.;
}

shape_deriv() [170/233]

Real libMesh::FE< 0, XYZ >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 72 of file fe_xyz_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [171/233]

Real libMesh::FE< 1, XYZ >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 163 of file fe_xyz_shape_1D.C.

{
  libmesh_error_msg("XYZ polynomials require the element.");
  return 0.;
}

shape_deriv() [172/233]

Real libMesh::FE< 2, XYZ >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 367 of file fe_xyz_shape_2D.C.

{
  libmesh_error_msg("XYZ polynomials require the element.");
  return 0.;
}

shape_deriv() [173/233]

Real libMesh::FE< 3, XYZ >::shape_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 704 of file fe_xyz_shape_3D.C.

{
  libmesh_error_msg("XYZ polynomials require the element.");
  return 0.;
}

shape_deriv() [174/233]

Real libMesh::FE< 1, BERNSTEIN >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 395 of file fe_bernstein_shape_1D.C.

{
  libmesh_assert(elem);
  return FE<1,BERNSTEIN>::shape_deriv
    (elem->type(),
     fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [175/233]

Real libMesh::FE< 2, BERNSTEIN >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 526 of file fe_bernstein_shape_2D.C.

{
  return FE<2,BERNSTEIN>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [176/233]

Real libMesh::FE< 3, BERNSTEIN >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 2326 of file fe_bernstein_shape_3D.C.

{
  return FE<3,BERNSTEIN>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [177/233]

Real libMesh::FE< 1, CLOUGH >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 370 of file fe_clough_shape_1D.C.

{
  return FE<1,CLOUGH>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [178/233]

Real libMesh::FE< 2, CLOUGH >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 2167 of file fe_clough_shape_2D.C.

{
  return FE<2,CLOUGH>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [179/233]

Real libMesh::FE< 1, HERMITE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 319 of file fe_hermite_shape_1D.C.

{
  return FE<1,HERMITE>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [180/233]

Real libMesh::FE< 2, HERMITE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 347 of file fe_hermite_shape_2D.C.

{
  return FE<2,HERMITE>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [181/233]

Real libMesh::FE< 3, HERMITE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 559 of file fe_hermite_shape_3D.C.

{
  return FE<3,HERMITE>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [182/233]

Real libMesh::FE< 1, HIERARCHIC >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 230 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_hierarchic_1D_shape_deriv(elem->type(), fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [183/233]

Real libMesh::FE< 1, L2_HIERARCHIC >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 261 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_hierarchic_1D_shape_deriv(elem->type(), fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [184/233]

Real libMesh::FE< 2, HIERARCHIC >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 453 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape_deriv<HIERARCHIC>(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [185/233]

Real libMesh::FE< 2, L2_HIERARCHIC >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 479 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape_deriv<L2_HIERARCHIC>(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [186/233]

Real libMesh::FE< 2, SIDE_HIERARCHIC >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 681 of file fe_hierarchic_shape_2D.C.

{
  return FE<2,SIDE_HIERARCHIC>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [187/233]

Real libMesh::FE< 3, HIERARCHIC >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1560 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape_deriv<HIERARCHIC>(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [188/233]

Real libMesh::FE< 3, L2_HIERARCHIC >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1585 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape_deriv<L2_HIERARCHIC>(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [189/233]

Real libMesh::FE< 3, SIDE_HIERARCHIC >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1754 of file fe_hierarchic_shape_3D.C.

{
  return FE<3,SIDE_HIERARCHIC>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [190/233]

Real libMesh::FE< 1, LAGRANGE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 156 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_1D_shape_deriv(fet.order + add_p_level*elem->p_level(), i, j, p(0));
}

shape_deriv() [191/233]

Real libMesh::FE< 1, L2_LAGRANGE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 169 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_1D_shape_deriv(fet.order + add_p_level*elem->p_level(), i, j, p(0));
}

shape_deriv() [192/233]

Real libMesh::FE< 2, LAGRANGE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 203 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_2D_shape_deriv<LAGRANGE>(elem->type(), elem, fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [193/233]

Real libMesh::FE< 2, L2_LAGRANGE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 217 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_2D_shape_deriv<L2_LAGRANGE>(elem->type(), elem, fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [194/233]

Real libMesh::FE< 3, LAGRANGE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 549 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_3D_shape_deriv<LAGRANGE>(elem->type(), fet.order + add_p_level*elem->p_level(), elem, i, j, p);
}

shape_deriv() [195/233]

Real libMesh::FE< 3, L2_LAGRANGE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 562 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_3D_shape_deriv<L2_LAGRANGE>(elem->type(), fet.order + add_p_level*elem->p_level(), elem, i, j, p);
}

shape_deriv() [196/233]

Real libMesh::FE< 1, MONOMIAL >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 155 of file fe_monomial_shape_1D.C.

{
  libmesh_assert(elem);
  return FE<1,MONOMIAL>::shape_deriv(elem->type(), fet.order + add_p_level*elem->p_level(), i, j, p);
 
 
}

shape_deriv() [197/233]

Real libMesh::FE< 2, MONOMIAL >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 340 of file fe_monomial_shape_2D.C.

{
  libmesh_assert(elem);
  // by default call the orientation-independent shape functions
  return FE<2,MONOMIAL>::shape_deriv(elem->type(), fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [198/233]

Real libMesh::FE< 3, MONOMIAL >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 674 of file fe_monomial_shape_3D.C.

{
  libmesh_assert(elem);
  // by default call the orientation-independent shape functions
  return FE<3,MONOMIAL>::shape_deriv(elem->type(), fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_deriv() [199/233]

RealGradient libMesh::FE< 2, NEDELEC_ONE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1989 of file fe_nedelec_one_shape_2D.C.

{
  return FE<2,NEDELEC_ONE>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [200/233]

RealGradient libMesh::FE< 3, NEDELEC_ONE >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 410 of file fe_nedelec_one_shape_3D.C.

{
  return FE<3,NEDELEC_ONE>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [201/233]

Real libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 113 of file fe_rational_shape_1D.C.

{
  libmesh_assert(elem);
  return FE<1,RATIONAL_BERNSTEIN>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [202/233]

Real libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 113 of file fe_rational_shape_2D.C.

{
  return FE<2,RATIONAL_BERNSTEIN>::shape_deriv
    (elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [203/233]

Real libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 110 of file fe_rational_shape_3D.C.

{
  return FE<3,RATIONAL_BERNSTEIN>::shape_deriv
    (elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [204/233]

RealGradient libMesh::FE< 2, RAVIART_THOMAS >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 136 of file fe_raviart_shape_2D.C.

{
  return FE<2,RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [205/233]

RealGradient libMesh::FE< 2, L2_RAVIART_THOMAS >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 147 of file fe_raviart_shape_2D.C.

{
  return FE<2,L2_RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [206/233]

RealGradient libMesh::FE< 3, RAVIART_THOMAS >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 378 of file fe_raviart_shape_3D.C.

{
  return FE<3,RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [207/233]

RealGradient libMesh::FE< 3, L2_RAVIART_THOMAS >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 390 of file fe_raviart_shape_3D.C.

{
  return FE<3,L2_RAVIART_THOMAS>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [208/233]

Real libMesh::FE< 2, SUBDIVISION >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 803 of file fe_subdivision_2D.C.

{
  libmesh_assert(elem);
  const Order totalorder = fet.order + add_p_level*elem->p_level();
  return FE<2,SUBDIVISION>::shape_deriv(elem->type(), totalorder, i, j, p);
}

shape_deriv() [209/233]

Real libMesh::FE< 1, SZABAB >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 172 of file fe_szabab_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape_deriv(elem->type(),
                                   fet.order + add_p_level*elem->p_level(),
                                   i,
                                   j,
                                   p);
}

shape_deriv() [210/233]

Real libMesh::FE< 2, SZABAB >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1033 of file fe_szabab_shape_2D.C.

{
  return FE<2,SZABAB>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [211/233]

Real libMesh::FE< 1, XYZ >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 175 of file fe_xyz_shape_1D.C.

{
  return FE<1,XYZ>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [212/233]

Real libMesh::FE< 2, XYZ >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 379 of file fe_xyz_shape_2D.C.

{
  return FE<2,XYZ>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [213/233]

Real libMesh::FE< 3, XYZ >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 717 of file fe_xyz_shape_3D.C.

{
  return FE<3,XYZ>::shape_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_deriv() [214/233]

static OutputShape libMesh::FE< Dim, T >::shape_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level = true  )

staticinherited

Returns

The \( j^{th} \) derivative of the \( i^{th} \) shape function. You must specify element type, and order (via FEType) directly.

On a p-refined element, o should be the base order of the element if add_p_level is left true, or can be the base order of the element if add_p_level is set to false.

shape_deriv() [215/233]

Real libMesh::FE< 0, BERNSTEIN >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 95 of file fe_bernstein_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [216/233]

Real libMesh::FE< 0, CLOUGH >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 96 of file fe_clough_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [217/233]

Real libMesh::FE< 0, HERMITE >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 97 of file fe_hermite_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [218/233]

Real libMesh::FE< 0, HIERARCHIC >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 176 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [219/233]

Real libMesh::FE< 0, L2_HIERARCHIC >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 216 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [220/233]

Real libMesh::FE< 0, SIDE_HIERARCHIC >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 256 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [221/233]

Real libMesh::FE< 1, SIDE_HIERARCHIC >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 288 of file fe_hierarchic_shape_1D.C.

{
  return 0;
}

shape_deriv() [222/233]

Real libMesh::FE< 0, L2_LAGRANGE >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 159 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [223/233]

Real libMesh::FE< 0, LAGRANGE >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 172 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [224/233]

Real libMesh::FE< 0, MONOMIAL >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 98 of file fe_monomial_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [225/233]

Real libMesh::FE< 0, RATIONAL_BERNSTEIN >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 96 of file fe_rational_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [226/233]

Real libMesh::FE< 0, SCALAR >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 85 of file fe_scalar_shape_0D.C.

{
  return 0.;
}

shape_deriv() [227/233]

Real libMesh::FE< 1, SCALAR >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 88 of file fe_scalar_shape_1D.C.

{
  return 0.;
}

shape_deriv() [228/233]

Real libMesh::FE< 2, SCALAR >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 87 of file fe_scalar_shape_2D.C.

{
  return 0.;
}

shape_deriv() [229/233]

Real libMesh::FE< 3, SCALAR >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 86 of file fe_scalar_shape_3D.C.

{
  return 0.;
}

shape_deriv() [230/233]

Real libMesh::FE< 0, SZABAB >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 98 of file fe_szabab_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [231/233]

Real libMesh::FE< 3, SZABAB >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 98 of file fe_szabab_shape_3D.C.

{
  libmesh_error_msg("Szabo-Babuska polynomials are not defined in 3D");
  return 0;
}

shape_deriv() [232/233]

Real libMesh::FE< 0, XYZ >::shape_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 99 of file fe_xyz_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_deriv() [233/233]

Real libMesh::FE< 3, CLOUGH >::shape_deriv ( const FEType  , const Elem *  libmesh_dbg_varelem, const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 104 of file fe_clough_shape_3D.C.

{
  libmesh_assert(elem);
  libmesh_not_implemented();
  return 0.;
}

shape_derivs() [1/5]

void libMesh::FE< 3, LAGRANGE >::shape_derivs ( const Elem *  elem, const Order  o, const unsigned int  i, const unsigned int  j, const std::vector< Point > &  p, std::vector< OutputShape > &  v, const bool  add_p_level  )

inherited

Definition at line 224 of file fe_lagrange_shape_3D.C.

{
  FE<3,LAGRANGE>::default_shape_derivs
    (elem,o,i,j,p,v,add_p_level);
}

shape_derivs() [2/5]

void libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape_derivs ( const Elem *  elem, const Order  o, const unsigned int  i, const unsigned int  j, const std::vector< Point > &  p, std::vector< OutputShape > &  v, const bool  add_p_level  )

inherited

Definition at line 207 of file fe_rational_shape_1D.C.

{
  libmesh_assert_equal_to(p.size(), v.size());
  for (auto vi : index_range(v))
    v[vi] = FE<1,RATIONAL_BERNSTEIN>::shape_deriv (elem, o, i, j, p[vi], add_p_level);
}

shape_derivs() [3/5]

void libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape_derivs ( const Elem *  elem, const Order  o, const unsigned int  i, const unsigned int  j, const std::vector< Point > &  p, std::vector< OutputShape > &  v, const bool  add_p_level  )

inherited

Definition at line 205 of file fe_rational_shape_2D.C.

{
  libmesh_assert_equal_to(p.size(), v.size());
  for (auto vi : index_range(v))
    v[vi] = FE<2,RATIONAL_BERNSTEIN>::shape_deriv (elem, o, i, j, p[vi], add_p_level);
}

shape_derivs() [4/5]

void libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape_derivs ( const Elem *  elem, const Order  o, const unsigned int  i, const unsigned int  j, const std::vector< Point > &  p, std::vector< OutputShape > &  v, const bool  add_p_level  )

inherited

Definition at line 201 of file fe_rational_shape_3D.C.

{
  libmesh_assert_equal_to(p.size(), v.size());
  for (auto vi : index_range(v))
    v[vi] = FE<3,RATIONAL_BERNSTEIN>::shape_deriv (elem, o, i, j, p[vi], add_p_level);
}

shape_derivs() [5/5]

static void libMesh::FE< Dim, T >::shape_derivs ( const Elem *  elem, const Order  o, const unsigned int  i, const unsigned int  j, const std::vector< Point > &  p, std::vector< OutputShape > &  v, const bool  add_p_level = true  )

staticinherited

Fills v with the \( j^{th} \) derivative of the \( i^{th} \) shape function, evaluated at all points p.

You must specify element order directly. v should already be the appropriate size.

On a p-refined element, o should be the base order of the element if add_p_level is left true, or can be the base order of the element if add_p_level is set to false.

shape_second_deriv() [1/233]

Real libMesh::FE< 0, BERNSTEIN >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 123 of file fe_bernstein_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [2/233]

Real libMesh::FE< 0, CLOUGH >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 126 of file fe_clough_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [3/233]

Real libMesh::FE< 0, HERMITE >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 127 of file fe_hermite_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [4/233]

Real libMesh::FE< 0, HIERARCHIC >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 284 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [5/233]

Real libMesh::FE< 0, L2_HIERARCHIC >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 323 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [6/233]

Real libMesh::FE< 0, SIDE_HIERARCHIC >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 363 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [7/233]

Real libMesh::FE< 1, SIDE_HIERARCHIC >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 398 of file fe_hierarchic_shape_1D.C.

{
  return 0.;
}

shape_second_deriv() [8/233]

Real libMesh::FE< 0, L2_LAGRANGE >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 201 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [9/233]

Real libMesh::FE< 0, LAGRANGE >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 226 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [10/233]

Real libMesh::FE< 0, MONOMIAL >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 128 of file fe_monomial_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [11/233]

RealGradient libMesh::FE< 0, NEDELEC_ONE >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 477 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [12/233]

RealGradient libMesh::FE< 1, NEDELEC_ONE >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 504 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [13/233]

Real libMesh::FE< 0, RATIONAL_BERNSTEIN >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 124 of file fe_rational_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [14/233]

RealGradient libMesh::FE< 0, RAVIART_THOMAS >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 583 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [15/233]

RealGradient libMesh::FE< 0, L2_RAVIART_THOMAS >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 591 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [16/233]

RealGradient libMesh::FE< 1, RAVIART_THOMAS >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 632 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [17/233]

RealGradient libMesh::FE< 1, L2_RAVIART_THOMAS >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 640 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [18/233]

Real libMesh::FE< 0, SCALAR >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 109 of file fe_scalar_shape_0D.C.

{
  return 0.;
}

shape_second_deriv() [19/233]

Real libMesh::FE< 1, SCALAR >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 113 of file fe_scalar_shape_1D.C.

{
  return 0.;
}

shape_second_deriv() [20/233]

Real libMesh::FE< 2, SCALAR >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 111 of file fe_scalar_shape_2D.C.

{
  return 0.;
}

shape_second_deriv() [21/233]

Real libMesh::FE< 3, SCALAR >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 110 of file fe_scalar_shape_3D.C.

{
  return 0.;
}

shape_second_deriv() [22/233]

Real libMesh::FE< 0, SZABAB >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 127 of file fe_szabab_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [23/233]

Real libMesh::FE< 1, SZABAB >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 211 of file fe_szabab_shape_1D.C.

{
  static bool warning_given = false;
 
  if (!warning_given)
    libMesh::err << "Second derivatives for Szabab elements "
                 << " are not yet implemented!"
                 << std::endl;
 
  warning_given = true;
  return 0.;
}

shape_second_deriv() [24/233]

Real libMesh::FE< 2, SZABAB >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 1069 of file fe_szabab_shape_2D.C.

{
  static bool warning_given = false;
 
  if (!warning_given)
    libMesh::err << "Second derivatives for Szabab elements "
                 << " are not yet implemented!"
                 << std::endl;
 
  warning_given = true;
  return 0.;
}

shape_second_deriv() [25/233]

Real libMesh::FE< 3, SZABAB >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 126 of file fe_szabab_shape_3D.C.

{
  libmesh_error_msg("Szabo-Babuska polynomials are not defined in 3D");
  return 0.;
}

shape_second_deriv() [26/233]

Real libMesh::FE< 0, XYZ >::shape_second_deriv ( const Elem *  , const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 128 of file fe_xyz_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [27/233]

Real libMesh::FE< 2, XYZ >::shape_second_deriv ( const Elem *  elem, const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  j, const Point &  point_in, const bool  libmesh_dbg_varadd_p_level  )

inherited

Definition at line 394 of file fe_xyz_shape_2D.C.

{
#if LIBMESH_DIM > 1
 
  libmesh_assert_less_equal (j, 2);
  libmesh_assert(elem);
 
  Point avg = elem->vertex_average();
  Point max_distance = Point(0.,0.,0.);
  for (auto p : make_range(elem->n_nodes()))
    for (unsigned int d = 0; d < 2; d++)
      {
        const Real distance = std::abs(avg(d) - elem->point(p)(d));
        max_distance(d) = std::max(distance, max_distance(d));
      }
 
  const Real x  = point_in(0);
  const Real y  = point_in(1);
  const Real xc = avg(0);
  const Real yc = avg(1);
  const Real distx = max_distance(0);
  const Real disty = max_distance(1);
  const Real dx = (x - xc)/distx;
  const Real dy = (y - yc)/disty;
  const Real dist2x = pow(distx,2.);
  const Real dist2y = pow(disty,2.);
  const Real distxy = distx * disty;
 
#ifndef NDEBUG
  // totalorder is only used in the assertion below, so
  // we avoid declaring it when asserts are not active.
  const unsigned int totalorder = order + add_p_level * elem->p_level();
#endif
  libmesh_assert_less (i, (totalorder+1)*(totalorder+2)/2);
 
  // monomials. since they are hierarchic we only need one case block.
 
  switch (j)
    {
      // d^2()/dx^2
    case 0:
      {
        switch (i)
          {
            // constants
          case 0:
            // linears
          case 1:
          case 2:
            return 0.;
 
            // quadratics
          case 3:
            return 2./dist2x;
 
          case 4:
          case 5:
            return 0.;
 
            // cubics
          case 6:
            return 6.*dx/dist2x;
 
          case 7:
            return 2.*dy/dist2x;
 
          case 8:
          case 9:
            return 0.;
 
            // quartics
          case 10:
            return 12.*dx*dx/dist2x;
 
          case 11:
            return 6.*dx*dy/dist2x;
 
          case 12:
            return 2.*dy*dy/dist2x;
 
          case 13:
          case 14:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            unsigned int i2 = i - (o*(o+1)/2);
            Real val = (o - i2) * (o - i2 - 1);
            for (unsigned int index=i2+2; index < o; index++)
              val *= dx;
            for (unsigned int index=0; index != i2; index++)
              val *= dy;
            return val/dist2x;
          }
      }
 
      // d^2()/dxdy
    case 1:
      {
        switch (i)
          {
            // constants
          case 0:
 
            // linears
          case 1:
          case 2:
            return 0.;
 
            // quadratics
          case 3:
            return 0.;
 
          case 4:
            return 1./distxy;
 
          case 5:
            return 0.;
 
            // cubics
          case 6:
            return 0.;
          case 7:
            return 2.*dx/distxy;
 
          case 8:
            return 2.*dy/distxy;
 
          case 9:
            return 0.;
 
            // quartics
          case 10:
            return 0.;
 
          case 11:
            return 3.*dx*dx/distxy;
 
          case 12:
            return 4.*dx*dy/distxy;
 
          case 13:
            return 3.*dy*dy/distxy;
 
          case 14:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            unsigned int i2 = i - (o*(o+1)/2);
            Real val = (o - i2) * i2;
            for (unsigned int index=i2+1; index < o; index++)
              val *= dx;
            for (unsigned int index=1; index < i2; index++)
              val *= dy;
            return val/distxy;
          }
      }
 
      // d^2()/dy^2
    case 2:
      {
        switch (i)
          {
            // constants
          case 0:
 
            // linears
          case 1:
          case 2:
            return 0.;
 
            // quadratics
          case 3:
          case 4:
            return 0.;
 
          case 5:
            return 2./dist2y;
 
            // cubics
          case 6:
            return 0.;
 
          case 7:
            return 0.;
 
          case 8:
            return 2.*dx/dist2y;
 
          case 9:
            return 6.*dy/dist2y;
 
            // quartics
          case 10:
          case 11:
            return 0.;
 
          case 12:
            return 2.*dx*dx/dist2y;
 
          case 13:
            return 6.*dx*dy/dist2y;
 
          case 14:
            return 12.*dy*dy/dist2y;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            unsigned int i2 = i - (o*(o+1)/2);
            Real val = i2 * (i2 - 1);
            for (unsigned int index=i2; index != o; index++)
              val *= dx;
            for (unsigned int index=2; index < i2; index++)
              val *= dy;
            return val/dist2y;
          }
      }
 
    default:
      libmesh_error_msg("Invalid shape function derivative j = " << j);
    }
 
#else // LIBMESH_DIM <= 1
  libmesh_assert(true || order || add_p_level);
  libmesh_ignore(elem, i, j, point_in);
  libmesh_not_implemented();
#endif
}

shape_second_deriv() [28/233]

Real libMesh::FE< 3, XYZ >::shape_second_deriv ( const Elem *  elem, const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  j, const Point &  point_in, const bool  libmesh_dbg_varadd_p_level  )

inherited

Definition at line 732 of file fe_xyz_shape_3D.C.

{
#if LIBMESH_DIM == 3
 
  libmesh_assert(elem);
  libmesh_assert_less (j, 6);
 
  Point avg = elem->vertex_average();
  Point max_distance = Point(0.,0.,0.);
  for (const Point & p : elem->node_ref_range())
    for (unsigned int d = 0; d < 3; d++)
      {
        const Real distance = std::abs(avg(d) - p(d));
        max_distance(d) = std::max(distance, max_distance(d));
      }
 
  const Real x  = point_in(0);
  const Real y  = point_in(1);
  const Real z  = point_in(2);
  const Real xc = avg(0);
  const Real yc = avg(1);
  const Real zc = avg(2);
  const Real distx = max_distance(0);
  const Real disty = max_distance(1);
  const Real distz = max_distance(2);
  const Real dx = (x - xc)/distx;
  const Real dy = (y - yc)/disty;
  const Real dz = (z - zc)/distz;
  const Real dist2x = pow(distx,2.);
  const Real dist2y = pow(disty,2.);
  const Real dist2z = pow(distz,2.);
  const Real distxy = distx * disty;
  const Real distxz = distx * distz;
  const Real distyz = disty * distz;
 
#ifndef NDEBUG
  // totalorder is only used in the assertion below, so
  // we avoid declaring it when asserts are not active.
  const unsigned int totalorder = order + add_p_level*elem->p_level();
#endif
  libmesh_assert_less (i, (totalorder+1) * (totalorder+2) *
                       (totalorder+3)/6);
 
  // monomials. since they are hierarchic we only need one case block.
  switch (j)
    {
      // d^2()/dx^2
    case 0:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
            return 2./dist2x;
 
          case 5:
          case 6:
          case 7:
          case 8:
          case 9:
            return 0.;
 
            // cubic
          case 10:
            return 6.*dx/dist2x;
 
          case 11:
            return 2.*dy/dist2x;
 
          case 12:
          case 13:
            return 0.;
 
          case 14:
            return 2.*dz/dist2x;
 
          case 15:
          case 16:
          case 17:
          case 18:
          case 19:
            return 0.;
 
            // quartics
          case 20:
            return 12.*dx*dx/dist2x;
 
          case 21:
            return 6.*dx*dy/dist2x;
 
          case 22:
            return 2.*dy*dy/dist2x;
 
          case 23:
          case 24:
            return 0.;
 
          case 25:
            return 6.*dx*dz/dist2x;
 
          case 26:
            return 2.*dy*dz/dist2x;
 
          case 27:
          case 28:
            return 0.;
 
          case 29:
            return 2.*dz*dz/dist2x;
 
          case 30:
          case 31:
          case 32:
          case 33:
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            unsigned int i2 = i - (o*(o+1)*(o+2)/6);
            unsigned int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const unsigned int nx = block - i2;
            const unsigned int ny = o - nx - nz;
            Real val = nx * (nx - 1);
            for (unsigned int index=2; index < nx; index++)
              val *= dx;
            for (unsigned int index=0; index != ny; index++)
              val *= dy;
            for (unsigned int index=0; index != nz; index++)
              val *= dz;
            return val/dist2x;
          }
      }
 
 
      // d^2()/dxdy
    case 1:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
            return 0.;
 
          case 5:
            return 1./distxy;
 
          case 6:
          case 7:
          case 8:
          case 9:
            return 0.;
 
            // cubic
          case 10:
            return 0.;
 
          case 11:
            return 2.*dx/distxy;
 
          case 12:
            return 2.*dy/distxy;
 
          case 13:
          case 14:
            return 0.;
 
          case 15:
            return dz/distxy;
 
          case 16:
          case 17:
          case 18:
          case 19:
            return 0.;
 
            // quartics
          case 20:
            return 0.;
 
          case 21:
            return 3.*dx*dx/distxy;
 
          case 22:
            return 4.*dx*dy/distxy;
 
          case 23:
            return 3.*dy*dy/distxy;
 
          case 24:
          case 25:
            return 0.;
 
          case 26:
            return 2.*dx*dz/distxy;
 
          case 27:
            return 2.*dy*dz/distxy;
 
          case 28:
          case 29:
            return 0.;
 
          case 30:
            return dz*dz/distxy;
 
          case 31:
          case 32:
          case 33:
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            unsigned int i2 = i - (o*(o+1)*(o+2)/6);
            unsigned int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const unsigned int nx = block - i2;
            const unsigned int ny = o - nx - nz;
            Real val = nx * ny;
            for (unsigned int index=1; index < nx; index++)
              val *= dx;
            for (unsigned int index=1; index < ny; index++)
              val *= dy;
            for (unsigned int index=0; index != nz; index++)
              val *= dz;
            return val/distxy;
          }
      }
 
 
      // d^2()/dy^2
    case 2:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
          case 5:
            return 0.;
 
          case 6:
            return 2./dist2y;
 
          case 7:
          case 8:
          case 9:
            return 0.;
 
            // cubic
          case 10:
          case 11:
            return 0.;
 
          case 12:
            return 2.*dx/dist2y;
          case 13:
            return 6.*dy/dist2y;
 
          case 14:
          case 15:
            return 0.;
 
          case 16:
            return 2.*dz/dist2y;
 
          case 17:
          case 18:
          case 19:
            return 0.;
 
            // quartics
          case 20:
          case 21:
            return 0.;
 
          case 22:
            return 2.*dx*dx/dist2y;
 
          case 23:
            return 6.*dx*dy/dist2y;
 
          case 24:
            return 12.*dy*dy/dist2y;
 
          case 25:
          case 26:
            return 0.;
 
          case 27:
            return 2.*dx*dz/dist2y;
 
          case 28:
            return 6.*dy*dz/dist2y;
 
          case 29:
          case 30:
            return 0.;
 
          case 31:
            return 2.*dz*dz/dist2y;
 
          case 32:
          case 33:
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            unsigned int i2 = i - (o*(o+1)*(o+2)/6);
            unsigned int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const unsigned int nx = block - i2;
            const unsigned int ny = o - nx - nz;
            Real val = ny * (ny - 1);
            for (unsigned int index=0; index != nx; index++)
              val *= dx;
            for (unsigned int index=2; index < ny; index++)
              val *= dy;
            for (unsigned int index=0; index != nz; index++)
              val *= dz;
            return val/dist2y;
          }
      }
 
 
      // d^2()/dxdz
    case 3:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
          case 5:
          case 6:
            return 0.;
 
          case 7:
            return 1./distxz;
 
          case 8:
          case 9:
            return 0.;
 
            // cubic
          case 10:
          case 11:
          case 12:
          case 13:
            return 0.;
 
          case 14:
            return 2.*dx/distxz;
 
          case 15:
            return dy/distxz;
 
          case 16:
            return 0.;
 
          case 17:
            return 2.*dz/distxz;
 
          case 18:
          case 19:
            return 0.;
 
            // quartics
          case 20:
          case 21:
          case 22:
          case 23:
          case 24:
            return 0.;
 
          case 25:
            return 3.*dx*dx/distxz;
 
          case 26:
            return 2.*dx*dy/distxz;
 
          case 27:
            return dy*dy/distxz;
 
          case 28:
            return 0.;
 
          case 29:
            return 4.*dx*dz/distxz;
 
          case 30:
            return 2.*dy*dz/distxz;
 
          case 31:
            return 0.;
 
          case 32:
            return 3.*dz*dz/distxz;
 
          case 33:
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            unsigned int i2 = i - (o*(o+1)*(o+2)/6);
            unsigned int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const unsigned int nx = block - i2;
            const unsigned int ny = o - nx - nz;
            Real val = nx * nz;
            for (unsigned int index=1; index < nx; index++)
              val *= dx;
            for (unsigned int index=0; index != ny; index++)
              val *= dy;
            for (unsigned int index=1; index < nz; index++)
              val *= dz;
            return val/distxz;
          }
      }
 
      // d^2()/dydz
    case 4:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
          case 5:
          case 6:
          case 7:
            return 0.;
 
          case 8:
            return 1./distyz;
 
          case 9:
            return 0.;
 
            // cubic
          case 10:
          case 11:
          case 12:
          case 13:
          case 14:
            return 0.;
 
          case 15:
            return dx/distyz;
 
          case 16:
            return 2.*dy/distyz;
 
          case 17:
            return 0.;
 
          case 18:
            return 2.*dz/distyz;
 
          case 19:
            return 0.;
 
            // quartics
          case 20:
          case 21:
          case 22:
          case 23:
          case 24:
          case 25:
            return 0.;
 
          case 26:
            return dx*dx/distyz;
 
          case 27:
            return 2.*dx*dy/distyz;
 
          case 28:
            return 3.*dy*dy/distyz;
 
          case 29:
            return 0.;
 
          case 30:
            return 2.*dx*dz/distyz;
 
          case 31:
            return 4.*dy*dz/distyz;
 
          case 32:
            return 0.;
 
          case 33:
            return 3.*dz*dz/distyz;
 
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            unsigned int i2 = i - (o*(o+1)*(o+2)/6);
            unsigned int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const unsigned int nx = block - i2;
            const unsigned int ny = o - nx - nz;
            Real val = ny * nz;
            for (unsigned int index=0; index != nx; index++)
              val *= dx;
            for (unsigned int index=1; index < ny; index++)
              val *= dy;
            for (unsigned int index=1; index < nz; index++)
              val *= dz;
            return val/distyz;
          }
      }
 
 
      // d^2()/dz^2
    case 5:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
          case 5:
          case 6:
          case 7:
          case 8:
            return 0.;
 
          case 9:
            return 2./dist2z;
 
            // cubic
          case 10:
          case 11:
          case 12:
          case 13:
          case 14:
          case 15:
          case 16:
            return 0.;
 
          case 17:
            return 2.*dx/dist2z;
 
          case 18:
            return 2.*dy/dist2z;
 
          case 19:
            return 6.*dz/dist2z;
 
            // quartics
          case 20:
          case 21:
          case 22:
          case 23:
          case 24:
          case 25:
          case 26:
          case 27:
          case 28:
            return 0.;
 
          case 29:
            return 2.*dx*dx/dist2z;
 
          case 30:
            return 2.*dx*dy/dist2z;
 
          case 31:
            return 2.*dy*dy/dist2z;
 
          case 32:
            return 6.*dx*dz/dist2z;
 
          case 33:
            return 6.*dy*dz/dist2z;
 
          case 34:
            return 12.*dz*dz/dist2z;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            unsigned int i2 = i - (o*(o+1)*(o+2)/6);
            unsigned int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const unsigned int nx = block - i2;
            const unsigned int ny = o - nx - nz;
            Real val = nz * (nz - 1);
            for (unsigned int index=0; index != nx; index++)
              val *= dx;
            for (unsigned int index=0; index != ny; index++)
              val *= dy;
            for (unsigned int index=2; index < nz; index++)
              val *= dz;
            return val/dist2z;
          }
      }
 
 
    default:
      libmesh_error_msg("Invalid j = " << j);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_assert(true || order || add_p_level);
  libmesh_ignore(elem, i, j, point_in);
  libmesh_not_implemented();
#endif
}

shape_second_deriv() [29/233]

Real libMesh::FE< 1, XYZ >::shape_second_deriv ( const Elem *  elem, const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  libmesh_dbg_varj, const Point &  point_in, const bool  libmesh_dbg_varadd_p_level  )

inherited

Definition at line 194 of file fe_xyz_shape_1D.C.

{
  libmesh_assert(elem);
  libmesh_assert_less_equal (i, order + add_p_level * elem->p_level());
 
  // only d2()/dxi2 in 1D!
 
  libmesh_assert_equal_to (j, 0);
 
  Point avg = elem->vertex_average();
  Real max_distance = 0.;
  for (const Point & p : elem->node_ref_range())
    {
      const Real distance = std::abs(avg(0) - p(0));
      max_distance = std::max(distance, max_distance);
    }
 
  const Real x  = point_in(0);
  const Real xc = avg(0);
  const Real dx = (x - xc)/max_distance;
  const Real dist2 = pow(max_distance,2.);
 
  // monomials. since they are hierarchic we only need one case block.
  switch (i)
    {
    case 0:
    case 1:
      return 0.;
 
    case 2:
      return 2./dist2;
 
    case 3:
      return 6.*dx/dist2;
 
    case 4:
      return 12.*dx*dx/dist2;
 
    default:
      Real val = 2.;
      for (unsigned int index = 2; index != i; ++index)
        val *= (index+1) * dx;
      return val/dist2;
    }
}

shape_second_deriv() [30/233]

Real libMesh::FE< 1, HERMITE >::shape_second_deriv ( const Elem *  elem, const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  , const Point &  p, const bool  libmesh_dbg_varadd_p_level  )

inherited

Definition at line 333 of file fe_hermite_shape_1D.C.

{
  libmesh_assert(elem);
 
  // Coefficient naming: d(1)d(2n) is the coefficient of the
  // global shape function corresponding to value 1 in terms of the
  // local shape function corresponding to normal derivative 2
  Real d1xd1x, d2xd2x;
 
  hermite_compute_coefs(elem, d1xd1x, d2xd2x);
 
  const ElemType type = elem->type();
 
#ifndef NDEBUG
  const unsigned int totalorder =
    order + add_p_level * elem->p_level();
#endif
 
  switch (type)
    {
      // C1 functions on the C1 cubic edge
    case EDGE2:
    case EDGE3:
      {
        libmesh_assert_less (i, totalorder+1);
 
        switch (i)
          {
          case 0:
            return FEHermite<1>::hermite_raw_shape_second_deriv(0, p(0));
          case 1:
            return d1xd1x * FEHermite<1>::hermite_raw_shape_second_deriv(2, p(0));
          case 2:
            return FEHermite<1>::hermite_raw_shape_second_deriv(1, p(0));
          case 3:
            return d2xd2x * FEHermite<1>::hermite_raw_shape_second_deriv(3, p(0));
          default:
            return FEHermite<1>::hermite_raw_shape_second_deriv(i, p(0));
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
    }
}

shape_second_deriv() [31/233]

static OutputShape libMesh::FE< Dim, T >::shape_second_deriv ( const Elem *  elem, const Order  o, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level = true  )

staticinherited

Returns

The second \( j^{th} \) derivative of the \( i^{th} \) shape function at the point p.

Note

Cross-derivatives are indexed according to: j = 0 ==> d^2 phi / dxi^2 j = 1 ==> d^2 phi / dxi deta j = 2 ==> d^2 phi / deta^2 j = 3 ==> d^2 phi / dxi dzeta j = 4 ==> d^2 phi / deta dzeta j = 5 ==> d^2 phi / dzeta^2

Computing second derivatives is not currently supported for all element types: \( C^1 \) (Clough, Hermite and Subdivision), Lagrange, Hierarchic, L2_Hierarchic, and Monomial are supported. All other element types return an error when asked for second derivatives.

On a p-refined element, o should be the base order of the element if add_p_level is left true, or can be the base order of the element if add_p_level is set to false.

shape_second_deriv() [32/233]

RealGradient libMesh::FE< 3, NEDELEC_ONE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  , const bool  add_p_level  )

inherited

Definition at line 424 of file fe_nedelec_one_shape_3D.C.

{
#if LIBMESH_DIM == 3
 
  libmesh_assert(elem);
 
  // j = 0 ==> d^2 phi / dxi^2
  // j = 1 ==> d^2 phi / dxi deta
  // j = 2 ==> d^2 phi / deta^2
  // j = 3 ==> d^2 phi / dxi dzeta
  // j = 4 ==> d^2 phi / deta dzeta
  // j = 5 ==> d^2 phi / dzeta^2
  libmesh_assert_less (j, 6);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = elem->positive_edge_orientation(i) ? 1 : -1;
 
  switch (totalorder)
    {
      // linear Nedelec (first kind) shape function second derivatives
    case FIRST:
      {
        switch (elem->type())
          {
          case HEX20:
          case HEX27:
            {
              switch (j)
                {
                  // d^2()/dxi^2, d^2()/deta^2, d^2()/dzeta^2
                case 0:
                case 2:
                case 5:
                  return RealGradient();
 
                  // d^2()/dxideta
                case 1:
                  {
                    switch(i)
                      {
                      case 0:
                      case 1:
                      case 2:
                      case 3:
                      case 8:
                      case 9:
                      case 10:
                      case 11:
                        return RealGradient();
                      case 4:
                      case 6:
                        return sign * RealGradient( 0.0, 0.0, -0.125 );
                      case 5:
                      case 7:
                        return sign * RealGradient( 0.0, 0.0, 0.125 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 1
 
                  // d^2()/dxidzeta
                case 3:
                  {
                    switch(i)
                      {
                      case 0:
                      case 2:
                      case 4:
                      case 5:
                      case 6:
                      case 7:
                      case 8:
                      case 10:
                        return RealGradient();
                      case 1:
                      case 3:
                      case 11:
                        return sign * RealGradient( 0.0, 0.125 );
                      case 9:
                        return sign * RealGradient( 0.0, -0.125, 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 3
 
                  // d^2()/detadzeta
                case 4:
                  {
                    switch(i)
                      {
                      case 0:
                        return sign * RealGradient( -0.125, 0.0, 0.0 );
                      case 1:
                      case 3:
                      case 4:
                      case 5:
                      case 6:
                      case 7:
                      case 9:
                      case 11:
                        return RealGradient();
                      case 2:
                      case 8:
                      case 10:
                        return sign * RealGradient( 0.125, 0.0, 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      } // switch(i)
 
                  } // j = 4
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
            // All second derivatives for linear tets are zero.
          case TET10:
          case TET14:
            return RealGradient();
 
          default:
            libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
 
          } //switch(type)
 
      }
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_assert(true || p(0));
  libmesh_ignore(elem, order, i, j, add_p_level);
  libmesh_not_implemented();
#endif
}

shape_second_deriv() [33/233]

Real libMesh::FE< 2, SUBDIVISION >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

shape_second_deriv() [34/233]

Real libMesh::FE< 1, BERNSTEIN >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 593 of file fe_bernstein_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,BERNSTEIN>::shape_second_deriv
    (elem->type(),
     order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [35/233]

Real libMesh::FE< 2, BERNSTEIN >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 544 of file fe_bernstein_shape_2D.C.

{
  libmesh_assert(elem);
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (type)
    {
      // Hierarchic shape functions on the quadrilateral.
    case QUAD4:
    case QUAD9:
    case QUADSHELL9:
      {
        // Compute quad shape functions as a tensor-product
        auto [i0, i1] = quad_i0_i1(i, totalorder, *elem);
 
        switch (j)
          {
            // d^2() / dxi^2
          case 0:
            return (FE<1,BERNSTEIN>::shape_second_deriv(EDGE3, totalorder, i0, 0, p(0))*
                    FE<1,BERNSTEIN>::shape             (EDGE3, totalorder, i1,    p(1)));
 
            // d^2() / dxi deta
          case 1:
            return (FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i0, 0, p(0))*
                    FE<1,BERNSTEIN>::shape_deriv(EDGE3, totalorder, i1, 0, p(1)));
 
            // d^2() / deta^2
          case 2:
            return (FE<1,BERNSTEIN>::shape             (EDGE3, totalorder, i0,    p(0))*
                    FE<1,BERNSTEIN>::shape_second_deriv(EDGE3, totalorder, i1, 0, p(1)));
 
          default:
            libmesh_error_msg("Invalid shape function derivative j = " << j);
          }
      }
 
      // Going to be lazy again about the hard cases.
    case TRI3:
    case TRISHELL3:
      libmesh_assert_less (totalorder, 2);
      libmesh_fallthrough();
    case QUAD8:
    case QUADSHELL8:
    case TRI6:
    case TRI7:
      {
        return fe_fdm_second_deriv(elem, order, i, j, p, add_p_level,
                                   FE<2,BERNSTEIN>::shape_deriv);
      }
 
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
    }
}

shape_second_deriv() [36/233]

Real libMesh::FE< 3, BERNSTEIN >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 2342 of file fe_bernstein_shape_3D.C.

{
  return fe_fdm_second_deriv(elem, order, i, j, p, add_p_level,
                             FE<3,BERNSTEIN>::shape_deriv);
}

shape_second_deriv() [37/233]

Real libMesh::FE< 1, CLOUGH >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 385 of file fe_clough_shape_1D.C.

{
  libmesh_assert(elem);
 
  clough_compute_coefs(elem);
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (totalorder)
    {
      // 3rd-order C1 cubic element
    case THIRD:
      {
        switch (type)
          {
            // C1 functions on the C1 cubic edge
          case EDGE2:
          case EDGE3:
            {
              switch (i)
                {
                case 0:
                  return clough_raw_shape_second_deriv(0, j, p);
                case 1:
                  return clough_raw_shape_second_deriv(1, j, p);
                case 2:
                  return d1xd1x * clough_raw_shape_second_deriv(2, j, p);
                case 3:
                  return d2xd2x * clough_raw_shape_second_deriv(3, j, p);
                default:
                  libmesh_error_msg("Invalid shape function index i = " << i);
                }
            }
          default:
            libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
          }
      }
      // by default throw an error
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order = " << totalorder);
    }
}

shape_second_deriv() [38/233]

Real libMesh::FE< 2, CLOUGH >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 2183 of file fe_clough_shape_2D.C.

{
  libmesh_assert(elem);
 
  CloughCoefs coefs;
  clough_compute_coefs(elem, coefs);
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (totalorder)
    {
      // 2nd-order restricted Clough-Tocher element
    case SECOND:
      {
        switch (type)
          {
            // C1 functions on the Clough-Tocher triangle.
          case TRI6:
          case TRI7:
            {
              libmesh_assert_less (i, 9);
              // FIXME: it would be nice to calculate (and cache)
              // clough_raw_shape(j,p) only once per triangle, not 1-7
              // times
              switch (i)
                {
                  // Note: these DoF numbers are "scrambled" because my
                  // initial numbering conventions didn't match libMesh
                case 0:
                  return clough_raw_shape_second_deriv(0, j, p)
                    + coefs.d1d2n * clough_raw_shape_second_deriv(10, j, p)
                    + coefs.d1d3n * clough_raw_shape_second_deriv(11, j, p);
                case 3:
                  return clough_raw_shape_second_deriv(1, j, p)
                    + coefs.d2d3n * clough_raw_shape_second_deriv(11, j, p)
                    + coefs.d2d1n * clough_raw_shape_second_deriv(9, j, p);
                case 6:
                  return clough_raw_shape_second_deriv(2, j, p)
                    + coefs.d3d1n * clough_raw_shape_second_deriv(9, j, p)
                    + coefs.d3d2n * clough_raw_shape_second_deriv(10, j, p);
                case 1:
                  return coefs.d1xd1x * clough_raw_shape_second_deriv(3, j, p)
                    + coefs.d1xd1y * clough_raw_shape_second_deriv(4, j, p)
                    + coefs.d1xd2n * clough_raw_shape_second_deriv(10, j, p)
                    + coefs.d1xd3n * clough_raw_shape_second_deriv(11, j, p)
                    + 0.5 * coefs.N01x * coefs.d3nd3n * clough_raw_shape_second_deriv(11, j, p)
                    + 0.5 * coefs.N02x * coefs.d2nd2n * clough_raw_shape_second_deriv(10, j, p);
                case 2:
                  return coefs.d1yd1y * clough_raw_shape_second_deriv(4, j, p)
                    + coefs.d1yd1x * clough_raw_shape_second_deriv(3, j, p)
                    + coefs.d1yd2n * clough_raw_shape_second_deriv(10, j, p)
                    + coefs.d1yd3n * clough_raw_shape_second_deriv(11, j, p)
                    + 0.5 * coefs.N01y * coefs.d3nd3n * clough_raw_shape_second_deriv(11, j, p)
                    + 0.5 * coefs.N02y * coefs.d2nd2n * clough_raw_shape_second_deriv(10, j, p);
                case 4:
                  return coefs.d2xd2x * clough_raw_shape_second_deriv(5, j, p)
                    + coefs.d2xd2y * clough_raw_shape_second_deriv(6, j, p)
                    + coefs.d2xd3n * clough_raw_shape_second_deriv(11, j, p)
                    + coefs.d2xd1n * clough_raw_shape_second_deriv(9, j, p)
                    + 0.5 * coefs.N10x * coefs.d3nd3n * clough_raw_shape_second_deriv(11, j, p)
                    + 0.5 * coefs.N12x * coefs.d1nd1n * clough_raw_shape_second_deriv(9, j, p);
                case 5:
                  return coefs.d2yd2y * clough_raw_shape_second_deriv(6, j, p)
                    + coefs.d2yd2x * clough_raw_shape_second_deriv(5, j, p)
                    + coefs.d2yd3n * clough_raw_shape_second_deriv(11, j, p)
                    + coefs.d2yd1n * clough_raw_shape_second_deriv(9, j, p)
                    + 0.5 * coefs.N10y * coefs.d3nd3n * clough_raw_shape_second_deriv(11, j, p)
                    + 0.5 * coefs.N12y * coefs.d1nd1n * clough_raw_shape_second_deriv(9, j, p);
                case 7:
                  return coefs.d3xd3x * clough_raw_shape_second_deriv(7, j, p)
                    + coefs.d3xd3y * clough_raw_shape_second_deriv(8, j, p)
                    + coefs.d3xd1n * clough_raw_shape_second_deriv(9, j, p)
                    + coefs.d3xd2n * clough_raw_shape_second_deriv(10, j, p)
                    + 0.5 * coefs.N20x * coefs.d2nd2n * clough_raw_shape_second_deriv(10, j, p)
                    + 0.5 * coefs.N21x * coefs.d1nd1n * clough_raw_shape_second_deriv(9, j, p);
                case 8:
                  return coefs.d3yd3y * clough_raw_shape_second_deriv(8, j, p)
                    + coefs.d3yd3x * clough_raw_shape_second_deriv(7, j, p)
                    + coefs.d3yd1n * clough_raw_shape_second_deriv(9, j, p)
                    + coefs.d3yd2n * clough_raw_shape_second_deriv(10, j, p)
                    + 0.5 * coefs.N20y * coefs.d2nd2n * clough_raw_shape_second_deriv(10, j, p)
                    + 0.5 * coefs.N21y * coefs.d1nd1n * clough_raw_shape_second_deriv(9, j, p);
                default:
                  libmesh_error_msg("Invalid shape function index i = " << i);
                }
            }
          default:
            libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
          }
      }
      // 3rd-order Clough-Tocher element
    case THIRD:
      {
        switch (type)
          {
            // C1 functions on the Clough-Tocher triangle.
          case TRI6:
          case TRI7:
            {
              libmesh_assert_less (i, 12);
 
              // FIXME: it would be nice to calculate (and cache)
              // clough_raw_shape(j,p) only once per triangle, not 1-7
              // times
              switch (i)
                {
                  // Note: these DoF numbers are "scrambled" because my
                  // initial numbering conventions didn't match libMesh
                case 0:
                  return clough_raw_shape_second_deriv(0, j, p)
                    + coefs.d1d2n * clough_raw_shape_second_deriv(10, j, p)
                    + coefs.d1d3n * clough_raw_shape_second_deriv(11, j, p);
                case 3:
                  return clough_raw_shape_second_deriv(1, j, p)
                    + coefs.d2d3n * clough_raw_shape_second_deriv(11, j, p)
                    + coefs.d2d1n * clough_raw_shape_second_deriv(9, j, p);
                case 6:
                  return clough_raw_shape_second_deriv(2, j, p)
                    + coefs.d3d1n * clough_raw_shape_second_deriv(9, j, p)
                    + coefs.d3d2n * clough_raw_shape_second_deriv(10, j, p);
                case 1:
                  return coefs.d1xd1x * clough_raw_shape_second_deriv(3, j, p)
                    + coefs.d1xd1y * clough_raw_shape_second_deriv(4, j, p)
                    + coefs.d1xd2n * clough_raw_shape_second_deriv(10, j, p)
                    + coefs.d1xd3n * clough_raw_shape_second_deriv(11, j, p);
                case 2:
                  return coefs.d1yd1y * clough_raw_shape_second_deriv(4, j, p)
                    + coefs.d1yd1x * clough_raw_shape_second_deriv(3, j, p)
                    + coefs.d1yd2n * clough_raw_shape_second_deriv(10, j, p)
                    + coefs.d1yd3n * clough_raw_shape_second_deriv(11, j, p);
                case 4:
                  return coefs.d2xd2x * clough_raw_shape_second_deriv(5, j, p)
                    + coefs.d2xd2y * clough_raw_shape_second_deriv(6, j, p)
                    + coefs.d2xd3n * clough_raw_shape_second_deriv(11, j, p)
                    + coefs.d2xd1n * clough_raw_shape_second_deriv(9, j, p);
                case 5:
                  return coefs.d2yd2y * clough_raw_shape_second_deriv(6, j, p)
                    + coefs.d2yd2x * clough_raw_shape_second_deriv(5, j, p)
                    + coefs.d2yd3n * clough_raw_shape_second_deriv(11, j, p)
                    + coefs.d2yd1n * clough_raw_shape_second_deriv(9, j, p);
                case 7:
                  return coefs.d3xd3x * clough_raw_shape_second_deriv(7, j, p)
                    + coefs.d3xd3y * clough_raw_shape_second_deriv(8, j, p)
                    + coefs.d3xd1n * clough_raw_shape_second_deriv(9, j, p)
                    + coefs.d3xd2n * clough_raw_shape_second_deriv(10, j, p);
                case 8:
                  return coefs.d3yd3y * clough_raw_shape_second_deriv(8, j, p)
                    + coefs.d3yd3x * clough_raw_shape_second_deriv(7, j, p)
                    + coefs.d3yd1n * clough_raw_shape_second_deriv(9, j, p)
                    + coefs.d3yd2n * clough_raw_shape_second_deriv(10, j, p);
                case 10:
                  return coefs.d1nd1n * clough_raw_shape_second_deriv(9, j, p);
                case 11:
                  return coefs.d2nd2n * clough_raw_shape_second_deriv(10, j, p);
                case 9:
                  return coefs.d3nd3n * clough_raw_shape_second_deriv(11, j, p);
 
                default:
                  libmesh_error_msg("Invalid shape function index i = " << i);
                }
            }
          default:
            libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
          }
      }
      // by default throw an error
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order = " << order);
    }
}

shape_second_deriv() [39/233]

Real libMesh::FE< 2, HERMITE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 364 of file fe_hermite_shape_2D.C.

{
  libmesh_assert(elem);
  libmesh_assert (j == 0 || j == 1 || j == 2);
 
  std::vector<std::vector<Real>> dxdxi(2, std::vector<Real>(2, 0));
 
#ifdef DEBUG
  std::vector<Real> dxdeta(2), dydxi(2);
#endif
 
  hermite_compute_coefs(elem,dxdxi
#ifdef DEBUG
                        ,dxdeta,dydxi
#endif
                        );
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (type)
    {
    case QUAD4:
    case QUADSHELL4:
      libmesh_assert_less (totalorder, 4);
      libmesh_fallthrough();
    case QUAD8:
    case QUADSHELL8:
    case QUAD9:
    case QUADSHELL9:
      {
        libmesh_assert_less (i, (totalorder+1u)*(totalorder+1u));
 
        std::vector<unsigned int> bases1D;
 
        Real coef = hermite_bases_2D(bases1D, dxdxi, totalorder, i);
 
        switch (j)
          {
          case 0:
            return coef *
              FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[0],p(0)) *
              FEHermite<1>::hermite_raw_shape(bases1D[1],p(1));
          case 1:
            return coef *
              FEHermite<1>::hermite_raw_shape_deriv(bases1D[0],p(0)) *
              FEHermite<1>::hermite_raw_shape_deriv(bases1D[1],p(1));
          case 2:
            return coef *
              FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
              FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[1],p(1));
          default:
            libmesh_error_msg("Invalid derivative index j = " << j);
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(type));
    }
}

shape_second_deriv() [40/233]

Real libMesh::FE< 3, HERMITE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 575 of file fe_hermite_shape_3D.C.

{
  libmesh_assert(elem);
 
  std::vector<std::vector<Real>> dxdxi(3, std::vector<Real>(2, 0));
 
#ifdef DEBUG
  std::vector<Real> dydxi(2), dzdeta(2), dxdzeta(2);
  std::vector<Real> dzdxi(2), dxdeta(2), dydzeta(2);
#endif //DEBUG
 
  hermite_compute_coefs(elem, dxdxi
#ifdef DEBUG
                        , dydxi, dzdeta, dxdzeta, dzdxi, dxdeta, dydzeta
#endif
                        );
 
  const ElemType type = elem->type();
 
  const Order totalorder =
    order + add_p_level*elem->p_level();
 
  switch (totalorder)
    {
      // 3rd-order tricubic Hermite functions
    case THIRD:
      {
        switch (type)
          {
          case HEX8:
          case HEX20:
          case HEX27:
            {
              libmesh_assert_less (i, 64);
 
              std::vector<unsigned int> bases1D;
 
              Real coef = hermite_bases_3D(bases1D, dxdxi, totalorder, i);
 
              switch (j) // Derivative type
                {
                case 0:
                  return coef *
                    FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[0],p(0)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[1],p(1)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[2],p(2));
                  break;
                case 1:
                  return coef *
                    FEHermite<1>::hermite_raw_shape_deriv(bases1D[0],p(0)) *
                    FEHermite<1>::hermite_raw_shape_deriv(bases1D[1],p(1)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[2],p(2));
                  break;
                case 2:
                  return coef *
                    FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
                    FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[1],p(1)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[2],p(2));
                  break;
                case 3:
                  return coef *
                    FEHermite<1>::hermite_raw_shape_deriv(bases1D[0],p(0)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[1],p(1)) *
                    FEHermite<1>::hermite_raw_shape_deriv(bases1D[2],p(2));
                  break;
                case 4:
                  return coef *
                    FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
                    FEHermite<1>::hermite_raw_shape_deriv(bases1D[1],p(1)) *
                    FEHermite<1>::hermite_raw_shape_deriv(bases1D[2],p(2));
                  break;
                case 5:
                  return coef *
                    FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
                    FEHermite<1>::hermite_raw_shape(bases1D[1],p(1)) *
                    FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[2],p(2));
                  break;
                default:
                  libmesh_error_msg("Invalid shape function derivative j = " << j);
                }
 
            }
          default:
            libmesh_error_msg("ERROR: Unsupported element type " << Utility::enum_to_string(type));
          }
      }
      // by default throw an error
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order " << totalorder);
    }
}

shape_second_deriv() [41/233]

Real libMesh::FE< 1, HIERARCHIC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 339 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_hierarchic_1D_shape_second_deriv(elem->type(),
                                             order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [42/233]

Real libMesh::FE< 1, L2_HIERARCHIC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 369 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_hierarchic_1D_shape_second_deriv(elem->type(),
                                             order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [43/233]

Real libMesh::FE< 2, HIERARCHIC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 734 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape_second_deriv<HIERARCHIC>(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [44/233]

Real libMesh::FE< 2, L2_HIERARCHIC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 758 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape_second_deriv<L2_HIERARCHIC>(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [45/233]

Real libMesh::FE< 2, SIDE_HIERARCHIC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 782 of file fe_hierarchic_shape_2D.C.

{
  libmesh_assert(elem);
  const ElemType type = elem->type();
 
  const Order totalorder = order + add_p_level*elem->p_level();
 
  if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
    return 0;
 
  const unsigned int dofs_per_side = totalorder+1u;
 
  switch (type)
    {
    case TRI6:
    case TRI7:
      {
        return fe_fdm_second_deriv(elem, order, i, j, p, add_p_level,
                                   FE<2,SIDE_HIERARCHIC>::shape_deriv);
      }
    case QUAD8:
    case QUADSHELL8:
    case QUAD9:
    case QUADSHELL9:
      {
        libmesh_assert_less(i, 4*dofs_per_side);
 
        // Flip odd degree of freedom values if necessary
        // to keep continuity on sides.  We'll flip xi/eta rather than
        // flipping phi, so that we can use this to handle the "nodal"
        // degrees of freedom too.
        Real f = 1.;
 
        const Real xi = p(0), eta = p(1);
        if (eta < xi)
          {
            if (eta < -xi) // side 0
              {
                if (i >= dofs_per_side)
                  return 0;
                if (j != 0)
                  return 0;
                if ((i < 2 || i % 2) &&
                    elem->positive_edge_orientation(0))
                  f = -1;
 
                return FE<1,HIERARCHIC>::shape_second_deriv(EDGE3, totalorder, i, 0, f*xi);
              }
            else           // side 1
              {
                if (i < dofs_per_side ||
                    i >= 2*dofs_per_side)
                  return 0;
                if (j != 2)
                  return 0;
 
                const unsigned int side_i = i - dofs_per_side;
 
                if ((side_i < 2 || side_i % 2) &&
                    elem->positive_edge_orientation(1))
                  f = -1;
 
                return FE<1,HIERARCHIC>::shape_second_deriv(EDGE3, totalorder, side_i, 0, f*eta);
              }
          }
        else // xi < eta
          {
            if (eta > -xi)    // side 2
              {
                if (i < 2*dofs_per_side ||
                    i >= 3*dofs_per_side)
                  return 0;
                if (j != 0)
                  return 0;
 
                const unsigned int side_i = i - 2*dofs_per_side;
 
                if ((side_i < 2 || side_i % 2) &&
                    !elem->positive_edge_orientation(2))
                  f = -1;
 
                return FE<1,HIERARCHIC>::shape_second_deriv(EDGE3, totalorder, side_i, 0, f*xi);
              }
            else           // side 3
              {
                if (i < 3*dofs_per_side)
                  return 0;
                if (j != 2)
                  return 0;
 
                const unsigned int side_i = i - 3*dofs_per_side;
 
                if ((side_i < 2 || side_i % 2) &&
                    !elem->positive_edge_orientation(3))
                  f = -1;
 
                return FE<1,HIERARCHIC>::shape_second_deriv(EDGE3, totalorder, side_i, 0, f*eta);
              }
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported element type = " << Utility::enum_to_string(elem->type()));
    }
  return 0;
}

shape_second_deriv() [46/233]

Real libMesh::FE< 3, HIERARCHIC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1807 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape_second_deriv<HIERARCHIC>(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [47/233]

Real libMesh::FE< 3, L2_HIERARCHIC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1833 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape_second_deriv<L2_HIERARCHIC>(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [48/233]

Real libMesh::FE< 3, SIDE_HIERARCHIC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1857 of file fe_hierarchic_shape_3D.C.

{
#if LIBMESH_DIM == 3
  libmesh_assert(elem);
  const ElemType type = elem->type();
 
  const Order totalorder = order + add_p_level*elem->p_level();
 
  if (totalorder == 0) // special case since raw HIERARCHIC lacks CONSTANTs
    return 0; // constants have zero derivative
 
  switch (type)
    {
    case HEX27:
      {
        // I need to debug the p>2 case here...
        if (totalorder > 2)
          return fe_fdm_second_deriv(elem, order, i, j, p, add_p_level,
                                     FE<3,SIDE_HIERARCHIC>::shape_deriv);
 
        const unsigned int dofs_per_side = (totalorder+1u)*(totalorder+1u);
        libmesh_assert_less(i, 6*dofs_per_side);
 
        const unsigned int sidenum = cube_side(p);
        if (sidenum > 5)
          return std::numeric_limits<Real>::quiet_NaN();
 
        const unsigned int dof_offset = sidenum * dofs_per_side;
 
        if (i < dof_offset) // i is on a previous side
          return 0;
 
        if (i >= dof_offset + dofs_per_side) // i is on a later side
          return 0;
 
        unsigned int side_i = i - dof_offset;
 
        std::unique_ptr<const Elem> side = elem->build_side_ptr(sidenum);
 
        Point sidep = cube_side_point(sidenum, p);
 
        cube_remap(side_i, *side, totalorder, sidep);
 
        // What second derivative or mixed derivative on the side
        // corresponds to the xi/eta/zeta mix we were asked for?
        unsigned int sidej = 100;
 
        // Do we need a -1 here to flip the final derivative value?
        Real f = 1.;
 
        switch (j)
          {
          case 0: // d^2()/dxi^2
            {
              switch (sidenum)
                {
                case 0:
                  sidej = 2;
                  break;
                case 1:
                  sidej = 0;
                  break;
                case 2:
                  return 0;
                case 3:
                  sidej = 0;
                  break;
                case 4:
                  return 0;
                case 5:
                  sidej = 0;
                  break;
                default:
                  libmesh_error();
                }
              break;
            }
          case 1: // d^2()/dxideta
            {
              switch (sidenum)
                {
                case 0:
                  sidej = 1;
                  break;
                case 1:
                case 2:
                case 3:
                case 4:
                  return 0;
                case 5:
                  sidej = 1;
                  break;
                default:
                  libmesh_error();
                }
              break;
            }
          case 2: // d^2()/deta^2
            {
              switch (sidenum)
                {
                case 0:
                  sidej = 0;
                  break;
                case 1:
                  return 0;
                case 2:
                  sidej = 0;
                  break;
                case 3:
                  return 0;
                case 4:
                  sidej = 0;
                  break;
                case 5:
                  sidej = 2;
                  break;
                default:
                  libmesh_error();
                }
              break;
            }
          case 3: // d^2()/dxidzeta
            {
              switch (sidenum)
                {
                case 0:
                  return 0;
                case 1:
                  sidej = 1;
                  break;
                case 2:
                  return 0;
                case 3:
                  sidej = 1;
                  f = -1;
                  break;
                case 4:
                case 5:
                  return 0;
                default:
                  libmesh_error();
                }
              break;
            }
          case 4: // d^2()/detadzeta
            {
              switch (sidenum)
                {
                case 0:
                case 1:
                  return 0;
                case 2:
                  sidej = 1;
                  break;
                case 3:
                  return 0;
                case 4:
                  sidej = 1;
                  f = -1;
                  break;
                case 5:
                  return 0;
                default:
                  libmesh_error();
                }
              break;
            }
          case 5: // d^2()/dzeta^2
            {
              switch (sidenum)
                {
                case 0:
                  return 0;
                case 1:
                case 2:
                case 3:
                case 4:
                  sidej = 2;
                  break;
                case 5:
                  return 0;
                default:
                  libmesh_error();
                }
              break;
            }
 
          default:
            libmesh_error_msg("Invalid derivative index j = " << j);
          }
 
        return f * FE<2,HIERARCHIC>::shape_second_deriv(side.get(),
                                                        order, side_i,
                                                        sidej, sidep,
                                                        add_p_level);
      }
 
    case TET14:
    case PRISM20:
    case PRISM21:
      {
        return fe_fdm_second_deriv(elem, order, i, j, p, add_p_level,
                                   FE<3,SIDE_HIERARCHIC>::shape_deriv);
      }
 
    default:
      libmesh_error_msg("Invalid element type = " << Utility::enum_to_string(type));
    }
 
#else // LIBMESH_DIM != 3
  libmesh_ignore(elem, order, i, j, p, add_p_level);
  libmesh_not_implemented();
#endif
}

shape_second_deriv() [49/233]

RealGradient libMesh::FE< 0, HIERARCHIC_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 436 of file fe_hierarchic_vec.C.

{
  Real value = FE<0,HIERARCHIC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
  return libMesh::RealGradient( value );
}

shape_second_deriv() [50/233]

RealGradient libMesh::FE< 0, L2_HIERARCHIC_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 464 of file fe_hierarchic_vec.C.

{
  return FE<0,HIERARCHIC_VEC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [51/233]

RealGradient libMesh::FE< 1, HIERARCHIC_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 492 of file fe_hierarchic_vec.C.

{
  Real value = FE<1,HIERARCHIC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
  return libMesh::RealGradient( value );
}

shape_second_deriv() [52/233]

RealGradient libMesh::FE< 1, L2_HIERARCHIC_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 520 of file fe_hierarchic_vec.C.

{
  return FE<1,HIERARCHIC_VEC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [53/233]

RealGradient libMesh::FE< 2, HIERARCHIC_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 576 of file fe_hierarchic_vec.C.

{
  const Real value = FE<2,HIERARCHIC>::shape_second_deriv(elem, order, i/2, j, p, add_p_level);
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_second_deriv() [54/233]

RealGradient libMesh::FE< 2, L2_HIERARCHIC_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 617 of file fe_hierarchic_vec.C.

{
  return FE<2,HIERARCHIC_VEC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [55/233]

RealGradient libMesh::FE< 3, HIERARCHIC_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 681 of file fe_hierarchic_vec.C.

{
  const Real value = FE<3,HIERARCHIC>::shape_second_deriv(elem, order, i/3, j, p, add_p_level);
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_second_deriv() [56/233]

RealGradient libMesh::FE< 3, L2_HIERARCHIC_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 726 of file fe_hierarchic_vec.C.

{
  return FE<3,HIERARCHIC_VEC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [57/233]

Real libMesh::FE< 1, LAGRANGE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 208 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_lagrange_1D_shape_second_deriv(order + add_p_level*elem->p_level(), i, j, p(0));
}

shape_second_deriv() [58/233]

Real libMesh::FE< 1, L2_LAGRANGE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 223 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
 
  return fe_lagrange_1D_shape_second_deriv(order + add_p_level*elem->p_level(), i, j, p(0));
}

shape_second_deriv() [59/233]

Real libMesh::FE< 2, LAGRANGE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 257 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape functions
  return fe_lagrange_2D_shape_second_deriv<LAGRANGE>(elem->type(), elem, order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [60/233]

Real libMesh::FE< 2, L2_LAGRANGE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 273 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape functions
  return fe_lagrange_2D_shape_second_deriv<L2_LAGRANGE>(elem->type(), elem, order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [61/233]

Real libMesh::FE< 3, LAGRANGE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 600 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape function derivatives
  return fe_lagrange_3D_shape_second_deriv<LAGRANGE>
    (elem->type(), order + add_p_level*elem->p_level(), elem, i, j, p);
}

shape_second_deriv() [62/233]

Real libMesh::FE< 3, L2_LAGRANGE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 617 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape function derivatives
  return fe_lagrange_3D_shape_second_deriv<L2_LAGRANGE>
    (elem->type(), order + add_p_level*elem->p_level(), elem, i, j, p);
}

shape_second_deriv() [63/233]

RealGradient libMesh::FE< 0, LAGRANGE_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 976 of file fe_lagrange_vec.C.

{
  Real value = FE<0,LAGRANGE>::shape_second_deriv( elem->type(), order + add_p_level*elem->p_level(), i, j, p);
  return libMesh::RealGradient( value );
}

shape_second_deriv() [64/233]

RealGradient libMesh::FE< 0, L2_LAGRANGE_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1003 of file fe_lagrange_vec.C.

{
  return FE<0,LAGRANGE_VEC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [65/233]

RealGradient libMesh::FE< 1, LAGRANGE_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1031 of file fe_lagrange_vec.C.

{
  Real value = FE<1,LAGRANGE>::shape_second_deriv( elem->type(), order + add_p_level*elem->p_level(), i, j, p);
  return libMesh::RealGradient( value );
}

shape_second_deriv() [66/233]

RealGradient libMesh::FE< 1, L2_LAGRANGE_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1058 of file fe_lagrange_vec.C.

{
  return FE<1,LAGRANGE_VEC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [67/233]

RealGradient libMesh::FE< 2, LAGRANGE_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1114 of file fe_lagrange_vec.C.

{
  Real value = FE<2,LAGRANGE>::shape_second_deriv( elem->type(), order + add_p_level*elem->p_level(), i/2, j, p );
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_second_deriv() [68/233]

RealGradient libMesh::FE< 2, L2_LAGRANGE_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1155 of file fe_lagrange_vec.C.

{
  return FE<2,LAGRANGE_VEC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [69/233]

RealGradient libMesh::FE< 3, LAGRANGE_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1218 of file fe_lagrange_vec.C.

{
  Real value = FE<3,LAGRANGE>::shape_second_deriv( elem->type(), order + add_p_level*elem->p_level(), i/3, j, p );
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_second_deriv() [70/233]

RealGradient libMesh::FE< 3, L2_LAGRANGE_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1262 of file fe_lagrange_vec.C.

{
  return FE<3,LAGRANGE_VEC>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [71/233]

Real libMesh::FE< 1, MONOMIAL >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 211 of file fe_monomial_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,MONOMIAL>::shape_second_deriv(elem->type(),
                                            order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [72/233]

Real libMesh::FE< 2, MONOMIAL >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 577 of file fe_monomial_shape_2D.C.

{
  libmesh_assert(elem);
 
  // by default call the orientation-independent shape functions
  return FE<2,MONOMIAL>::shape_second_deriv(elem->type(), order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [73/233]

Real libMesh::FE< 3, MONOMIAL >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1340 of file fe_monomial_shape_3D.C.

{
  libmesh_assert(elem);
 
  // call the orientation-independent shape function derivatives
  return FE<3,MONOMIAL>::shape_second_deriv(elem->type(), order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [74/233]

RealVectorValue libMesh::FE< 0, MONOMIAL_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 421 of file fe_monomial_vec.C.

{
  Real value = FE<0, MONOMIAL>::shape_second_deriv(
      elem->type(), order + add_p_level*elem->p_level(), i, j, p);
  return libMesh::RealVectorValue(value);
}

shape_second_deriv() [75/233]

RealVectorValue libMesh::FE< 1, MONOMIAL_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 465 of file fe_monomial_vec.C.

{
  Real value = FE<1, MONOMIAL>::shape_second_deriv(
      elem->type(), order + add_p_level*elem->p_level(), i, j, p);
  return libMesh::RealVectorValue(value);
}

shape_second_deriv() [76/233]

RealVectorValue libMesh::FE< 2, MONOMIAL_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 537 of file fe_monomial_vec.C.

{
  Real value = FE<2, MONOMIAL>::shape_second_deriv(
      elem->type(), order + add_p_level*elem->p_level(), i / 2, j, p);
 
  switch (i % 2)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape_second_deriv() [77/233]

RealVectorValue libMesh::FE< 3, MONOMIAL_VEC >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 630 of file fe_monomial_vec.C.

{
  Real value = FE<3, MONOMIAL>::shape_second_deriv(
      elem->type(), order + add_p_level*elem->p_level(), i / 3, j, p);
 
  switch (i % 3)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    case 2:
      return libMesh::RealVectorValue(Real(0), Real(0), value);
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape_second_deriv() [78/233]

RealGradient libMesh::FE< 2, NEDELEC_ONE >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 2006 of file fe_nedelec_one_shape_2D.C.

{
#if LIBMESH_DIM > 1
  libmesh_assert(elem);
 
  // j = 0 ==> d^2 phi / dxi^2
  // j = 1 ==> d^2 phi / dxi deta
  // j = 2 ==> d^2 phi / deta^2
  libmesh_assert_less (j, 3);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  const char sign = i >= totalorder * elem->n_edges() || elem->positive_edge_orientation(i / totalorder) ? 1 : -1;
  const unsigned int ii = sign > 0 ? i : (i / totalorder * 2 + 1) * totalorder - 1 - i;
 
  const Real xi  = p(0);
  const Real eta = p(1);
 
  switch (totalorder)
    {
      // linear Nedelec (first kind) shape function second derivatives
    case FIRST:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
          case TRI6:
          case TRI7:
            // All second derivatives for linear quads and triangles are zero.
            return RealGradient();
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
 
          } // end switch (type)
      } // end case FIRST
 
      // quadratic Nedelec (first kind) shape function second derivatives
    case SECOND:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              // Even with a loose inverse_map tolerance we ought to
              // be nearly on the element interior in master
              // coordinates
              libmesh_assert_less_equal ( std::fabs(xi), 1.0+10*TOLERANCE );
              libmesh_assert_less_equal ( std::fabs(eta), 1.0+10*TOLERANCE );
 
              const Real x = 0.5 * (xi + 1.0);
              const Real y = 0.5 * (eta + 1.0);
 
              switch (j)
                {
                  // d^2()/dxi^2
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                      case 1:
                      case 4:
                      case 5:
                      case 9:
                      case 10:
                        return RealGradient();
                      case 2:
                        return sign * RealGradient( 0.0, 0.125*(-36.0*y+24.0) );
                      case 3:
                        return sign * RealGradient( 0.0, 0.125*( 36.0*y-12.0) );
                      case 6:
                        return sign * RealGradient( 0.0, 0.125*(-36.0*y+12.0) );
                      case 7:
                        return sign * RealGradient( 0.0, 0.125*( 36.0*y-24.0) );
                      case 8:
                        return RealGradient( 0.0,  0.75*(6.0*y-4.0) );
                      case 11:
                        return RealGradient( 0.0,  0.75*(-6.0*y+2.0) );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d^2()/dxideta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient( 0.125*(-36.0*y+24.0), 0.0 );
                      case 1:
                        return sign * RealGradient( 0.125*( 36.0*y-24.0), 0.0 );
                      case 2:
                       return sign * RealGradient( 0.0, 0.125*(-36.0*x+12.0) );
                      case 3:
                       return sign * RealGradient( 0.0, 0.125*( 36.0*x-12.0) );
                      case 4:
                        return sign * RealGradient( 0.125*(-36.0*y+12.0), 0.0 );
                      case 5:
                        return sign * RealGradient( 0.125*( 36.0*y-12.0), 0.0 );
                      case 6:
                        return sign * RealGradient( 0.0, 0.125*(-36.0*x+24.0) );
                      case 7:
                        return sign * RealGradient( 0.0, 0.125*( 36.0*x-24.0) );
                      case 8:
                        return RealGradient( 0.0,  0.75*(6.0*x-3.0) );
                      case 9:
                        return RealGradient( 0.75*(-6.0*y), 0.0 );
                      case 10:
                        return RealGradient( 0.75*(6.0*y), 0.0 );
                      case 11:
                        return RealGradient( 0.0, 0.75*(-6.0*x+3.0) );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                  // d^2()/deta^2
                case 2:
                  {
                    switch(ii)
                      {
                      case 2:
                      case 3:
                      case 6:
                      case 7:
                      case 8:
                      case 11:
                        return RealGradient();
                      case 0:
                        return sign * RealGradient( 0.125*(-36.0*x+24.0), 0.0 );
                      case 1:
                        return sign * RealGradient( 0.125*( 36.0*x-12.0), 0.0 );
                      case 4:
                        return sign * RealGradient( 0.125*(-36.0*x+12.0), 0.0 );
                      case 5:
                        return sign * RealGradient( 0.125*( 36.0*x-24.0), 0.0 );
                      case 9:
                        return RealGradient( 0.75*(-6.0*x+4.0), 0.0 );
                      case 10:
                        return RealGradient( 0.75*( 6.0*x-2.0), 0.0 );
 
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch (j)
                {
                  // d^2()/dxi^2
                case 0:
                  {
                    switch(ii)
                      {
                      case 3:
                      case 4:
                        return RealGradient();
                      case 0:
                        return sign * RealGradient( 0.0, -16.0 );
                      case 1:
                        return sign * RealGradient( 0.0, 16.0 );
                      case 2:
                        return sign * RealGradient( 0.0, 16.0 );
                      case 5:
                        return sign * RealGradient( 0.0, -16.0 );
                      case 6:
                        return RealGradient( 0.0, 16.0 );
                      case 7:
                        return RealGradient( 0.0,-32.0 );
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d^2()/dxideta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient( 8.0, -8.0 );
                      case 1:
                        return sign * RealGradient( -8.0, 0.0 );
                      case 2:
                        return sign * RealGradient( -8.0, 0.0 );
                      case 3:
                        return sign * RealGradient( 0.0, 8.0 );
                      case 4:
                        return sign * RealGradient( 0.0, 8.0 );
                      case 5:
                        return sign * RealGradient( 8.0, -8.0 );
                      case 6:
                        return RealGradient( -8.0, 16.0 );
                      case 7:
                        return RealGradient( 16.0, -8.0 );
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                  // d^2()/deta^2
                case 2:
                  {
                    switch(ii)
                      {
                      case 1:
                      case 2:
                        return RealGradient();
                      case 0:
                        return sign * RealGradient( 16.0, 0.0 );
                      case 3:
                        return sign * RealGradient( -16.0, 0.0 );
                      case 4:
                        return sign * RealGradient( -16.0, 0.0 );
                      case 5:
                        return sign * RealGradient( 16.0, 0.0 );
                      case 6:
                        return RealGradient( -32.0, 0.0 );
                      case 7:
                        return RealGradient( 16.0, 0.0 );
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
 
          } // end switch (type)
      } // end case SECOND
 
      // cubic Nedelec (first kind) shape function second derivatives
    case THIRD:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch (j)
                {
                  // d^2()/dxi^2
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-135.*eta/4. - 105./4. + 135.*((eta + 1.)*(eta + 1.))/4. - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 1:
                        return sign * RealGradient(135.*eta/8. + 105./8. - 135.*(eta + 1.)*(eta + 1.)/8. + 75.*((eta + 1.)*(eta + 1.)*(eta + 1.))/16., 0.);
                      case 2:
                        return sign * RealGradient(-135.*eta/4. - 105./4. + 135.*((eta + 1.)*(eta + 1.))/4. - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 3:
                        return sign * RealGradient(0., 54.*eta + 135.*xi/4. - 135.*(eta + 1.)*(xi + 1.)/2. + 225.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 243./4. - 45.*(eta + 1.)*(eta + 1.)/2.);
                      case 4:
                        return sign * RealGradient(0., -45.*eta/2. - 45.*xi/8. + 225.*(eta + 1.)*(xi + 1.)/8. - 225.*(xi + 1.)*(eta + 1.)*(eta + 1.)/16. - 189./8. + 45.*((eta + 1.)*(eta + 1.))/4.);
                      case 5:
                        return sign * RealGradient(0., 36.*eta + 45.*xi/4. - 45.*(eta + 1.)*(xi + 1.) + 225.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 153./4. - 45.*(eta + 1.)*(eta + 1.)/2.);
                      case 6:
                        return sign * RealGradient(-45.*eta/4. - 45./4. + 45.*((eta + 1.)*(eta + 1.))/2. - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 7:
                        return sign * RealGradient(45.*eta/8. + 45./8. - 45.*(eta + 1.)*(eta + 1.)/4. + 75.*((eta + 1.)*(eta + 1.)*(eta + 1.))/16., 0.);
                      case 8:
                        return sign * RealGradient(-45.*eta/4. - 45./4. + 45.*((eta + 1.)*(eta + 1.))/2. - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 9:
                        return sign * RealGradient(0., 54.*eta + 45.*xi/4. - 45.*(eta + 1.)*(xi + 1.) + 225.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 207./4. - 135.*(eta + 1.)*(eta + 1.)/4.);
                      case 10:
                        return sign * RealGradient(0., -135.*eta/4. - 45.*xi/8. + 225.*(eta + 1.)*(xi + 1.)/8. - 225.*(xi + 1.)*(eta + 1.)*(eta + 1.)/16. - 261./8. + 135.*((eta + 1.)*(eta + 1.))/8.);
                      case 11:
                        return sign * RealGradient(0., 81.*eta + 135.*xi/4. - 135.*(eta + 1.)*(xi + 1.)/2. + 225.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 297./4. - 135.*(eta + 1.)*(eta + 1.)/4.);
                      case 12:
                        return RealGradient(0., 81.*eta + 135.*xi/4. - 135.*(eta + 1.)*(xi + 1.)/2. + 225.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 297./4. - 135.*(eta + 1.)*(eta + 1.)/4.);
                      case 13:
                        return RealGradient(0., -54.*eta - 135.*xi/4. + 135.*(eta + 1.)*(xi + 1.)/2. - 225.*(xi + 1.)*(eta + 1.)*(eta + 1.)/8. - 243./4. + 45.*((eta + 1.)*(eta + 1.))/2.);
                      case 14:
                        return RealGradient(-30.*eta - 30. + 135.*((eta + 1.)*(eta + 1.))/4. - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 15:
                        return RealGradient(15.*eta/2. + 15./2. - 45.*(eta + 1.)*(eta + 1.)/2. + 75.*((eta + 1.)*(eta + 1.)*(eta + 1.))/8., 0.);
                      case 16:
                        return RealGradient(-30.*eta - 30. + 135.*((eta + 1.)*(eta + 1.))/4. - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 17:
                        return RealGradient(15.*eta/2. + 15./2. - 45.*(eta + 1.)*(eta + 1.)/2. + 75.*((eta + 1.)*(eta + 1.)*(eta + 1.))/8., 0.);
                      case 18:
                        return RealGradient(0., 54.*eta + 45.*xi/4. - 45.*(eta + 1.)*(xi + 1.) + 225.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 207./4. - 135.*(eta + 1.)*(eta + 1.)/4.);
                      case 19:
                        return RealGradient(0., -36.*eta - 45.*xi/4. + 45.*(eta + 1.)*(xi + 1.) - 225.*(xi + 1.)*(eta + 1.)*(eta + 1.)/8. - 153./4. + 45.*((eta + 1.)*(eta + 1.))/2.);
                      case 20:
                        return RealGradient(0., 0.);
                      case 21:
                        return RealGradient(0., 15.*xi/4. - 3./4.);
                      case 22:
                        return RealGradient(0., -15.*xi/4. - 3./4.);
                      case 23:
                        return RealGradient(0., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d^2()/dxideta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-81.*eta - 135.*xi/4. + 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 297./4. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                      case 1:
                        return sign * RealGradient(135.*eta/4. + 135.*xi/8. - 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 135./4. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)/4., 0.);
                      case 2:
                        return sign * RealGradient(-54.*eta - 135.*xi/4. + 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 243./4. + 90.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                      case 3:
                        return sign * RealGradient(0., 45.*eta/4. + 54.*xi - 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 207./4. - 135.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      case 4:
                        return sign * RealGradient(0., -45.*eta/8. - 45.*xi/2. + 90.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. - 45./2. + 225.*((xi + 1.)*(xi + 1.)/(2.*2.))/4.);
                      case 5:
                        return sign * RealGradient(0., 45.*eta/4. + 36.*xi - 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 153./4. - 90.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      case 6:
                        return sign * RealGradient(-36.*eta - 45.*xi/4. + 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 153./4. + 90.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                      case 7:
                        return sign * RealGradient(45.*eta/2. + 45.*xi/8. - 90.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 45./2. - 225.*(eta + 1.)*(eta + 1.)/(2.*2.)/4., 0.);
                      case 8:
                        return sign * RealGradient(-54.*eta - 45.*xi/4. + 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 207./4. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                      case 9:
                        return sign * RealGradient(0., 135.*eta/4. + 54.*xi - 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 243./4. - 90.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      case 10:
                        return sign * RealGradient(0., -135.*eta/8. - 135.*xi/4. + 135.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. - 135./4. + 225.*((xi + 1.)*(xi + 1.)/(2.*2.))/4.);
                      case 11:
                        return sign * RealGradient(0., 135.*eta/4. + 81.*xi - 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 297./4. - 135.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      case 12:
                        return RealGradient(0., 30.*eta + 81.*xi - 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 75. - 135.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      case 13:
                        return RealGradient(0., -15.*eta/2. - 54.*xi + 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 105./2. + 135.*((xi + 1.)*(xi + 1.)/(2.*2.)));
                      case 14:
                        return RealGradient(-81.*eta - 30.*xi + 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 75. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                      case 15:
                        return RealGradient(54.*eta + 15.*xi/2. - 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 105./2. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.), 0.);
                      case 16:
                        return RealGradient(-54.*eta - 30.*xi + 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 60. + 90.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                      case 17:
                        return RealGradient(36.*eta + 15.*xi/2. - 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 75./2. - 90.*(eta + 1.)*(eta + 1.)/(2.*2.), 0.);
                      case 18:
                        return RealGradient(0., 30.*eta + 54.*xi - 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 60. - 90.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      case 19:
                        return RealGradient(0., -15.*eta/2. - 36.*xi + 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 75./2. + 90.*((xi + 1.)*(xi + 1.)/(2.*2.)));
                      case 20:
                        return RealGradient(0., 0.);
                      case 21:
                        return RealGradient(0., 0.);
                      case 22:
                        return RealGradient(0., 0.);
                      case 23:
                        return RealGradient(0., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                  // d^2()/deta^2
                case 2:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-135.*eta/4. - 81.*xi + 135.*(eta + 1.)*(xi + 1.)/2. - 225.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 297./4. + 135.*((xi + 1.)*(xi + 1.))/4., 0.);
                      case 1:
                        return sign * RealGradient(45.*eta/8. + 135.*xi/4. - 225.*(eta + 1.)*(xi + 1.)/8. + 225.*(eta + 1.)*((xi + 1.)*(xi + 1.))/16. + 261./8. - 135.*(xi + 1.)*(xi + 1.)/8., 0.);
                      case 2:
                        return sign * RealGradient(-45.*eta/4. - 54.*xi + 45.*(eta + 1.)*(xi + 1.) - 225.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 207./4. + 135.*((xi + 1.)*(xi + 1.))/4., 0.);
                      case 3:
                        return sign * RealGradient(0., 45.*xi/4. + 45./4. - 45.*(xi + 1.)*(xi + 1.)/2. + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 4:
                        return sign * RealGradient(0., -45.*xi/8. - 45./8. + 45.*((xi + 1.)*(xi + 1.))/4. - 75.*(xi + 1.)*(xi + 1.)*(xi + 1.)/16.);
                      case 5:
                        return sign * RealGradient(0., 45.*xi/4. + 45./4. - 45.*(xi + 1.)*(xi + 1.)/2. + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 6:
                        return sign * RealGradient(-45.*eta/4. - 36.*xi + 45.*(eta + 1.)*(xi + 1.) - 225.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 153./4. + 45.*((xi + 1.)*(xi + 1.))/2., 0.);
                      case 7:
                        return sign * RealGradient(45.*eta/8. + 45.*xi/2. - 225.*(eta + 1.)*(xi + 1.)/8. + 225.*(eta + 1.)*((xi + 1.)*(xi + 1.))/16. + 189./8. - 45.*(xi + 1.)*(xi + 1.)/4., 0.);
                      case 8:
                        return sign * RealGradient(-135.*eta/4. - 54.*xi + 135.*(eta + 1.)*(xi + 1.)/2. - 225.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 243./4. + 45.*((xi + 1.)*(xi + 1.))/2., 0.);
                      case 9:
                        return sign * RealGradient(0., 135.*xi/4. + 105./4. - 135.*(xi + 1.)*(xi + 1.)/4. + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 10:
                        return sign * RealGradient(0., -135.*xi/8. - 105./8. + 135.*((xi + 1.)*(xi + 1.))/8. - 75.*(xi + 1.)*(xi + 1.)*(xi + 1.)/16.);
                      case 11:
                        return sign * RealGradient(0., 135.*xi/4. + 105./4. - 135.*(xi + 1.)*(xi + 1.)/4. + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 12:
                        return RealGradient(0., 30.*xi + 30. - 135.*(xi + 1.)*(xi + 1.)/4. + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 13:
                        return RealGradient(0., -15.*xi/2. - 15./2. + 45.*((xi + 1.)*(xi + 1.))/2. - 75.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8.);
                      case 14:
                        return RealGradient(-135.*eta/4. - 81.*xi + 135.*(eta + 1.)*(xi + 1.)/2. - 225.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 297./4. + 135.*((xi + 1.)*(xi + 1.))/4., 0.);
                      case 15:
                        return RealGradient(135.*eta/4. + 54.*xi - 135.*(eta + 1.)*(xi + 1.)/2. + 225.*(eta + 1.)*((xi + 1.)*(xi + 1.))/8. + 243./4. - 45.*(xi + 1.)*(xi + 1.)/2., 0.);
                      case 16:
                        return RealGradient(-45.*eta/4. - 54.*xi + 45.*(eta + 1.)*(xi + 1.) - 225.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 207./4. + 135.*((xi + 1.)*(xi + 1.))/4., 0.);
                      case 17:
                        return RealGradient(45.*eta/4. + 36.*xi - 45.*(eta + 1.)*(xi + 1.) + 225.*(eta + 1.)*((xi + 1.)*(xi + 1.))/8. + 153./4. - 45.*(xi + 1.)*(xi + 1.)/2., 0.);
                      case 18:
                        return RealGradient(0., 30.*xi + 30. - 135.*(xi + 1.)*(xi + 1.)/4. + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 19:
                        return RealGradient(0., -15.*xi/2. - 15./2. + 45.*((xi + 1.)*(xi + 1.))/2. - 75.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8.);
                      case 20:
                        return RealGradient(15.*eta/4. - 3./4., 0.);
                      case 21:
                        return RealGradient(0., 0.);
                      case 22:
                        return RealGradient(0., 0.);
                      case 23:
                        return RealGradient(-15.*eta/4. - 3./4., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch (j)
                {
                  // d^2()/dxi^2
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(60. - 90.*eta, 180.*eta + 270.*xi - 120.);
                      case 1:
                        return sign * RealGradient(45.*eta - 30., -45.*eta - 135.*xi + 105./2.);
                      case 2:
                        return sign * RealGradient(60. - 90.*eta, 270.*xi - 90.);
                      case 3:
                        return sign * RealGradient(-90.*eta, 270.*xi - 90.);
                      case 4:
                        return sign * RealGradient(-45.*eta/2., 90.*eta + 135.*xi/2. - 75./2.);
                      case 5:
                        return sign * RealGradient(0., 0.);
                      case 6:
                        return sign * RealGradient(0., 0.);
                      case 7:
                        return sign * RealGradient(-45.*eta/2., -45.*eta + 135.*xi/2. - 30.);
                      case 8:
                        return sign * RealGradient(-90.*eta, 180.*eta + 270.*xi - 180.);
                      case 9:
                        return RealGradient(180.*eta, -720.*eta - 540.*xi + 300.);
                      case 10:
                        return RealGradient(-540.*eta, 720.*eta + 1620.*xi - 900.);
                      case 11:
                        return RealGradient(-360.*eta, 720.*eta + 1080.*xi - 480.);
                      case 12:
                        return RealGradient(540.*eta, -360.*eta - 1620.*xi + 720.);
                      case 13:
                        return RealGradient(0., 360.*eta - 60.);
                      case 14:
                        return RealGradient(0., 120. - 720.*eta);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d^2()/dxideta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-180.*eta - 90.*xi + 120., 90.*eta + 180.*xi - 60.);
                      case 1:
                        return sign * RealGradient(45.*eta + 45.*xi - 75./2., 45.*eta/2. - 45.*xi);
                      case 2:
                        return sign * RealGradient(30. - 90.*xi, 0.);
                      case 3:
                        return sign * RealGradient(30. - 90.*xi, 0.);
                      case 4:
                        return sign * RealGradient(-90.*eta - 45.*xi/2. + 45./2., 45.*eta/2. + 90.*xi - 45./2.);
                      case 5:
                        return sign * RealGradient(0., 90.*eta - 30.);
                      case 6:
                        return sign * RealGradient(0., 90.*eta - 30.);
                      case 7:
                        return sign * RealGradient(45.*eta - 45.*xi/2., -45.*eta - 45.*xi + 75./2.);
                      case 8:
                        return sign * RealGradient(-180.*eta - 90.*xi + 60., 90.*eta + 180.*xi - 120.);
                      case 9:
                        return RealGradient(720.*eta + 180.*xi - 300., -540.*eta - 720.*xi + 300.);
                      case 10:
                        return RealGradient(-720.*eta - 540.*xi + 300., 180.*eta + 720.*xi - 300.);
                      case 11:
                        return RealGradient(-720.*eta - 360.*xi + 360., 720.*xi - 120.);
                      case 12:
                        return RealGradient(360.*eta + 540.*xi - 240., 60. - 360.*xi);
                      case 13:
                        return RealGradient(60. - 360.*eta, 540.*eta + 360.*xi - 240.);
                      case 14:
                        return RealGradient(720.*eta - 120., -360.*eta - 720.*xi + 360.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                  // d^2()/deta^2
                case 2:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-270.*eta - 180.*xi + 180., 90.*xi);
                      case 1:
                        return sign * RealGradient(-135.*eta/2. + 45.*xi + 30., 45.*xi/2.);
                      case 2:
                        return sign * RealGradient(0., 0.);
                      case 3:
                        return sign * RealGradient(0., 0.);
                      case 4:
                        return sign * RealGradient(-135.*eta/2. - 90.*xi + 75./2., 45.*xi/2.);
                      case 5:
                        return sign * RealGradient(90. - 270.*eta, 90.*xi);
                      case 6:
                        return sign * RealGradient(90. - 270.*eta, 90.*xi - 60.);
                      case 7:
                        return sign * RealGradient(135.*eta + 45.*xi - 105./2., 30. - 45.*xi);
                      case 8:
                        return sign * RealGradient(-270.*eta - 180.*xi + 120., 90.*xi - 60.);
                      case 9:
                        return RealGradient(1620.*eta + 720.*xi - 900., -540.*xi);
                      case 10:
                        return RealGradient(-540.*eta - 720.*xi + 300., 180.*xi);
                      case 11:
                        return RealGradient(120. - 720.*xi, 0.);
                      case 12:
                        return RealGradient(360.*xi - 60., 0.);
                      case 13:
                        return RealGradient(-1620.*eta - 360.*xi + 720., 540.*xi);
                      case 14:
                        return RealGradient(1080.*eta + 720.*xi - 480., -360.*xi);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          } // end switch (type)
      } // end case THIRD
 
      // quartic Nedelec (first kind) shape function second derivatives
    case FOURTH:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch (j)
                {
                  // d^2()/dxi^2
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-480.*eta - 105.*xi/2. + 420.*(eta + 1.)*(xi + 1.) - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. + 525.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 3675.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. - 945./2. + 900.*((eta + 1.)*(eta + 1.)) - 600.*(eta + 1.)*(eta + 1.)*(eta + 1.) + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4., 0.);
                      case 1:
                        return sign * RealGradient(1720.*eta/9. + 385.*xi/18. - 1540.*(eta + 1.)*(xi + 1.)/9. + 1925.*(xi + 1.)*((eta + 1.)*(eta + 1.))/6. - 1925.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/9. + 13475.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/288. + 3395./18. - 1075.*(eta + 1.)*(eta + 1.)/3. + 2150.*((eta + 1.)*(eta + 1.)*(eta + 1.))/9. - 7525.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/144., 0.);
                      case 2:
                        return sign * RealGradient(-1360.*eta/9. - 385.*xi/18. + 1540.*(eta + 1.)*(xi + 1.)/9. - 1925.*(xi + 1.)*(eta + 1.)*(eta + 1.)/6. + 1925.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/9. - 13475.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/288. - 2765./18. + 850.*((eta + 1.)*(eta + 1.))/3. - 1700.*(eta + 1.)*(eta + 1.)*(eta + 1.)/9. + 2975.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/72., 0.);
                      case 3:
                        return sign * RealGradient(360.*eta + 105.*xi/2. - 420.*(eta + 1.)*(xi + 1.) + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. - 525.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.) + 3675.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. + 735./2. - 675.*(eta + 1.)*(eta + 1.) + 450.*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16., 0.);
                      case 4:
                        return sign * RealGradient(0., -450.*eta - 360.*xi + 1350.*(eta + 1.)*(xi + 1.) - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. - 1350.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 690. + 450.*((eta + 1.)*(eta + 1.)) + 1575.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. + 210.*((xi + 1.)*(xi + 1.)) - 3675.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 525.*(eta + 1.)*(eta + 1.)*(eta + 1.)/4.);
                      case 5:
                        return sign * RealGradient(0., 475.*eta/3. + 170.*xi/3. - 475.*(eta + 1.)*(xi + 1.) + 3325.*(eta + 1.)*((xi + 1.)*(xi + 1.))/12. + 1075.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. - 1925.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/12. + 1765./9. - 1075.*(eta + 1.)*(eta + 1.)/6. - 7525.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/24. - 595.*(xi + 1.)*(xi + 1.)/18. + 13475.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/144. + 1925.*((eta + 1.)*(eta + 1.)*(eta + 1.))/36.);
                      case 6:
                        return sign * RealGradient(0., -250.*eta/3. - 80.*xi/3. + 250.*(eta + 1.)*(xi + 1.) - 875.*(eta + 1.)*(xi + 1.)*(xi + 1.)/6. - 425.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 1925.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/12. - 910./9. + 425.*((eta + 1.)*(eta + 1.))/3. + 2975.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/12. + 140.*((xi + 1.)*(xi + 1.))/9. - 13475.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/144. - 1925.*(eta + 1.)*(eta + 1.)*(eta + 1.)/36.);
                      case 7:
                        return sign * RealGradient(0., 225.*eta + 90.*xi - 675.*(eta + 1.)*(xi + 1.) + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.))/4. + 2025.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 285. - 675.*(eta + 1.)*(eta + 1.)/2. - 4725.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 105.*(xi + 1.)*(xi + 1.)/2. + 3675.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.))/4.);
                      case 8:
                        return sign * RealGradient(-90.*eta + 105.*(eta + 1.)*(xi + 1.) - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)/4. + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 3675.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. - 90. + 675.*((eta + 1.)*(eta + 1.))/2. - 675.*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16., 0.);
                      case 9:
                        return sign * RealGradient(340.*eta/9. - 385.*(eta + 1.)*(xi + 1.)/9. + 1925.*(xi + 1.)*((eta + 1.)*(eta + 1.))/12. - 1925.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/12. + 13475.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/288. + 340./9. - 425.*(eta + 1.)*(eta + 1.)/3. + 425.*((eta + 1.)*(eta + 1.)*(eta + 1.))/3. - 2975.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/72., 0.);
                      case 10:
                        return sign * RealGradient(-430.*eta/9. + 385.*(eta + 1.)*(xi + 1.)/9. - 1925.*(xi + 1.)*(eta + 1.)*(eta + 1.)/12. + 1925.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/12. - 13475.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/288. - 430./9. + 1075.*((eta + 1.)*(eta + 1.))/6. - 1075.*(eta + 1.)*(eta + 1.)*(eta + 1.)/6. + 7525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/144., 0.);
                      case 11:
                        return sign * RealGradient(120.*eta - 105.*(eta + 1.)*(xi + 1.) + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.))/4. - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 3675.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. + 120. - 450.*(eta + 1.)*(eta + 1.) + 450.*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 525.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4., 0.);
                      case 12:
                        return sign * RealGradient(0., -450.*eta - 120.*xi + 900.*(eta + 1.)*(xi + 1.) - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)/4. - 1350.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 525.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 510. + 675.*((eta + 1.)*(eta + 1.)) + 4725.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. + 105.*((xi + 1.)*(xi + 1.))/2. - 3675.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 525.*(eta + 1.)*(eta + 1.)*(eta + 1.)/2.);
                      case 13:
                        return sign * RealGradient(0., 500.*eta/3. + 320.*xi/9. - 1000.*(eta + 1.)*(xi + 1.)/3. + 875.*(eta + 1.)*((xi + 1.)*(xi + 1.))/6. + 1700.*(xi + 1.)*((eta + 1.)*(eta + 1.))/3. - 1925.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/9. + 1660./9. - 850.*(eta + 1.)*(eta + 1.)/3. - 2975.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/12. - 140.*(xi + 1.)*(xi + 1.)/9. + 13475.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/144. + 1925.*((eta + 1.)*(eta + 1.)*(eta + 1.))/18.);
                      case 14:
                        return sign * RealGradient(0., -950.*eta/3. - 680.*xi/9. + 1900.*(eta + 1.)*(xi + 1.)/3. - 3325.*(eta + 1.)*(xi + 1.)*(xi + 1.)/12. - 2150.*(xi + 1.)*(eta + 1.)*(eta + 1.)/3. + 1925.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/9. - 3190./9. + 1075.*((eta + 1.)*(eta + 1.))/3. + 7525.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/24. + 595.*((xi + 1.)*(xi + 1.))/18. - 13475.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/144. - 1925.*(eta + 1.)*(eta + 1.)*(eta + 1.)/18.);
                      case 15:
                        return sign * RealGradient(0., 900.*eta + 480.*xi - 1800.*(eta + 1.)*(xi + 1.) + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. + 1800.*(xi + 1.)*((eta + 1.)*(eta + 1.)) - 525.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.) + 1140. - 900.*(eta + 1.)*(eta + 1.) - 1575.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. - 210.*(xi + 1.)*(xi + 1.) + 3675.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.))/2.);
                      case 16:
                        return RealGradient(0., 870.*eta + 480.*xi - 1800.*(eta + 1.)*(xi + 1.) + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. + 1800.*(xi + 1.)*((eta + 1.)*(eta + 1.)) - 525.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.) + 1118. - 870.*(eta + 1.)*(eta + 1.) - 1575.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. - 210.*(xi + 1.)*(xi + 1.) + 3675.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. + 1015.*((eta + 1.)*(eta + 1.)*(eta + 1.))/4.);
                      case 17:
                        return RealGradient(0., 420.*eta + 360.*xi - 1350.*(eta + 1.)*(xi + 1.) + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. + 1350.*(xi + 1.)*((eta + 1.)*(eta + 1.)) - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 668. - 420.*(eta + 1.)*(eta + 1.) - 1575.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. - 210.*(xi + 1.)*(xi + 1.) + 3675.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. + 245.*((eta + 1.)*(eta + 1.)*(eta + 1.))/2.);
                      case 18:
                        return RealGradient(0., 60.*eta + 44. - 60.*(eta + 1.)*(eta + 1.) + 35.*((eta + 1.)*(eta + 1.)*(eta + 1.))/2.);
                      case 19:
                        return RealGradient(-390.*eta + 1365.*(eta + 1.)*(xi + 1.)/4. - 3045.*(xi + 1.)*(eta + 1.)*(eta + 1.)/4. + 525.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 3675.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. - 390. + 870.*((eta + 1.)*(eta + 1.)) - 600.*(eta + 1.)*(eta + 1.)*(eta + 1.) + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4., 0.);
                      case 20:
                        return RealGradient(-90.*eta + 315.*(eta + 1.)*(xi + 1.)/4. - 735.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 3675.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. - 90. + 420.*((eta + 1.)*(eta + 1.)) - 450.*(eta + 1.)*(eta + 1.)*(eta + 1.) + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4., 0.);
                      case 21:
                        return RealGradient(-120.*eta + 105.*(eta + 1.)*(xi + 1.) - 105.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. - 120. + 60.*((eta + 1.)*(eta + 1.)), 0.);
                      case 22:
                        return RealGradient(585.*eta/2. - 1365.*(eta + 1.)*(xi + 1.)/4. + 3045.*(xi + 1.)*((eta + 1.)*(eta + 1.))/4. - 525.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.) + 3675.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. + 585./2. - 1305.*(eta + 1.)*(eta + 1.)/2. + 450.*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16., 0.);
                      case 23:
                        return RealGradient(135.*eta/2. - 315.*(eta + 1.)*(xi + 1.)/4. + 735.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 3675.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. + 135./2. - 315.*(eta + 1.)*(eta + 1.) + 675.*((eta + 1.)*(eta + 1.)*(eta + 1.))/2. - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16., 0.);
                      case 24:
                        return RealGradient(90.*eta - 105.*(eta + 1.)*(xi + 1.) + 105.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. + 90. - 45.*(eta + 1.)*(eta + 1.), 0.);
                      case 25:
                        return RealGradient(0., -435.*eta - 120.*xi + 900.*(eta + 1.)*(xi + 1.) - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)/4. - 1350.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 525.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 497. + 1305.*((eta + 1.)*(eta + 1.))/2. + 4725.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. + 105.*((xi + 1.)*(xi + 1.))/2. - 3675.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 1015.*(eta + 1.)*(eta + 1.)*(eta + 1.)/4.);
                      case 26:
                        return RealGradient(0., -210.*eta - 90.*xi + 675.*(eta + 1.)*(xi + 1.) - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)/4. - 2025.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 272. + 315.*((eta + 1.)*(eta + 1.)) + 4725.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. + 105.*((xi + 1.)*(xi + 1.))/2. - 3675.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 245.*(eta + 1.)*(eta + 1.)*(eta + 1.)/2.);
                      case 27:
                        return RealGradient(0., -30.*eta - 26. + 45.*((eta + 1.)*(eta + 1.)) - 35.*(eta + 1.)*(eta + 1.)*(eta + 1.)/2.);
                      case 28:
                        return RealGradient(0., 0.);
                      case 29:
                        return RealGradient(0., 0.);
                      case 30:
                        return RealGradient(0., 171.*eta/4. + 120.*xi - 90.*(eta + 1.)*(xi + 1.) + 315.*(eta + 1.)*((xi + 1.)*(xi + 1.))/8. + 423./4. - 105.*(xi + 1.)*(xi + 1.)/2.);
                      case 31:
                        return RealGradient(0., -171.*eta/4. - 60.*xi + 90.*(eta + 1.)*(xi + 1.) - 315.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 297./4. + 105.*((xi + 1.)*(xi + 1.))/4.);
                      case 32:
                        return RealGradient(0., 81.*eta/4. + 90.*xi - 135.*(eta + 1.)*(xi + 1.)/2. + 315.*(eta + 1.)*((xi + 1.)*(xi + 1.))/8. + 333./4. - 105.*(xi + 1.)*(xi + 1.)/2.);
                      case 33:
                        return RealGradient(0., -81.*eta/4. - 45.*xi + 135.*(eta + 1.)*(xi + 1.)/2. - 315.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 207./4. + 105.*((xi + 1.)*(xi + 1.))/4.);
                      case 34:
                        return RealGradient(0., 0.);
                      case 35:
                        return RealGradient(0., 0.);
                      case 36:
                        return RealGradient(0., 9.*eta/2. - 3./2.);
                      case 37:
                        return RealGradient(0., 0.);
                      case 38:
                        return RealGradient(0., 0.);
                      case 39:
                        return RealGradient(0., -9.*eta/2. - 3./2.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d^2()/dxideta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-900.*eta - 480.*xi + 7200.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 6300.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 14400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 8400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1140. + 3600.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 12600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 840.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7350.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 2100.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 1:
                        return sign * RealGradient(950.*eta/3. + 1720.*xi/9. - 8600.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. + 7700.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. + 17200.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. - 30100.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 1270./3. - 3800.*(eta + 1.)*(eta + 1.)/(2.*2.)/3. - 15400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. - 3080.*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 26950.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. + 6650.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9., 0.);
                      case 2:
                        return sign * RealGradient(-500.*eta/3. - 1360.*xi/9. + 6800.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. - 7700.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. - 13600.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. + 23800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 820./3. + 2000.*((eta + 1.)*(eta + 1.)/(2.*2.))/3. + 15400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. + 3080.*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 26950.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. - 3500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9., 0.);
                      case 3:
                        return sign * RealGradient(450.*eta + 360.*xi - 5400.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 6300.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 10800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 6300.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 690. - 1800.*(eta + 1.)*(eta + 1.)/(2.*2.) - 12600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 840.*(xi + 1.)*(xi + 1.)/(2.*2.) + 7350.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 1050.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 4:
                        return sign * RealGradient(0., -120.*eta - 450.*xi + 3600.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 10800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3150.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 510. + 210.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 9450.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7350.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2700.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2100.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 5:
                        return sign * RealGradient(0., 430.*eta/9. + 475.*xi/3. - 4300.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. + 4300.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 30100.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 3850.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. + 185. - 770.*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 3850.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 26950.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 950.*(xi + 1.)*(xi + 1.)/(2.*2.) + 6650.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9.);
                      case 6:
                        return sign * RealGradient(0., -340.*eta/9. - 250.*xi/3. + 3400.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. - 3400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 23800.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 3850.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. - 110. + 770.*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 3850.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 26950.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 500.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3500.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9.);
                      case 7:
                        return sign * RealGradient(0., 90.*eta + 225.*xi - 2700.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 8100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 6300.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 3150.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 285. - 210.*(eta + 1.)*(eta + 1.)/(2.*2.) - 9450.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 7350.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1350.*(xi + 1.)*(xi + 1.)/(2.*2.) + 1050.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 8:
                        return sign * RealGradient(-225.*eta - 90.*xi + 2700.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 3150.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 8100.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 6300.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 285. + 1350.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 9450.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 210.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7350.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 1050.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 9:
                        return sign * RealGradient(250.*eta/3. + 340.*xi/9. - 3400.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. + 3850.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. + 3400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 23800.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. + 110. - 500.*(eta + 1.)*(eta + 1.)/(2.*2.) - 3850.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 770.*(xi + 1.)*(xi + 1.)/(2.*2.)/9. + 26950.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. + 3500.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9., 0.);
                      case 10:
                        return sign * RealGradient(-475.*eta/3. - 430.*xi/9. + 4300.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. - 3850.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. - 4300.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 30100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/9. - 185. + 950.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 3850.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 770.*((xi + 1.)*(xi + 1.)/(2.*2.))/9. - 26950.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9. - 6650.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/9., 0.);
                      case 11:
                        return sign * RealGradient(450.*eta + 120.*xi - 3600.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 3150.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 10800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 8400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 510. - 2700.*(eta + 1.)*(eta + 1.)/(2.*2.) - 9450.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 210.*(xi + 1.)*(xi + 1.)/(2.*2.) + 7350.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 2100.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 12:
                        return sign * RealGradient(0., -360.*eta - 450.*xi + 5400.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 10800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 6300.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 690. + 840.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 12600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7350.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1800.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1050.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 13:
                        return sign * RealGradient(0., 1360.*eta/9. + 500.*xi/3. - 6800.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. + 13600.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 23800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 7700.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/3. + 820./3. - 3080.*(eta + 1.)*(eta + 1.)/(2.*2.)/9. - 15400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 26950.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 2000.*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 3500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9.);
                      case 14:
                        return sign * RealGradient(0., -1720.*eta/9. - 950.*xi/3. + 8600.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/3. - 17200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/3. + 30100.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/9. - 7700.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/3. - 1270./3. + 3080.*((eta + 1.)*(eta + 1.)/(2.*2.))/9. + 15400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 26950.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9. + 3800.*((xi + 1.)*(xi + 1.)/(2.*2.))/3. - 6650.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/9.);
                      case 15:
                        return sign * RealGradient(0., 480.*eta + 900.*xi - 7200.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 14400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 6300.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 1140. - 840.*(eta + 1.)*(eta + 1.)/(2.*2.) - 12600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 7350.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3600.*(xi + 1.)*(xi + 1.)/(2.*2.) + 2100.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 16:
                        return RealGradient(0., 390.*eta + 870.*xi - 6960.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 14400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 6090.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 1065. - 1365.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 12600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 7350.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 3600.*(xi + 1.)*(xi + 1.)/(2.*2.) + 2100.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 17:
                        return RealGradient(0., 90.*eta + 420.*xi - 3360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 10800.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 8400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2940.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 465. - 315.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 9450.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 7350.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2700.*(xi + 1.)*(xi + 1.)/(2.*2.) + 2100.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 18:
                        return RealGradient(0., 120.*eta + 60.*xi - 480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 420.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 120. - 210.*(eta + 1.)*(eta + 1.)/(2.*2.));
                      case 19:
                        return RealGradient(-870.*eta - 390.*xi + 6960.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 6090.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 14400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 8400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1065. + 3600.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 12600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 1365.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 7350.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 2100.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 20:
                        return RealGradient(-420.*eta - 90.*xi + 3360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 2940.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 10800.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 8400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 465. + 2700.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 9450.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 315.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 7350.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) - 2100.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 21:
                        return RealGradient(-60.*eta - 120.*xi + 480.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 420.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 120. + 210.*((xi + 1.)*(xi + 1.)/(2.*2.)), 0.);
                      case 22:
                        return RealGradient(435.*eta + 585.*xi/2. - 5220.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 6090.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 10800.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 6300.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 630. - 1800.*(eta + 1.)*(eta + 1.)/(2.*2.) - 12600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 1365.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 7350.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 1050.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 23:
                        return RealGradient(210.*eta + 135.*xi/2. - 2520.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 2940.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 8100.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 6300.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 255. - 1350.*(eta + 1.)*(eta + 1.)/(2.*2.) - 9450.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 315.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 7350.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 1050.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 24:
                        return RealGradient(30.*eta + 90.*xi - 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 420.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 90. - 210.*(xi + 1.)*(xi + 1.)/(2.*2.), 0.);
                      case 25:
                        return RealGradient(0., -585.*eta/2. - 435.*xi + 5220.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 10800.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 6090.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 630. + 1365.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 12600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7350.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1800.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1050.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 26:
                        return RealGradient(0., -135.*eta/2. - 210.*xi + 2520.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 8100.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2940.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 255. + 315.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 9450.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 7350.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1350.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 1050.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 27:
                        return RealGradient(0., -90.*eta - 30.*xi + 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 420.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 90. + 210.*((eta + 1.)*(eta + 1.)/(2.*2.)));
                      case 28:
                        return RealGradient(171.*eta/4. + 135./4. - 180.*(eta + 1.)*(eta + 1.)/(2.*2.) + 105.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 29:
                        return RealGradient(-171.*eta/4. - 135./4. + 180.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 105.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 30:
                        return RealGradient(0., 171.*xi/4. + 135./4. - 180.*(xi + 1.)*(xi + 1.)/(2.*2.) + 105.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 31:
                        return RealGradient(0., -171.*xi/4. - 135./4. + 180.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 105.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 32:
                        return RealGradient(0., 81.*xi/4. + 75./4. - 135.*(xi + 1.)*(xi + 1.)/(2.*2.) + 105.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)));
                      case 33:
                        return RealGradient(0., -81.*xi/4. - 75./4. + 135.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 105.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.));
                      case 34:
                        return RealGradient(81.*eta/4. + 75./4. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.) + 105.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)), 0.);
                      case 35:
                        return RealGradient(-81.*eta/4. - 75./4. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 105.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.), 0.);
                      case 36:
                        return RealGradient(0., 9.*xi/2.);
                      case 37:
                        return RealGradient(-9.*eta/2., 0.);
                      case 38:
                        return RealGradient(9.*eta/2., 0.);
                      case 39:
                        return RealGradient(0., -9.*xi/2.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                  // d^2()/deta^2
                case 2:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-480.*eta - 900.*xi + 1800.*(eta + 1.)*(xi + 1.) - 1800.*(eta + 1.)*(xi + 1.)*(xi + 1.) + 525.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. - 1140. + 210.*((eta + 1.)*(eta + 1.)) + 1575.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. - 3675.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 900.*((xi + 1.)*(xi + 1.)) - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)/2., 0.);
                      case 1:
                        return sign * RealGradient(680.*eta/9. + 950.*xi/3. - 1900.*(eta + 1.)*(xi + 1.)/3. + 2150.*(eta + 1.)*((xi + 1.)*(xi + 1.))/3. - 1925.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/9. + 3325.*(xi + 1.)*((eta + 1.)*(eta + 1.))/12. + 3190./9. - 595.*(eta + 1.)*(eta + 1.)/18. - 7525.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/24. + 13475.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/144. - 1075.*(xi + 1.)*(xi + 1.)/3. + 1925.*((xi + 1.)*(xi + 1.)*(xi + 1.))/18., 0.);
                      case 2:
                        return sign * RealGradient(-320.*eta/9. - 500.*xi/3. + 1000.*(eta + 1.)*(xi + 1.)/3. - 1700.*(eta + 1.)*(xi + 1.)*(xi + 1.)/3. + 1925.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/9. - 875.*(xi + 1.)*(eta + 1.)*(eta + 1.)/6. - 1660./9. + 140.*((eta + 1.)*(eta + 1.))/9. + 2975.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/12. - 13475.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/144. + 850.*((xi + 1.)*(xi + 1.))/3. - 1925.*(xi + 1.)*(xi + 1.)*(xi + 1.)/18., 0.);
                      case 3:
                        return sign * RealGradient(120.*eta + 450.*xi - 900.*(eta + 1.)*(xi + 1.) + 1350.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 525.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.))/4. + 510. - 105.*(eta + 1.)*(eta + 1.)/2. - 4725.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 3675.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 675.*(xi + 1.)*(xi + 1.) + 525.*((xi + 1.)*(xi + 1.)*(xi + 1.))/2., 0.);
                      case 4:
                        return sign * RealGradient(0., -120.*xi + 105.*(eta + 1.)*(xi + 1.) - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)/4. + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 3675.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. - 120. + 450.*((xi + 1.)*(xi + 1.)) - 450.*(xi + 1.)*(xi + 1.)*(xi + 1.) + 525.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4.);
                      case 5:
                        return sign * RealGradient(0., 430.*xi/9. - 385.*(eta + 1.)*(xi + 1.)/9. + 1925.*(eta + 1.)*((xi + 1.)*(xi + 1.))/12. - 1925.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/12. + 13475.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/288. + 430./9. - 1075.*(xi + 1.)*(xi + 1.)/6. + 1075.*((xi + 1.)*(xi + 1.)*(xi + 1.))/6. - 7525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/144.);
                      case 6:
                        return sign * RealGradient(0., -340.*xi/9. + 385.*(eta + 1.)*(xi + 1.)/9. - 1925.*(eta + 1.)*(xi + 1.)*(xi + 1.)/12. + 1925.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/12. - 13475.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/288. - 340./9. + 425.*((xi + 1.)*(xi + 1.))/3. - 425.*(xi + 1.)*(xi + 1.)*(xi + 1.)/3. + 2975.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/72.);
                      case 7:
                        return sign * RealGradient(0., 90.*xi - 105.*(eta + 1.)*(xi + 1.) + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.))/4. - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 3675.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. + 90. - 675.*(xi + 1.)*(xi + 1.)/2. + 675.*((xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16.);
                      case 8:
                        return sign * RealGradient(-90.*eta - 225.*xi + 675.*(eta + 1.)*(xi + 1.) - 2025.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)/4. - 285. + 105.*((eta + 1.)*(eta + 1.))/2. + 4725.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. - 3675.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 675.*((xi + 1.)*(xi + 1.))/2. - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)/4., 0.);
                      case 9:
                        return sign * RealGradient(80.*eta/3. + 250.*xi/3. - 250.*(eta + 1.)*(xi + 1.) + 425.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 1925.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/12. + 875.*(xi + 1.)*((eta + 1.)*(eta + 1.))/6. + 910./9. - 140.*(eta + 1.)*(eta + 1.)/9. - 2975.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/12. + 13475.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/144. - 425.*(xi + 1.)*(xi + 1.)/3. + 1925.*((xi + 1.)*(xi + 1.)*(xi + 1.))/36., 0.);
                      case 10:
                        return sign * RealGradient(-170.*eta/3. - 475.*xi/3. + 475.*(eta + 1.)*(xi + 1.) - 1075.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 1925.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/12. - 3325.*(xi + 1.)*(eta + 1.)*(eta + 1.)/12. - 1765./9. + 595.*((eta + 1.)*(eta + 1.))/18. + 7525.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/24. - 13475.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/144. + 1075.*((xi + 1.)*(xi + 1.))/6. - 1925.*(xi + 1.)*(xi + 1.)*(xi + 1.)/36., 0.);
                      case 11:
                        return sign * RealGradient(360.*eta + 450.*xi - 1350.*(eta + 1.)*(xi + 1.) + 1350.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. + 690. - 210.*(eta + 1.)*(eta + 1.) - 1575.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 3675.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 450.*(xi + 1.)*(xi + 1.) + 525.*((xi + 1.)*(xi + 1.)*(xi + 1.))/4., 0.);
                      case 12:
                        return sign * RealGradient(0., -105.*eta/2. - 360.*xi + 420.*(eta + 1.)*(xi + 1.) - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 525.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 3675.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. - 735./2. + 675.*((xi + 1.)*(xi + 1.)) - 450.*(xi + 1.)*(xi + 1.)*(xi + 1.) + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/16.);
                      case 13:
                        return sign * RealGradient(0., 385.*eta/18. + 1360.*xi/9. - 1540.*(eta + 1.)*(xi + 1.)/9. + 1925.*(eta + 1.)*((xi + 1.)*(xi + 1.))/6. - 1925.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/9. + 13475.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/288. + 2765./18. - 850.*(xi + 1.)*(xi + 1.)/3. + 1700.*((xi + 1.)*(xi + 1.)*(xi + 1.))/9. - 2975.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/72.);
                      case 14:
                        return sign * RealGradient(0., -385.*eta/18. - 1720.*xi/9. + 1540.*(eta + 1.)*(xi + 1.)/9. - 1925.*(eta + 1.)*(xi + 1.)*(xi + 1.)/6. + 1925.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/9. - 13475.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/288. - 3395./18. + 1075.*((xi + 1.)*(xi + 1.))/3. - 2150.*(xi + 1.)*(xi + 1.)*(xi + 1.)/9. + 7525.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/144.);
                      case 15:
                        return sign * RealGradient(0., 105.*eta/2. + 480.*xi - 420.*(eta + 1.)*(xi + 1.) + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. - 525.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 3675.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. + 945./2. - 900.*(xi + 1.)*(xi + 1.) + 600.*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4.);
                      case 16:
                        return RealGradient(0., 390.*xi - 1365.*(eta + 1.)*(xi + 1.)/4. + 3045.*(eta + 1.)*((xi + 1.)*(xi + 1.))/4. - 525.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 3675.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. + 390. - 870.*(xi + 1.)*(xi + 1.) + 600.*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4.);
                      case 17:
                        return RealGradient(0., 90.*xi - 315.*(eta + 1.)*(xi + 1.)/4. + 735.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 3675.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. + 90. - 420.*(xi + 1.)*(xi + 1.) + 450.*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4.);
                      case 18:
                        return RealGradient(0., 120.*xi - 105.*(eta + 1.)*(xi + 1.) + 105.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. + 120. - 60.*(xi + 1.)*(xi + 1.));
                      case 19:
                        return RealGradient(-480.*eta - 870.*xi + 1800.*(eta + 1.)*(xi + 1.) - 1800.*(eta + 1.)*(xi + 1.)*(xi + 1.) + 525.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. - 1118. + 210.*((eta + 1.)*(eta + 1.)) + 1575.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. - 3675.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 870.*((xi + 1.)*(xi + 1.)) - 1015.*(xi + 1.)*(xi + 1.)*(xi + 1.)/4., 0.);
                      case 20:
                        return RealGradient(-360.*eta - 420.*xi + 1350.*(eta + 1.)*(xi + 1.) - 1350.*(eta + 1.)*(xi + 1.)*(xi + 1.) + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 1575.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. - 668. + 210.*((eta + 1.)*(eta + 1.)) + 1575.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. - 3675.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 420.*((xi + 1.)*(xi + 1.)) - 245.*(xi + 1.)*(xi + 1.)*(xi + 1.)/2., 0.);
                      case 21:
                        return RealGradient(-60.*xi - 44. + 60.*((xi + 1.)*(xi + 1.)) - 35.*(xi + 1.)*(xi + 1.)*(xi + 1.)/2., 0.);
                      case 22:
                        return RealGradient(120.*eta + 435.*xi - 900.*(eta + 1.)*(xi + 1.) + 1350.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 525.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.))/4. + 497. - 105.*(eta + 1.)*(eta + 1.)/2. - 4725.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 3675.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 1305.*(xi + 1.)*(xi + 1.)/2. + 1015.*((xi + 1.)*(xi + 1.)*(xi + 1.))/4., 0.);
                      case 23:
                        return RealGradient(90.*eta + 210.*xi - 675.*(eta + 1.)*(xi + 1.) + 2025.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. - 1575.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.))/4. + 272. - 105.*(eta + 1.)*(eta + 1.)/2. - 4725.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 3675.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 315.*(xi + 1.)*(xi + 1.) + 245.*((xi + 1.)*(xi + 1.)*(xi + 1.))/2., 0.);
                      case 24:
                        return RealGradient(30.*xi + 26. - 45.*(xi + 1.)*(xi + 1.) + 35.*((xi + 1.)*(xi + 1.)*(xi + 1.))/2., 0.);
                      case 25:
                        return RealGradient(0., -585.*xi/2. + 1365.*(eta + 1.)*(xi + 1.)/4. - 3045.*(eta + 1.)*(xi + 1.)*(xi + 1.)/4. + 525.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 3675.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. - 585./2. + 1305.*((xi + 1.)*(xi + 1.))/2. - 450.*(xi + 1.)*(xi + 1.)*(xi + 1.) + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/16.);
                      case 26:
                        return RealGradient(0., -135.*xi/2. + 315.*(eta + 1.)*(xi + 1.)/4. - 735.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 3675.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. - 135./2. + 315.*((xi + 1.)*(xi + 1.)) - 675.*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/16.);
                      case 27:
                        return RealGradient(0., -90.*xi + 105.*(eta + 1.)*(xi + 1.) - 105.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. - 90. + 45.*((xi + 1.)*(xi + 1.)));
                      case 28:
                        return RealGradient(120.*eta + 171.*xi/4. - 90.*(eta + 1.)*(xi + 1.) + 315.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 423./4. - 105.*(eta + 1.)*(eta + 1.)/2., 0.);
                      case 29:
                        return RealGradient(-60.*eta - 171.*xi/4. + 90.*(eta + 1.)*(xi + 1.) - 315.*(xi + 1.)*(eta + 1.)*(eta + 1.)/8. - 297./4. + 105.*((eta + 1.)*(eta + 1.))/4., 0.);
                      case 30:
                        return RealGradient(0., 0.);
                      case 31:
                        return RealGradient(0., 0.);
                      case 32:
                        return RealGradient(0., 0.);
                      case 33:
                        return RealGradient(0., 0.);
                      case 34:
                        return RealGradient(90.*eta + 81.*xi/4. - 135.*(eta + 1.)*(xi + 1.)/2. + 315.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 333./4. - 105.*(eta + 1.)*(eta + 1.)/2., 0.);
                      case 35:
                        return RealGradient(-45.*eta - 81.*xi/4. + 135.*(eta + 1.)*(xi + 1.)/2. - 315.*(xi + 1.)*(eta + 1.)*(eta + 1.)/8. - 207./4. + 105.*((eta + 1.)*(eta + 1.))/4., 0.);
                      case 36:
                        return RealGradient(0., 0.);
                      case 37:
                        return RealGradient(3./2. - 9.*xi/2., 0.);
                      case 38:
                        return RealGradient(9.*xi/2. + 3./2., 0.);
                      case 39:
                        return RealGradient(0., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch (j)
                {
                  // d^2()/dxi^2
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(1344.*eta*xi - 1680.*eta - 840.*xi + 480. + 1344.*(eta*eta), -4032.*eta*xi + 1680.*eta + 2520.*xi - 480. - 1344.*eta*eta - 2688.*xi*xi);
                      case 1:
                        return sign * RealGradient(-4928.*eta*xi/9. + 5768.*eta/9. + 3080.*xi/9. - 1720./9. - 4480.*eta*eta/9., 4480.*eta*xi/3. - 4256.*eta/9. - 1008.*xi + 1600./9. + 1792.*(eta*eta)/9. + 9856.*(xi*xi)/9.);
                      case 2:
                        return sign * RealGradient(4928.*eta*xi/9. - 2240.*eta/9. - 3080.*xi/9. + 1360./9. + 448.*(eta*eta)/9., -448.*eta*xi/3. - 784.*eta/9. + 840.*xi - 1024./9. + 2240.*(eta*eta)/9. - 9856.*xi*xi/9.);
                      case 3:
                        return sign * RealGradient(-1344.*eta*xi + 504.*eta + 840.*xi - 360., -2016.*xi + 288. + 2688.*(xi*xi));
                      case 4:
                        return sign * RealGradient(168.*eta*(3. - 8.*xi), -2016.*xi + 288. + 2688.*(xi*xi));
                      case 5:
                        return sign * RealGradient(896.*eta*(-6.*eta - 4.*xi + 3.)/9., 1792.*eta*xi - 1792.*eta/3. - 2464.*xi/3. + 160. + 896.*(eta*eta)/3. + 7168.*(xi*xi)/9.);
                      case 6:
                        return sign * RealGradient(56.*eta*(-48.*eta - 8.*xi + 15.)/9., 896.*eta*xi - 1568.*eta/3. - 560.*xi/3. + 64. + 1792.*(eta*eta)/3. + 896.*(xi*xi)/9.);
                      case 7:
                        return sign * RealGradient(0., 0.);
                      case 8:
                        return sign * RealGradient(0., 0.);
                      case 9:
                        return sign * RealGradient(56.*eta*(-40.*eta + 8.*xi + 7.)/9., 2240.*eta*xi/3. - 952.*eta/3. + 112.*xi/9. + 208./9. - 448.*eta*eta/9. - 896.*xi*xi/9.);
                      case 10:
                        return sign * RealGradient(896.*eta*(-2.*eta + 4.*xi - 1.)/9., 1792.*eta*xi/3. - 1568.*eta/3. + 6944.*xi/9. - 1216./9. + 4480.*(eta*eta)/9. - 7168.*xi*xi/9.);
                      case 11:
                        return sign * RealGradient(168.*eta*(8.*eta + 8.*xi - 5.), -4032.*eta*xi + 2520.*eta + 3360.*xi - 960. - 1344.*eta*eta - 2688.*xi*xi);
                      case 12:
                        return RealGradient(2016.*eta*(-4.*eta - 2.*xi + 3.), 24192.*eta*xi - 12096.*eta - 9072.*xi + 2160. + 12096.*(eta*eta) + 8064.*(xi*xi));
                      case 13:
                        return RealGradient(1008.*eta*(12.*eta + 16.*xi - 9.), -36288.*eta*xi + 18144.*eta + 36288.*xi - 8640. - 8064.*eta*eta - 32256.*xi*xi);
                      case 14:
                        return RealGradient(1008.*eta*(-8.*eta - 12.*xi + 9.), 24192.*eta*xi - 6048.*eta - 21168.*xi + 3456. + 24192.*(xi*xi));
                      case 15:
                        return RealGradient(1008.*eta*(4.*eta + 16.*xi - 7.), -12096.*eta*xi + 3024.*eta + 28224.*xi - 4608. - 32256.*xi*xi);
                      case 16:
                        return RealGradient(0., -2016.*eta + 144. + 4032.*(eta*eta));
                      case 17:
                        return RealGradient(0., 4032.*eta - 288. - 8064.*eta*eta);
                      case 18:
                        return RealGradient(252.*eta*(-24.*eta - 12.*xi + 13.), 18144.*eta*xi - 8064.*eta - 6804.*xi + 1548. + 7056.*(eta*eta) + 6048.*(xi*xi));
                      case 19:
                        return RealGradient(252.*eta*(28.*eta + 16.*xi - 13.), -21168.*eta*xi + 9576.*eta + 9324.*xi - 2196. - 6048.*eta*eta - 8064.*xi*xi);
                      case 20:
                        return RealGradient(1008.*eta*(1. - xi), 1008.*eta - 1512.*xi + 144. - 2016.*eta*eta + 2016.*(xi*xi));
                      case 21:
                        return RealGradient(252.*eta*(-12.*eta + 16.*xi - 3.), 9072.*eta*xi - 5544.*eta + 6804.*xi - 936. + 4032.*(eta*eta) - 8064.*xi*xi);
                      case 22:
                        return RealGradient(1008.*eta*(4.*eta + 2.*xi - 3.), -12096.*eta*xi + 4536.*eta + 4536.*xi - 972. - 3024.*eta*eta - 4032.*xi*xi);
                      case 23:
                        return RealGradient(2016.*eta*(-eta - 2.*xi + 1.), 6048.*eta*xi - 1512.*eta - 8064.*xi + 1440. + 8064.*(xi*xi));
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d^2()/dxideta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(2688.*eta*xi - 2520.*eta - 1680.*xi + 720. + 2016.*(eta*eta) + 672.*(xi*xi), -2688.*eta*xi + 840.*eta + 1680.*xi - 240. - 672.*eta*eta - 2016.*xi*xi);
                      case 1:
                        return sign * RealGradient(-8960.*eta*xi/9. + 1568.*eta/3. + 5768.*xi/9. - 200. - 896.*eta*eta/3. - 2464.*xi*xi/9., 3584.*eta*xi/9. + 896.*eta/9. - 4256.*xi/9. + 176./9. - 1792.*eta*eta/9. + 2240.*(xi*xi)/3.);
                      case 2:
                        return sign * RealGradient(896.*eta*xi/9. + 952.*eta/3. - 2240.*xi/9. - 16. - 1120.*eta*eta/3. + 2464.*(xi*xi)/9., 4480.*eta*xi/9. - 392.*eta/9. - 784.*xi/9. + 112./9. - 224.*eta*eta/9. - 224.*xi*xi/3.);
                      case 3:
                        return sign * RealGradient(504.*xi - 72. - 672.*xi*xi, 0.);
                      case 4:
                        return sign * RealGradient(504.*xi - 72. - 672.*xi*xi, 0.);
                      case 5:
                        return sign * RealGradient(-3584.*eta*xi/3. + 1568.*eta/3. + 896.*xi/3. - 80. - 448.*eta*eta - 1792.*xi*xi/9., 1792.*eta*xi/3. - 280.*eta/3. - 1792.*xi/3. + 56. + 224.*(eta*eta)/9. + 896.*(xi*xi));
                      case 6:
                        return sign * RealGradient(-1792.*eta*xi/3. + 1792.*eta/3. + 280.*xi/3. - 56. - 896.*eta*eta - 224.*xi*xi/9., 3584.*eta*xi/3. - 896.*eta/3. - 1568.*xi/3. + 80. + 1792.*(eta*eta)/9. + 448.*(xi*xi));
                      case 7:
                        return sign * RealGradient(0., -504.*eta + 72. + 672.*(eta*eta));
                      case 8:
                        return sign * RealGradient(0., -504.*eta + 72. + 672.*(eta*eta));
                      case 9:
                        return sign * RealGradient(-4480.*eta*xi/9. + 784.*eta/9. + 392.*xi/9. - 112./9. + 224.*(eta*eta)/3. + 224.*(xi*xi)/9., -896.*eta*xi/9. + 2240.*eta/9. - 952.*xi/3. + 16. - 2464.*eta*eta/9. + 1120.*(xi*xi)/3.);
                      case 10:
                        return sign * RealGradient(-3584.*eta*xi/9. + 4256.*eta/9. - 896.*xi/9. - 176./9. - 2240.*eta*eta/3. + 1792.*(xi*xi)/9., 8960.*eta*xi/9. - 5768.*eta/9. - 1568.*xi/3. + 200. + 2464.*(eta*eta)/9. + 896.*(xi*xi)/3.);
                      case 11:
                        return sign * RealGradient(2688.*eta*xi - 1680.*eta - 840.*xi + 240. + 2016.*(eta*eta) + 672.*(xi*xi), -2688.*eta*xi + 1680.*eta + 2520.*xi - 720. - 672.*eta*eta - 2016.*xi*xi);
                      case 12:
                        return RealGradient(-16128.*eta*xi + 18144.*eta + 6048.*xi - 3240. - 18144.*eta*eta - 2016.*xi*xi, 24192.*eta*xi - 9072.*eta - 12096.*xi + 2160. + 8064.*(eta*eta) + 12096.*(xi*xi));
                      case 13:
                        return RealGradient(24192.*eta*xi - 12096.*eta - 9072.*xi + 2160. + 12096.*(eta*eta) + 8064.*(xi*xi), -16128.*eta*xi + 6048.*eta + 18144.*xi - 3240. - 2016.*eta*eta - 18144.*xi*xi);
                      case 14:
                        return RealGradient(-16128.*eta*xi + 4032.*eta + 9072.*xi - 1944. - 6048.*xi*xi, -6048.*xi + 432. + 12096.*(xi*xi));
                      case 15:
                        return RealGradient(8064.*eta*xi - 2016.*eta - 7056.*xi + 1152. + 8064.*(xi*xi), 3024.*xi - 216. - 6048.*xi*xi);
                      case 16:
                        return RealGradient(3024.*eta - 216. - 6048.*eta*eta, 8064.*eta*xi - 7056.*eta - 2016.*xi + 1152. + 8064.*(eta*eta));
                      case 17:
                        return RealGradient(-6048.*eta + 432. + 12096.*(eta*eta), -16128.*eta*xi + 9072.*eta + 4032.*xi - 1944. - 6048.*eta*eta);
                      case 18:
                        return RealGradient(-12096.*eta*xi + 9576.*eta + 3276.*xi - 1332. - 10584.*eta*eta - 1512.*xi*xi, 14112.*eta*xi - 3276.*eta - 8064.*xi + 1044. + 2016.*(eta*eta) + 9072.*(xi*xi));
                      case 19:
                        return RealGradient(14112.*eta*xi - 8064.*eta - 3276.*xi + 1044. + 9072.*(eta*eta) + 2016.*(xi*xi), -12096.*eta*xi + 3276.*eta + 9576.*xi - 1332. - 1512.*eta*eta - 10584.*xi*xi);
                      case 20:
                        return RealGradient(-1512.*eta + 1008.*xi - 216. + 3024.*(eta*eta) - 504.*xi*xi, -4032.*eta*xi + 2016.*eta + 1008.*xi - 360. - 2016.*eta*eta);
                      case 21:
                        return RealGradient(-6048.*eta*xi + 4536.*eta - 756.*xi - 216. - 6048.*eta*eta + 2016.*(xi*xi), 8064.*eta*xi - 3024.*eta - 5544.*xi + 1188. + 1008.*(eta*eta) + 4536.*(xi*xi));
                      case 22:
                        return RealGradient(8064.*eta*xi - 5544.*eta - 3024.*xi + 1188. + 4536.*(eta*eta) + 1008.*(xi*xi), -6048.*eta*xi - 756.*eta + 4536.*xi - 216. + 2016.*(eta*eta) - 6048.*xi*xi);
                      case 23:
                        return RealGradient(-4032.*eta*xi + 1008.*eta + 2016.*xi - 360. - 2016.*xi*xi, 1008.*eta - 1512.*xi - 216. - 504.*eta*eta + 3024.*(xi*xi));
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                  // d^2()/deta^2
                case 2:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(4032.*eta*xi - 3360.*eta - 2520.*xi + 960. + 2688.*(eta*eta) + 1344.*(xi*xi), 168.*xi*(-8.*eta - 8.*xi + 5.));
                      case 1:
                        return sign * RealGradient(-1792.*eta*xi/3. - 6944.*eta/9. + 1568.*xi/3. + 1216./9. + 7168.*(eta*eta)/9. - 4480.*xi*xi/9., 896.*xi*(-4.*eta + 2.*xi + 1.)/9.);
                      case 2:
                        return sign * RealGradient(-2240.*eta*xi/3. - 112.*eta/9. + 952.*xi/3. - 208./9. + 896.*(eta*eta)/9. + 448.*(xi*xi)/9., 56.*xi*(-8.*eta + 40.*xi - 7.)/9.);
                      case 3:
                        return sign * RealGradient(0., 0.);
                      case 4:
                        return sign * RealGradient(0., 0.);
                      case 5:
                        return sign * RealGradient(-896.*eta*xi + 560.*eta/3. + 1568.*xi/3. - 64. - 896.*eta*eta/9. - 1792.*xi*xi/3., 56.*xi*(8.*eta + 48.*xi - 15.)/9.);
                      case 6:
                        return sign * RealGradient(-1792.*eta*xi + 2464.*eta/3. + 1792.*xi/3. - 160. - 7168.*eta*eta/9. - 896.*xi*xi/3., 896.*xi*(4.*eta + 6.*xi - 3.)/9.);
                      case 7:
                        return sign * RealGradient(2016.*eta - 288. - 2688.*eta*eta, 168.*xi*(8.*eta - 3.));
                      case 8:
                        return sign * RealGradient(2016.*eta - 288. - 2688.*eta*eta, 1344.*eta*xi - 840.*eta - 504.*xi + 360.);
                      case 9:
                        return sign * RealGradient(448.*eta*xi/3. - 840.*eta + 784.*xi/9. + 1024./9. + 9856.*(eta*eta)/9. - 2240.*xi*xi/9., -4928.*eta*xi/9. + 3080.*eta/9. + 2240.*xi/9. - 1360./9. - 448.*xi*xi/9.);
                      case 10:
                        return sign * RealGradient(-4480.*eta*xi/3. + 1008.*eta + 4256.*xi/9. - 1600./9. - 9856.*eta*eta/9. - 1792.*xi*xi/9., 4928.*eta*xi/9. - 3080.*eta/9. - 5768.*xi/9. + 1720./9. + 4480.*(xi*xi)/9.);
                      case 11:
                        return sign * RealGradient(4032.*eta*xi - 2520.*eta - 1680.*xi + 480. + 2688.*(eta*eta) + 1344.*(xi*xi), -1344.*eta*xi + 840.*eta + 1680.*xi - 480. - 1344.*xi*xi);
                      case 12:
                        return RealGradient(-36288.*eta*xi + 36288.*eta + 18144.*xi - 8640. - 32256.*eta*eta - 8064.*xi*xi, 1008.*xi*(16.*eta + 12.*xi - 9.));
                      case 13:
                        return RealGradient(24192.*eta*xi - 9072.*eta - 12096.*xi + 2160. + 8064.*(eta*eta) + 12096.*(xi*xi), 2016.*xi*(-2.*eta - 4.*xi + 3.));
                      case 14:
                        return RealGradient(4032.*xi - 288. - 8064.*xi*xi, 0.);
                      case 15:
                        return RealGradient(-2016.*xi + 144. + 4032.*(xi*xi), 0.);
                      case 16:
                        return RealGradient(-12096.*eta*xi + 28224.*eta + 3024.*xi - 4608. - 32256.*eta*eta, 1008.*xi*(16.*eta + 4.*xi - 7.));
                      case 17:
                        return RealGradient(24192.*eta*xi - 21168.*eta - 6048.*xi + 3456. + 24192.*(eta*eta), 1008.*xi*(-12.*eta - 8.*xi + 9.));
                      case 18:
                        return RealGradient(-21168.*eta*xi + 9324.*eta + 9576.*xi - 2196. - 8064.*eta*eta - 6048.*xi*xi, 252.*xi*(16.*eta + 28.*xi - 13.));
                      case 19:
                        return RealGradient(18144.*eta*xi - 6804.*eta - 8064.*xi + 1548. + 6048.*(eta*eta) + 7056.*(xi*xi), 252.*xi*(-12.*eta - 24.*xi + 13.));
                      case 20:
                        return RealGradient(6048.*eta*xi - 8064.*eta - 1512.*xi + 1440. + 8064.*(eta*eta), 2016.*xi*(-2.*eta - xi + 1.));
                      case 21:
                        return RealGradient(-12096.*eta*xi + 4536.*eta + 4536.*xi - 972. - 4032.*eta*eta - 3024.*xi*xi, 1008.*xi*(2.*eta + 4.*xi - 3.));
                      case 22:
                        return RealGradient(9072.*eta*xi + 6804.*eta - 5544.*xi - 936. - 8064.*eta*eta + 4032.*(xi*xi), 252.*xi*(16.*eta - 12.*xi - 3.));
                      case 23:
                        return RealGradient(-1512.*eta + 1008.*xi + 144. + 2016.*(eta*eta) - 2016.*xi*xi, 1008.*xi*(1. - eta));
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          } // end switch (type)
      } // end case FOURTH
 
      // quintic Nedelec (first kind) shape function second derivatives
    case FIFTH:
      {
        switch (elem->type())
          {
          case QUAD8:
          case QUAD9:
            {
              switch (j)
                {
                  // d^2()/dxi^2
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-13125.*eta/4. - 525.*xi + 13125.*(eta + 1.)*(xi + 1.)/2. - 23625.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 39375.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. + 91875.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 91875.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 33075.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 14175./4. + 39375.*((eta + 1.)*(eta + 1.))/4. + 70875.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. + 945.*((xi + 1.)*(xi + 1.))/4. - 165375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 165375.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 59535.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. - 91875.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 91875.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 33075.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 1:
                        return sign * RealGradient(527625.*eta/512. + 40845.*xi/256. - 1021125.*(eta + 1.)*(xi + 1.)/512. + 874125.*(eta + 1.)*((xi + 1.)*(xi + 1.))/1024. + 3063375.*(xi + 1.)*((eta + 1.)*(eta + 1.))/512. - 7147875.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/1024. + 7147875.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/2048. - 2573235.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. + 567105./512. - 1582875.*(eta + 1.)*(eta + 1.)/512. - 2622375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/1024. - 34965.*(xi + 1.)*(xi + 1.)/512. + 6118875.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/2048. - 6118875.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. + 2202795.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/8192. + 3693375.*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 3693375.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/2048. + 1329615.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4096., 0.);
                      case 2:
                        return sign * RealGradient(-28875.*eta/32. - 2835.*xi/16. + 70875.*(eta + 1.)*(xi + 1.)/32. - 70875.*(eta + 1.)*(xi + 1.)*(xi + 1.)/64. - 212625.*(xi + 1.)*(eta + 1.)*(eta + 1.)/32. + 496125.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 496125.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128. + 178605.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/256. - 32235./32. + 86625.*((eta + 1.)*(eta + 1.))/32. + 212625.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/64. + 2835.*((xi + 1.)*(xi + 1.))/32. - 496125.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128. + 496125.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/256. - 178605.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. - 202125.*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 202125.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/128. - 72765.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/256., 0.);
                      case 3:
                        return sign * RealGradient(233625.*eta/512. + 29085.*xi/256. - 727125.*(eta + 1.)*(xi + 1.)/512. + 874125.*(eta + 1.)*((xi + 1.)*(xi + 1.))/1024. + 2181375.*(xi + 1.)*((eta + 1.)*(eta + 1.))/512. - 5089875.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/1024. + 5089875.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/2048. - 1832355.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. + 273105./512. - 700875.*(eta + 1.)*(eta + 1.)/512. - 2622375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/1024. - 34965.*(xi + 1.)*(xi + 1.)/512. + 6118875.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/2048. - 6118875.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. + 2202795.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/8192. + 1635375.*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 1635375.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/2048. + 588735.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4096., 0.);
                      case 4:
                        return sign * RealGradient(-7875.*eta/4. - 420.*xi + 5250.*(eta + 1.)*(xi + 1.) - 23625.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 15750.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 18375.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 18375.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 6615.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 8925./4. + 23625.*((eta + 1.)*(eta + 1.))/4. + 70875.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. + 945.*((xi + 1.)*(xi + 1.))/4. - 165375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 165375.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 59535.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. - 55125.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 55125.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 19845.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 5:
                        return sign * RealGradient(0., 2250.*eta + 7875.*xi/4. - 23625.*(eta + 1.)*(xi + 1.)/2. + 15750.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 23625.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 165375.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. - 55125.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 99225.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. + 15375./4. - 7875.*(eta + 1.)*(eta + 1.)/2. - 55125.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 2625.*(xi + 1.)*(xi + 1.) + 18375.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 33075.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 2625.*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 55125.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. + 7875.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. + 99225.*((xi + 1.)*(xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 4725.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8.);
                      case 6:
                        return sign * RealGradient(0., -42975.*eta/64. - 152775.*xi/512. + 902475.*(eta + 1.)*(xi + 1.)/256. - 300825.*(eta + 1.)*(xi + 1.)*(xi + 1.)/64. + 902475.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 6648075.*(xi + 1.)*(eta + 1.)*(eta + 1.)/1024. + 4288725.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 3671325.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. - 467475./512. + 316575.*((eta + 1.)*(eta + 1.))/256. + 2216025.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/256. - 6648075.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 50925.*((xi + 1.)*(xi + 1.))/128. - 1429575.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/256. + 1223775.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 204225.*(eta + 1.)*(eta + 1.)*(eta + 1.)/256. + 4288725.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/2048. - 152775.*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. - 3671325.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8192. + 174825.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/1024.);
                      case 7:
                        return sign * RealGradient(0., 1575.*eta/4. + 4725.*xi/32. - 33075.*(eta + 1.)*(xi + 1.)/16. + 11025.*(eta + 1.)*((xi + 1.)*(xi + 1.))/4. - 33075.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 363825.*(xi + 1.)*((eta + 1.)*(eta + 1.))/64. - 297675.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 297675.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/256. + 16425./32. - 17325.*(eta + 1.)*(eta + 1.)/16. - 121275.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/16. + 363825.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/128. - 1575.*(xi + 1.)*(xi + 1.)/8. + 99225.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 99225.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 14175.*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 297675.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/128. + 4725.*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. + 297675.*((xi + 1.)*(xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/512. - 14175.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64.);
                      case 8:
                        return sign * RealGradient(0., -10575.*eta/64. - 26775.*xi/512. + 222075.*(eta + 1.)*(xi + 1.)/256. - 74025.*(eta + 1.)*(xi + 1.)*(xi + 1.)/64. + 222075.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 2943675.*(xi + 1.)*(eta + 1.)*(eta + 1.)/1024. + 3053925.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 3671325.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. - 106275./512. + 140175.*((eta + 1.)*(eta + 1.))/256. + 981225.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/256. - 2943675.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 8925.*((xi + 1.)*(xi + 1.))/128. - 1017975.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/256. + 1223775.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 145425.*(eta + 1.)*(eta + 1.)*(eta + 1.)/256. + 3053925.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/2048. - 26775.*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. - 3671325.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8192. + 174825.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/1024.);
                      case 9:
                        return sign * RealGradient(0., 900.*eta + 1575.*xi/4. - 4725.*(eta + 1.)*(xi + 1.) + 6300.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 4725.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 99225.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. - 11025.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.) + 99225.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. + 4875./4. - 4725.*(eta + 1.)*(eta + 1.)/2. - 33075.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 99225.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 525.*(xi + 1.)*(xi + 1.) + 14700.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 33075.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 2100.*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 11025.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. + 99225.*((xi + 1.)*(xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 4725.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8.);
                      case 10:
                        return sign * RealGradient(-1575.*eta/4. + 1050.*(eta + 1.)*(xi + 1.) - 4725.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 6300.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 11025.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 7350.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.) + 6615.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 1575./4. + 4725.*((eta + 1.)*(eta + 1.))/2. + 14175.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/4. - 99225.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 33075.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/8. - 59535.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. - 33075.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 11025.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 19845.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 11:
                        return sign * RealGradient(46725.*eta/512. - 145425.*(eta + 1.)*(xi + 1.)/512. + 174825.*(eta + 1.)*((xi + 1.)*(xi + 1.))/1024. + 436275.*(xi + 1.)*((eta + 1.)*(eta + 1.))/256. - 3053925.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/1024. + 1017975.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/512. - 1832355.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. + 46725./512. - 140175.*(eta + 1.)*(eta + 1.)/256. - 524475.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/512. + 3671325.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/2048. - 1223775.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/1024. + 2202795.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/8192. + 981225.*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 327075.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. + 588735.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4096., 0.);
                      case 12:
                        return sign * RealGradient(-5775.*eta/32. + 14175.*(eta + 1.)*(xi + 1.)/32. - 14175.*(eta + 1.)*(xi + 1.)*(xi + 1.)/64. - 42525.*(xi + 1.)*(eta + 1.)*(eta + 1.)/16. + 297675.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 99225.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. + 178605.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/256. - 5775./32. + 17325.*((eta + 1.)*(eta + 1.))/16. + 42525.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/32. - 297675.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128. + 99225.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 178605.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. - 121275.*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 40425.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 72765.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/256., 0.);
                      case 13:
                        return sign * RealGradient(105525.*eta/512. - 204225.*(eta + 1.)*(xi + 1.)/512. + 174825.*(eta + 1.)*((xi + 1.)*(xi + 1.))/1024. + 612675.*(xi + 1.)*((eta + 1.)*(eta + 1.))/256. - 4288725.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/1024. + 1429575.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/512. - 2573235.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. + 105525./512. - 316575.*(eta + 1.)*(eta + 1.)/256. - 524475.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/512. + 3671325.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/2048. - 1223775.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/1024. + 2202795.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/8192. + 2216025.*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 738675.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. + 1329615.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4096., 0.);
                      case 14:
                        return sign * RealGradient(-2625.*eta/4. + 2625.*(eta + 1.)*(xi + 1.)/2. - 4725.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 7875.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 55125.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 18375.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 33075.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 2625./4. + 7875.*((eta + 1.)*(eta + 1.))/2. + 14175.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/4. - 99225.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 33075.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/8. - 59535.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. - 55125.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 18375.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 33075.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 15:
                        return sign * RealGradient(0., 2250.*eta + 2625.*xi/4. - 7875.*(eta + 1.)*(xi + 1.) + 7875.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 4725.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 165375.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. - 18375.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.) + 165375.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. + 10875./4. - 23625.*(eta + 1.)*(eta + 1.)/4. - 165375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 99225.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 2625.*(xi + 1.)*(xi + 1.)/4. + 18375.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 165375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. + 5250.*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 11025.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. + 99225.*((xi + 1.)*(xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 23625.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16.);
                      case 16:
                        return sign * RealGradient(0., -52875.*eta/128. - 44625.*xi/512. + 370125.*(eta + 1.)*(xi + 1.)/256. - 370125.*(eta + 1.)*(xi + 1.)*(xi + 1.)/256. + 222075.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 4906125.*(xi + 1.)*(eta + 1.)*(eta + 1.)/1024. + 5089875.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 6118875.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. - 243375./512. + 700875.*((eta + 1.)*(eta + 1.))/512. + 4906125.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/1024. - 2943675.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 44625.*((xi + 1.)*(xi + 1.))/512. - 5089875.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/1024. + 6118875.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4096. - 727125.*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. + 3053925.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/2048. - 26775.*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. - 3671325.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8192. + 874125.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/2048.);
                      case 17:
                        return sign * RealGradient(0., 7875.*eta/8. + 7875.*xi/32. - 55125.*(eta + 1.)*(xi + 1.)/16. + 55125.*(eta + 1.)*((xi + 1.)*(xi + 1.))/16. - 33075.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 606375.*(xi + 1.)*((eta + 1.)*(eta + 1.))/64. - 496125.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 496125.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/256. + 37125./32. - 86625.*(eta + 1.)*(eta + 1.)/32. - 606375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/64. + 363825.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/128. - 7875.*(xi + 1.)*(xi + 1.)/32. + 496125.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 496125.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/256. + 70875.*((eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 297675.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/128. + 4725.*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. + 297675.*((xi + 1.)*(xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/512. - 70875.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128.);
                      case 18:
                        return sign * RealGradient(0., -214875.*eta/128. - 254625.*xi/512. + 1504125.*(eta + 1.)*(xi + 1.)/256. - 1504125.*(eta + 1.)*(xi + 1.)*(xi + 1.)/256. + 902475.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 11080125.*(xi + 1.)*(eta + 1.)*(eta + 1.)/1024. + 7147875.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 6118875.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4096. - 1041375./512. + 1582875.*((eta + 1.)*(eta + 1.))/512. + 11080125.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/1024. - 6648075.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 254625.*((xi + 1.)*(xi + 1.))/512. - 7147875.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/1024. + 6118875.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4096. - 1021125.*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. + 4288725.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/2048. - 152775.*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. - 3671325.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8192. + 874125.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/2048.);
                      case 19:
                        return sign * RealGradient(0., 5625.*eta + 13125.*xi/4. - 39375.*(eta + 1.)*(xi + 1.)/2. + 39375.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. - 23625.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 275625.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. - 91875.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 165375.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. + 31875./4. - 39375.*(eta + 1.)*(eta + 1.)/4. - 275625.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 13125.*(xi + 1.)*(xi + 1.)/4. + 91875.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 165375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. + 13125.*((eta + 1.)*(eta + 1.)*(eta + 1.))/2. - 55125.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. + 7875.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. + 99225.*((xi + 1.)*(xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 23625.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16.);
                      case 20:
                        return RealGradient(0., 10575.*eta/2. + 51825.*xi/16. - 155475.*(eta + 1.)*(xi + 1.)/8. + 39375.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. - 23625.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 1088325.*(xi + 1.)*((eta + 1.)*(eta + 1.))/32. - 362775.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 652995.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/128. + 122325./16. - 74025.*(eta + 1.)*(eta + 1.)/8. - 275625.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 13125.*(xi + 1.)*(xi + 1.)/4. + 91875.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 165375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. + 24675.*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 55125.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. + 7875.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. + 99225.*((xi + 1.)*(xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 44415.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32.);
                      case 21:
                        return RealGradient(0., -8325.*eta/4. - 30825.*xi/16. + 92475.*(eta + 1.)*(xi + 1.)/8. - 15750.*(eta + 1.)*(xi + 1.)*(xi + 1.) + 23625.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 647325.*(xi + 1.)*(eta + 1.)*(eta + 1.)/32. + 215775.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 388395.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128. - 58575./16. + 58275.*((eta + 1.)*(eta + 1.))/16. + 55125.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. - 165375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 2625.*((xi + 1.)*(xi + 1.)) - 18375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.) + 33075.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/8. - 19425.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 55125.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 7875.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. - 99225.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 34965.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64.);
                      case 22:
                        return RealGradient(0., 3375.*eta/4. + 2025.*xi/16. - 6075.*(eta + 1.)*(xi + 1.)/8. + 42525.*(xi + 1.)*((eta + 1.)*(eta + 1.))/32. - 14175.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 25515.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/128. + 13275./16. - 23625.*(eta + 1.)*(eta + 1.)/16. + 7875.*((eta + 1.)*(eta + 1.)*(eta + 1.))/8. - 14175.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64.);
                      case 23:
                        return RealGradient(0., -675.*eta - 2025.*xi/16. + 6075.*(eta + 1.)*(xi + 1.)/8. - 42525.*(xi + 1.)*(eta + 1.)*(eta + 1.)/32. + 14175.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 25515.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128. - 11025./16. + 4725.*((eta + 1.)*(eta + 1.))/4. - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 2835.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16.);
                      case 24:
                        return RealGradient(-20475.*eta/8. + 20475.*(eta + 1.)*(xi + 1.)/4. - 36855.*(eta + 1.)*(xi + 1.)*(xi + 1.)/16. - 74025.*(xi + 1.)*(eta + 1.)*(eta + 1.)/4. + 362775.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 91875.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 33075.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 20475./8. + 74025.*((eta + 1.)*(eta + 1.))/8. + 133245.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/16. - 652995.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 165375.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 59535.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. - 362775.*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. + 91875.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 33075.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 25:
                        return RealGradient(525.*eta - 1050.*(eta + 1.)*(xi + 1.) + 945.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. + 58275.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. - 215775.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 18375.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/2. - 33075.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 525. - 58275.*(eta + 1.)*(eta + 1.)/16. - 104895.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/32. + 388395.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 33075.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 59535.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64. + 215775.*((eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 18375.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 33075.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32., 0.);
                      case 26:
                        return RealGradient(-4725.*eta/4. + 4725.*(eta + 1.)*(xi + 1.)/2. - 8505.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 23625.*(xi + 1.)*(eta + 1.)*(eta + 1.)/8. + 14175.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 4725./4. + 23625.*((eta + 1.)*(eta + 1.))/16. + 42525.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/32. - 25515.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. - 14175.*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 27:
                        return RealGradient(4725.*eta/8. - 4725.*(eta + 1.)*(xi + 1.)/4. + 8505.*(eta + 1.)*((xi + 1.)*(xi + 1.))/16. + 4725.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. - 14175.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 4725./8. - 4725.*(eta + 1.)*(eta + 1.)/4. - 8505.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 25515.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/64. + 14175.*((eta + 1.)*(eta + 1.)*(eta + 1.))/32., 0.);
                      case 28:
                        return RealGradient(-12285.*eta/8. + 4095.*(eta + 1.)*(xi + 1.) - 36855.*(eta + 1.)*(xi + 1.)*(xi + 1.)/16. - 14805.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 72555.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 18375.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 6615.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 12285./8. + 44415.*((eta + 1.)*(eta + 1.))/8. + 133245.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/16. - 652995.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 165375.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 59535.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. - 217665.*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. + 55125.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 19845.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 29:
                        return RealGradient(315.*eta - 840.*(eta + 1.)*(xi + 1.) + 945.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. + 11655.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. - 43155.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 7350.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)) - 6615.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 315. - 34965.*(eta + 1.)*(eta + 1.)/16. - 104895.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/32. + 388395.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 33075.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 59535.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64. + 129465.*((eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 11025.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 19845.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32., 0.);
                      case 30:
                        return RealGradient(-2835.*eta/4. + 1890.*(eta + 1.)*(xi + 1.) - 8505.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 4725.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. + 2835.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 2835./4. + 14175.*((eta + 1.)*(eta + 1.))/16. + 42525.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/32. - 25515.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. - 8505.*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 31:
                        return RealGradient(2835.*eta/8. - 945.*(eta + 1.)*(xi + 1.) + 8505.*(eta + 1.)*((xi + 1.)*(xi + 1.))/16. + 1890.*(xi + 1.)*((eta + 1.)*(eta + 1.)) - 2835.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 2835./8. - 2835.*(eta + 1.)*(eta + 1.)/4. - 8505.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 25515.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/64. + 8505.*((eta + 1.)*(eta + 1.)*(eta + 1.))/32., 0.);
                      case 32:
                        return RealGradient(0., 2115.*eta + 10365.*xi/16. - 31095.*(eta + 1.)*(xi + 1.)/4. + 7875.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 4725.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 652995.*(xi + 1.)*((eta + 1.)*(eta + 1.))/32. - 72555.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 652995.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/128. + 41385./16. - 44415.*(eta + 1.)*(eta + 1.)/8. - 165375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 99225.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 2625.*(xi + 1.)*(xi + 1.)/4. + 18375.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 165375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. + 4935.*((eta + 1.)*(eta + 1.)*(eta + 1.)) - 11025.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. + 99225.*((xi + 1.)*(xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64. - 44415.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32.);
                      case 33:
                        return RealGradient(0., -1665.*eta/2. - 6165.*xi/16. + 18495.*(eta + 1.)*(xi + 1.)/4. - 6300.*(eta + 1.)*(xi + 1.)*(xi + 1.) + 4725.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 388395.*(xi + 1.)*(eta + 1.)*(eta + 1.)/32. + 43155.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 388395.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128. - 18375./16. + 34965.*((eta + 1.)*(eta + 1.))/16. + 33075.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. - 99225.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 525.*((xi + 1.)*(xi + 1.)) - 14700.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.) + 33075.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/8. - 3885.*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 11025.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. - 99225.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 34965.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64.);
                      case 34:
                        return RealGradient(0., 675.*eta/2. + 405.*xi/16. - 1215.*(eta + 1.)*(xi + 1.)/4. + 25515.*(xi + 1.)*((eta + 1.)*(eta + 1.))/32. - 2835.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 25515.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/128. + 5355./16. - 14175.*(eta + 1.)*(eta + 1.)/16. + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.))/2. - 14175.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64.);
                      case 35:
                        return RealGradient(0., -270.*eta - 405.*xi/16. + 1215.*(eta + 1.)*(xi + 1.)/4. - 25515.*(xi + 1.)*(eta + 1.)*(eta + 1.)/32. + 2835.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 25515.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128. - 4365./16. + 2835.*((eta + 1.)*(eta + 1.))/4. - 630.*(eta + 1.)*(eta + 1.)*(eta + 1.) + 2835.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/16.);
                      case 36:
                        return RealGradient(60.*eta + 60. - 495.*(eta + 1.)*(eta + 1.)/2. + 1275.*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 2625.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 945.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32., 0.);
                      case 37:
                        return RealGradient(60.*eta + 60. - 495.*(eta + 1.)*(eta + 1.)/2. + 1275.*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 2625.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 945.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32., 0.);
                      case 38:
                        return RealGradient(-30.*eta - 30. + 495.*((eta + 1.)*(eta + 1.))/4. - 1275.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 2625.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/64., 0.);
                      case 39:
                        return RealGradient(0., 594.*eta + 2295.*xi/2. - 2295.*(eta + 1.)*(xi + 1.) + 4725.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. - 2835.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 3825.*(xi + 1.)*((eta + 1.)*(eta + 1.))/4. + 2889./2. - 495.*(eta + 1.)*(eta + 1.)/2. - 7875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 4725.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 4725.*(xi + 1.)*(xi + 1.)/4. + 2835.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 40:
                        return RealGradient(0., 396.*eta + 765.*xi/2. - 1530.*(eta + 1.)*(xi + 1.) + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 945.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 3825.*(xi + 1.)*((eta + 1.)*(eta + 1.))/4. + 1359./2. - 495.*(eta + 1.)*(eta + 1.)/2. - 7875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 4725.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 1575.*(xi + 1.)*(xi + 1.)/4. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 41:
                        return RealGradient(0., -495.*eta/2. - 765.*xi/4. + 3825.*(eta + 1.)*(xi + 1.)/4. - 7875.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 4725.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 3825.*(xi + 1.)*(eta + 1.)*(eta + 1.)/8. - 1557./4. + 495.*((eta + 1.)*(eta + 1.))/4. + 7875.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/16. - 4725.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 1575.*((xi + 1.)*(xi + 1.))/8. - 945.*(xi + 1.)*(xi + 1.)*(xi + 1.)/16.);
                      case 42:
                        return RealGradient(0., -216.*eta - 675.*xi + 1350.*(eta + 1.)*(xi + 1.) - 1890.*(eta + 1.)*(xi + 1.)*(xi + 1.) + 2835.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 1125.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. - 783. + 90.*((eta + 1.)*(eta + 1.)) + 1575.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. - 4725.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 945.*((xi + 1.)*(xi + 1.)) - 2835.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8.);
                      case 43:
                        return RealGradient(0., -144.*eta - 225.*xi + 900.*(eta + 1.)*(xi + 1.) - 1260.*(eta + 1.)*(xi + 1.)*(xi + 1.) + 945.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 1125.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. - 333. + 90.*((eta + 1.)*(eta + 1.)) + 1575.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. - 4725.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 315.*((xi + 1.)*(xi + 1.)) - 945.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8.);
                      case 44:
                        return RealGradient(0., 90.*eta + 225.*xi/2. - 1125.*(eta + 1.)*(xi + 1.)/2. + 1575.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. - 4725.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 1125.*(xi + 1.)*((eta + 1.)*(eta + 1.))/4. + 369./2. - 45.*(eta + 1.)*(eta + 1.) - 1575.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/4. + 4725.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/32. - 315.*(xi + 1.)*(xi + 1.)/2. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.))/16.);
                      case 45:
                        return RealGradient(-15.*eta/2. - 15./2. + 90.*((eta + 1.)*(eta + 1.)) - 375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 46:
                        return RealGradient(-15.*eta/2. - 15./2. + 90.*((eta + 1.)*(eta + 1.)) - 375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 525.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32., 0.);
                      case 47:
                        return RealGradient(15.*eta/4. + 15./4. - 45.*(eta + 1.)*(eta + 1.) + 375.*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 525.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 945.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.))/64., 0.);
                      case 48:
                        return RealGradient(0., 81.*eta + 135.*xi/4. - 135.*(eta + 1.)*(xi + 1.)/2. + 225.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 297./4. - 135.*(eta + 1.)*(eta + 1.)/4.);
                      case 49:
                        return RealGradient(0., -54.*eta - 135.*xi/4. + 135.*(eta + 1.)*(xi + 1.)/2. - 225.*(xi + 1.)*(eta + 1.)*(eta + 1.)/8. - 243./4. + 45.*((eta + 1.)*(eta + 1.))/2.);
                      case 50:
                        return RealGradient(-30.*eta - 30. + 135.*((eta + 1.)*(eta + 1.))/4. - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 51:
                        return RealGradient(15.*eta/2. + 15./2. - 45.*(eta + 1.)*(eta + 1.)/2. + 75.*((eta + 1.)*(eta + 1.)*(eta + 1.))/8., 0.);
                      case 52:
                        return RealGradient(-30.*eta - 30. + 135.*((eta + 1.)*(eta + 1.))/4. - 75.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 53:
                        return RealGradient(15.*eta/2. + 15./2. - 45.*(eta + 1.)*(eta + 1.)/2. + 75.*((eta + 1.)*(eta + 1.)*(eta + 1.))/8., 0.);
                      case 54:
                        return RealGradient(0., 54.*eta + 45.*xi/4. - 45.*(eta + 1.)*(xi + 1.) + 225.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 207./4. - 135.*(eta + 1.)*(eta + 1.)/4.);
                      case 55:
                        return RealGradient(0., -36.*eta - 45.*xi/4. + 45.*(eta + 1.)*(xi + 1.) - 225.*(xi + 1.)*(eta + 1.)*(eta + 1.)/8. - 153./4. + 45.*((eta + 1.)*(eta + 1.))/2.);
                      case 56:
                        return RealGradient(0., 0.);
                      case 57:
                        return RealGradient(0., 15.*xi/4. - 3./4.);
                      case 58:
                        return RealGradient(0., -15.*xi/4. - 3./4.);
                      case 59:
                        return RealGradient(0., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d^2()/dxideta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-5625.*eta - 13125.*xi/4. + 78750.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 157500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 94500.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 275625.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 367500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 165375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 31875./4. + 39375.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 551250.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 330750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 13125.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 735000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 330750.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 52500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 441000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 7875.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 198450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 23625.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 1:
                        return sign * RealGradient(214875.*eta/128. + 527625.*xi/512. - 1582875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/64. + 3063375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 874125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 11080125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/128. - 3693375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/32. + 6648075.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/128. + 1243875./512. - 1504125.*(eta + 1.)*(eta + 1.)/(2.*2.)/128. - 21443625.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 6118875.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 1021125.*(xi + 1.)*(xi + 1.)/(2.*2.)/256. + 7147875.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/32. - 12866175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. + 501375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/32. - 2039625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. + 291375.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/128. + 3671325.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. - 902475.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128., 0.);
                      case 2:
                        return sign * RealGradient(-7875.*eta/8. - 28875.*xi/32. + 86625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/4. - 212625.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 70875.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 606375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/8. + 202125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 363825.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/8. - 55125./32. + 55125.*((eta + 1.)*(eta + 1.)/(2.*2.))/8. + 1488375.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 496125.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 70875.*((xi + 1.)*(xi + 1.)/(2.*2.))/16. - 496125.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 893025.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8. - 18375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 165375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 23625.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/8. - 297675.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. + 33075.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8., 0.);
                      case 3:
                        return sign * RealGradient(52875.*eta/128. + 233625.*xi/512. - 700875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/64. + 2181375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/64. - 874125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 4906125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/128. - 1635375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/32. + 2943675.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/128. + 409875./512. - 370125.*(eta + 1.)*(eta + 1.)/(2.*2.)/128. - 15269625.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 6118875.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 727125.*(xi + 1.)*(xi + 1.)/(2.*2.)/256. + 5089875.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/32. - 9161775.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. + 123375.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/32. - 2039625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. + 291375.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/128. + 3671325.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. - 222075.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128., 0.);
                      case 4:
                        return sign * RealGradient(-2250.*eta - 7875.*xi/4. + 47250.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 126000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 94500.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 165375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 220500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 99225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 15375./4. + 15750.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 441000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 330750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 10500.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 588000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 264600.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 21000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 441000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 7875.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 198450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 9450.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 5:
                        return sign * RealGradient(0., 2625.*eta/4. + 2250.*xi - 31500.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 165375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 294000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 165375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 63000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 37800.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 10875./4. - 2625.*(eta + 1.)*(eta + 1.)/(2.*2.) - 330750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 588000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 330750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 23625.*(xi + 1.)*(xi + 1.)/(2.*2.) + 198450.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 352800.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 198450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 42000.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 23625.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 6:
                        return sign * RealGradient(0., -105525.*eta/512. - 42975.*xi/64. + 316575.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/32. - 6648075.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 738675.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/8. - 6648075.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 612675.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/32. + 174825.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/16. - 420675./512. + 204225.*((eta + 1.)*(eta + 1.)/(2.*2.))/256. + 12866175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 1429575.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/8. + 12866175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 902475.*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 3671325.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. - 58275.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/128. + 407925.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 3671325.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. - 100275.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/8. + 902475.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128.);
                      case 7:
                        return sign * RealGradient(0., 5775.*eta/32. + 1575.*xi/4. - 17325.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 363825.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 80850.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 363825.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/8. + 42525.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 14175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 17325./32. - 14175.*(eta + 1.)*(eta + 1.)/(2.*2.)/16. - 893025.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 198450.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 893025.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. - 33075.*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 297675.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. + 4725.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/8. - 132300.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 297675.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. + 7350.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 33075.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8.);
                      case 8:
                        return sign * RealGradient(0., -46725.*eta/512. - 10575.*xi/64. + 140175.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/32. - 2943675.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 327075.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/8. - 2943675.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 436275.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/32. + 174825.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/16. - 124275./512. + 145425.*((eta + 1.)*(eta + 1.)/(2.*2.))/256. + 9161775.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 1017975.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/8. + 9161775.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 222075.*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 3671325.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. - 58275.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/128. + 407925.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/4. - 3671325.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. - 24675.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/8. + 222075.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128.);
                      case 9:
                        return sign * RealGradient(0., 1575.*eta/4. + 900.*xi - 18900.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 99225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 176400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 99225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 50400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 37800.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4875./4. - 2100.*(eta + 1.)*(eta + 1.)/(2.*2.) - 264600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 470400.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 264600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 9450.*(xi + 1.)*(xi + 1.)/(2.*2.) + 198450.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 352800.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 198450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 16800.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 9450.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 10:
                        return sign * RealGradient(-900.*eta - 1575.*xi/4. + 18900.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 50400.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 37800.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 99225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 176400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 99225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 4875./4. + 9450.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 264600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 198450.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2100.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 470400.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 264600.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 16800.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 352800.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 198450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 9450.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 11:
                        return sign * RealGradient(10575.*eta/64. + 46725.*xi/512. - 140175.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/32. + 436275.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/32. - 174825.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. + 2943675.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/128. - 327075.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/8. + 2943675.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/128. + 124275./512. - 222075.*(eta + 1.)*(eta + 1.)/(2.*2.)/128. - 9161775.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 3671325.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 145425.*(xi + 1.)*(xi + 1.)/(2.*2.)/256. + 1017975.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/8. - 9161775.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. + 24675.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/8. - 407925.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 58275.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/128. + 3671325.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. - 222075.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128., 0.);
                      case 12:
                        return sign * RealGradient(-1575.*eta/4. - 5775.*xi/32. + 17325.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 42525.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 14175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 363825.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/8. + 80850.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 363825.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/8. - 17325./32. + 33075.*((eta + 1.)*(eta + 1.)/(2.*2.))/8. + 893025.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 297675.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 14175.*((xi + 1.)*(xi + 1.)/(2.*2.))/16. - 198450.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 893025.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8. - 7350.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 132300.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/8. - 297675.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4. + 33075.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/8., 0.);
                      case 13:
                        return sign * RealGradient(42975.*eta/64. + 105525.*xi/512. - 316575.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/32. + 612675.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/32. - 174825.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/16. + 6648075.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/128. - 738675.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/8. + 6648075.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/128. + 420675./512. - 902475.*(eta + 1.)*(eta + 1.)/(2.*2.)/128. - 12866175.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 3671325.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/64. - 204225.*(xi + 1.)*(xi + 1.)/(2.*2.)/256. + 1429575.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/8. - 12866175.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128. + 100275.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/8. - 407925.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/4. + 58275.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/128. + 3671325.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/64. - 902475.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/128., 0.);
                      case 14:
                        return sign * RealGradient(-2250.*eta - 2625.*xi/4. + 31500.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 63000.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 37800.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 165375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 294000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 165375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 10875./4. + 23625.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 330750.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 198450.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2625.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 588000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 330750.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 42000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 352800.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) - 198450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 23625.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 15:
                        return sign * RealGradient(0., 7875.*eta/4. + 2250.*xi - 47250.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 165375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 220500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 99225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 126000.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 94500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 15375./4. - 10500.*(eta + 1.)*(eta + 1.)/(2.*2.) - 441000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 588000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 264600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 15750.*(xi + 1.)*(xi + 1.)/(2.*2.) + 330750.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 7875.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 441000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 198450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 21000.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 9450.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 16:
                        return sign * RealGradient(0., -233625.*eta/512. - 52875.*xi/128. + 700875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/64. - 4906125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 1635375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 2943675.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 2181375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/64. + 874125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/32. - 409875./512. + 727125.*((eta + 1.)*(eta + 1.)/(2.*2.))/256. + 15269625.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 5089875.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 9161775.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 370125.*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 6118875.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. - 291375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/128. + 2039625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/16. - 3671325.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. - 123375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 222075.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128.);
                      case 17:
                        return sign * RealGradient(0., 28875.*eta/32. + 7875.*xi/8. - 86625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/4. + 606375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/8. - 202125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 363825.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/8. + 212625.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/4. - 70875.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. + 55125./32. - 70875.*(eta + 1.)*(eta + 1.)/(2.*2.)/16. - 1488375.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 496125.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 893025.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8. - 55125.*(xi + 1.)*(xi + 1.)/(2.*2.)/8. + 496125.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/4. + 23625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/8. - 165375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 297675.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4. + 18375.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 33075.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/8.);
                      case 18:
                        return sign * RealGradient(0., -527625.*eta/512. - 214875.*xi/128. + 1582875.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/64. - 11080125.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/128. + 3693375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/32. - 6648075.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/128. - 3063375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/64. + 874125.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/32. - 1243875./512. + 1021125.*((eta + 1.)*(eta + 1.)/(2.*2.))/256. + 21443625.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 7147875.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 12866175.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128. + 1504125.*((xi + 1.)*(xi + 1.)/(2.*2.))/128. - 6118875.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/64. - 291375.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/128. + 2039625.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/16. - 3671325.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/64. - 501375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/32. + 902475.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/128.);
                      case 19:
                        return sign * RealGradient(0., 13125.*eta/4. + 5625.*xi - 78750.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 275625.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 367500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 165375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 157500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 94500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 31875./4. - 13125.*(eta + 1.)*(eta + 1.)/(2.*2.) - 551250.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 735000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 330750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 39375.*(xi + 1.)*(xi + 1.)/(2.*2.) + 330750.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) + 7875.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 441000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 198450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 52500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 23625.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 20:
                        return RealGradient(0., 20475.*eta/8. + 10575.*xi/2. - 74025.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 1088325.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 367500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 165375.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 148050.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 88830.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 56925./8. - 20475.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 1088325.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 735000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 330750.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 155475.*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 652995.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. + 12285.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 441000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 198450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 52500.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 23625.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 21:
                        return RealGradient(0., -525.*eta - 8325.*xi/4. + 58275.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 647325.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 294000.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 165375.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 58275.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 34965.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 9825./4. + 2100.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 647325.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 588000.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 330750.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 92475.*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 388395.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. - 1260.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 352800.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 198450.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 42000.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 23625.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                      case 22:
                        return RealGradient(0., 4725.*eta/4. + 3375.*xi/4. - 23625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 42525.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/4. + 23625.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 14175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3375./2. - 4725.*(eta + 1.)*(eta + 1.)/(2.*2.) - 42525.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. - 6075.*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 25515.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. + 2835.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)));
                      case 23:
                        return RealGradient(0., -4725.*eta/8. - 675.*xi + 9450.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 42525.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. - 18900.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 11340.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 8775./8. + 4725.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 42525.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. + 6075.*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 25515.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. - 2835.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2.);
                      case 24:
                        return RealGradient(-10575.*eta/2. - 20475.*xi/8. + 74025.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 148050.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 88830.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1088325.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/4. + 367500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 165375.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 56925./8. + 155475.*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 1088325.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 652995.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 20475.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 735000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 330750.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 52500.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 441000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 12285.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. - 198450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 23625.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 25:
                        return RealGradient(8325.*eta/4. + 525.*xi - 58275.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 58275.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 34965.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 647325.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/4. - 294000.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 165375.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 9825./4. - 92475.*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 647325.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 388395.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 2100.*(xi + 1.)*(xi + 1.)/(2.*2.) + 588000.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 330750.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 42000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 352800.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1260.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 198450.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 23625.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                      case 26:
                        return RealGradient(-3375.*eta/4. - 4725.*xi/4. + 23625.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 23625.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 14175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 42525.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 3375./2. + 6075.*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 42525.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 25515.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 4725.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2835.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                      case 27:
                        return RealGradient(675.*eta + 4725.*xi/8. - 9450.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 18900.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 11340.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 42525.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 8775./8. - 6075.*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 42525.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 25515.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 4725.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 2835.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2., 0.);
                      case 28:
                        return RealGradient(-2115.*eta - 12285.*xi/8. + 44415.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 118440.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 88830.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 652995.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/4. + 220500.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 99225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 26865./8. + 31095.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 435330.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 652995.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 8190.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 588000.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 264600.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 21000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 441000.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 12285.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. - 198450.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 9450.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 29:
                        return RealGradient(1665.*eta/2. + 315.*xi - 34965.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 46620.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 34965.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 388395.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/4. - 176400.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 99225.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 2175./2. - 18495.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 258930.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 388395.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 1680.*(xi + 1.)*(xi + 1.)/(2.*2.) + 470400.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 264600.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) + 16800.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 352800.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1260.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) + 198450.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) - 9450.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                      case 30:
                        return RealGradient(-675.*eta/2. - 2835.*xi/4. + 14175.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 18900.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 14175.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 25515.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.)/4. - 3645./4. + 1215.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. + 17010.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 25515.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)/2. + 3780.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 2835.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.), 0.);
                      case 31:
                        return RealGradient(270.*eta + 2835.*xi/8. - 5670.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 15120.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 11340.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 25515.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.))/4. + 4455./8. - 1215.*(eta + 1.)*(eta + 1.)/(2.*2.)/2. - 17010.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 25515.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2. - 1890.*(xi + 1.)*(xi + 1.)/(2.*2.) + 2835.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.))/2., 0.);
                      case 32:
                        return RealGradient(0., 12285.*eta/8. + 2115.*xi - 44415.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 652995.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/4. - 220500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 99225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 118440.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 88830.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 26865./8. - 8190.*(eta + 1.)*(eta + 1.)/(2.*2.) - 435330.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 588000.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 264600.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 31095.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 652995.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. + 12285.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. - 441000.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 198450.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 21000.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 9450.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 33:
                        return RealGradient(0., -315.*eta - 1665.*xi/2. + 34965.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. - 388395.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. + 176400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 99225.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 46620.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 34965.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2175./2. + 1680.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 258930.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) - 470400.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 264600.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 18495.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 388395.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. - 1260.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 352800.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 198450.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 16800.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 9450.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                      case 34:
                        return RealGradient(0., 2835.*eta/4. + 675.*xi/2. - 14175.*(eta/2. + 1./2.)*(xi/2. + 1./2.)/2. + 25515.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.))/4. + 18900.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 14175.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 3645./4. - 3780.*(eta + 1.)*(eta + 1.)/(2.*2.) - 17010.*(eta + 1.)*(eta + 1.)/(2.*2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 1215.*(xi + 1.)*(xi + 1.)/(2.*2.)/2. + 25515.*((xi + 1.)*(xi + 1.)/(2.*2.))*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.))/2. + 2835.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)));
                      case 35:
                        return RealGradient(0., -2835.*eta/8. - 270.*xi + 5670.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 25515.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.)/4. - 15120.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 11340.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4455./8. + 1890.*((eta + 1.)*(eta + 1.)/(2.*2.)) + 17010.*((eta + 1.)*(eta + 1.)/(2.*2.))*((xi + 1.)*(xi + 1.)/(2.*2.)) + 1215.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 25515.*(xi + 1.)*(xi + 1.)/(2.*2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2. - 2835.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)/2.);
                      case 36:
                        return RealGradient(594.*eta + 60.*xi - 1980.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 7650.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 10500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4725.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 582. - 4590.*(eta + 1.)*(eta + 1.)/(2.*2.) + 6300.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 2835.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                      case 37:
                        return RealGradient(396.*eta + 60.*xi - 1980.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 7650.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 10500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4725.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)) + 408. - 3060.*(eta + 1.)*(eta + 1.)/(2.*2.) + 4200.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 1890.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.), 0.);
                      case 38:
                        return RealGradient(-495.*eta/2. - 30.*xi + 990.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 3825.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 5250.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4725.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/2. - 495./2. + 3825.*((eta + 1.)*(eta + 1.)/(2.*2.))/2. - 2625.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4725.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/4., 0.);
                      case 39:
                        return RealGradient(0., 60.*eta + 594.*xi - 1980.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 7650.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 10500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4725.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 582. - 4590.*(xi + 1.)*(xi + 1.)/(2.*2.) + 6300.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 2835.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 40:
                        return RealGradient(0., 60.*eta + 396.*xi - 1980.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 7650.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 10500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4725.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)) + 408. - 3060.*(xi + 1.)*(xi + 1.)/(2.*2.) + 4200.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 1890.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.));
                      case 41:
                        return RealGradient(0., -30.*eta - 495.*xi/2. + 990.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 3825.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 5250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/2. - 495./2. + 3825.*((xi + 1.)*(xi + 1.)/(2.*2.))/2. - 2625.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4725.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/4.);
                      case 42:
                        return RealGradient(0., -15.*eta/2. - 216.*xi + 720.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 4500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 429./2. + 2700.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 5040.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 2835.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                      case 43:
                        return RealGradient(0., -15.*eta/2. - 144.*xi + 720.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 4500.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) + 8400.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.) - 291./2. + 1800.*((xi + 1.)*(xi + 1.)/(2.*2.)) - 3360.*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 1890.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)));
                      case 44:
                        return RealGradient(0., 15.*eta/4. + 90.*xi - 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 2250.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) - 4200.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.) + 4725.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.))/2. + 90. - 1125.*(xi + 1.)*(xi + 1.)/(2.*2.) + 2100.*((xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.)) - 4725.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/(2.*2.*2.*2.)/4.);
                      case 45:
                        return RealGradient(-216.*eta - 15.*xi/2. + 720.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 4500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 8400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4725.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 429./2. + 2700.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 5040.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 2835.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 46:
                        return RealGradient(-144.*eta - 15.*xi/2. + 720.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 4500.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) + 8400.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4725.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.) - 291./2. + 1800.*((eta + 1.)*(eta + 1.)/(2.*2.)) - 3360.*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 1890.*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)), 0.);
                      case 47:
                        return RealGradient(90.*eta + 15.*xi/4. - 360.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 2250.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) - 4200.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.) + 4725.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.))/2. + 90. - 1125.*(eta + 1.)*(eta + 1.)/(2.*2.) + 2100.*((eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.)) - 4725.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/(2.*2.*2.*2.)/4., 0.);
                      case 48:
                        return RealGradient(0., 30.*eta + 81.*xi - 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 75. - 135.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      case 49:
                        return RealGradient(0., -15.*eta/2. - 54.*xi + 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 105./2. + 135.*((xi + 1.)*(xi + 1.)/(2.*2.)));
                      case 50:
                        return RealGradient(-81.*eta - 30.*xi + 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 75. + 135.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                      case 51:
                        return RealGradient(54.*eta + 15.*xi/2. - 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 105./2. - 135.*(eta + 1.)*(eta + 1.)/(2.*2.), 0.);
                      case 52:
                        return RealGradient(-54.*eta - 30.*xi + 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(xi/2. + 1./2.)*(eta + 1.)*(eta + 1.)/(2.*2.) - 60. + 90.*((eta + 1.)*(eta + 1.)/(2.*2.)), 0.);
                      case 53:
                        return RealGradient(36.*eta + 15.*xi/2. - 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(xi/2. + 1./2.)*((eta + 1.)*(eta + 1.)/(2.*2.)) + 75./2. - 90.*(eta + 1.)*(eta + 1.)/(2.*2.), 0.);
                      case 54:
                        return RealGradient(0., 30.*eta + 54.*xi - 270.*(eta/2. + 1./2.)*(xi/2. + 1./2.) + 225.*(eta/2. + 1./2.)*((xi + 1.)*(xi + 1.)/(2.*2.)) + 60. - 90.*(xi + 1.)*(xi + 1.)/(2.*2.));
                      case 55:
                        return RealGradient(0., -15.*eta/2. - 36.*xi + 180.*(eta/2. + 1./2.)*(xi/2. + 1./2.) - 225.*(eta/2. + 1./2.)*(xi + 1.)*(xi + 1.)/(2.*2.) - 75./2. + 90.*((xi + 1.)*(xi + 1.)/(2.*2.)));
                      case 56:
                        return RealGradient(0., 0.);
                      case 57:
                        return RealGradient(0., 0.);
                      case 58:
                        return RealGradient(0., 0.);
                      case 59:
                        return RealGradient(0., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                  // d^2()/deta^2
                case 2:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(-13125.*eta/4. - 5625.*xi + 39375.*(eta + 1.)*(xi + 1.)/2. - 275625.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 91875.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 165375.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. - 39375.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. + 23625.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 31875./4. + 13125.*((eta + 1.)*(eta + 1.))/4. + 275625.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. - 91875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. + 39375.*((xi + 1.)*(xi + 1.))/4. - 165375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 7875.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 55125.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. - 13125.*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 23625.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/16., 0.);
                      case 1:
                        return sign * RealGradient(254625.*eta/512. + 214875.*xi/128. - 1504125.*(eta + 1.)*(xi + 1.)/256. + 11080125.*(eta + 1.)*((xi + 1.)*(xi + 1.))/1024. - 7147875.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. + 6118875.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. + 1504125.*(xi + 1.)*((eta + 1.)*(eta + 1.))/256. - 902475.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. + 1041375./512. - 254625.*(eta + 1.)*(eta + 1.)/512. - 11080125.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/1024. + 7147875.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/1024. - 6118875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4096. - 1582875.*(xi + 1.)*(xi + 1.)/512. + 6648075.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/2048. + 152775.*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 4288725.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 3671325.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8192. + 1021125.*((xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 874125.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048., 0.);
                      case 2:
                        return sign * RealGradient(-7875.*eta/32. - 7875.*xi/8. + 55125.*(eta + 1.)*(xi + 1.)/16. - 606375.*(eta + 1.)*(xi + 1.)*(xi + 1.)/64. + 496125.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 496125.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/256. - 55125.*(xi + 1.)*(eta + 1.)*(eta + 1.)/16. + 33075.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 37125./32. + 7875.*((eta + 1.)*(eta + 1.))/32. + 606375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/64. - 496125.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 496125.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/256. + 86625.*((xi + 1.)*(xi + 1.))/32. - 363825.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128. - 4725.*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 297675.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/128. - 297675.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/512. - 70875.*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 70875.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/128., 0.);
                      case 3:
                        return sign * RealGradient(44625.*eta/512. + 52875.*xi/128. - 370125.*(eta + 1.)*(xi + 1.)/256. + 4906125.*(eta + 1.)*((xi + 1.)*(xi + 1.))/1024. - 5089875.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. + 6118875.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. + 370125.*(xi + 1.)*((eta + 1.)*(eta + 1.))/256. - 222075.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. + 243375./512. - 44625.*(eta + 1.)*(eta + 1.)/512. - 4906125.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/1024. + 5089875.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/1024. - 6118875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4096. - 700875.*(xi + 1.)*(xi + 1.)/512. + 2943675.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/2048. + 26775.*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 3053925.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 3671325.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8192. + 727125.*((xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 874125.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048., 0.);
                      case 4:
                        return sign * RealGradient(-2625.*eta/4. - 2250.*xi + 7875.*(eta + 1.)*(xi + 1.) - 165375.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 18375.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 165375.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. - 7875.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 4725.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/2. - 10875./4. + 2625.*((eta + 1.)*(eta + 1.))/4. + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. - 18375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. + 23625.*((xi + 1.)*(xi + 1.))/4. - 99225.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 11025.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. - 5250.*(xi + 1.)*(xi + 1.)*(xi + 1.) + 23625.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/16., 0.);
                      case 5:
                        return sign * RealGradient(0., 2625.*xi/4. - 2625.*(eta + 1.)*(xi + 1.)/2. + 7875.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 55125.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 18375.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 33075.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 4725.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 2625./4. - 14175.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/4. + 99225.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 33075.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. + 59535.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 7875.*(xi + 1.)*(xi + 1.)/2. + 55125.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 18375.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 33075.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 6:
                        return sign * RealGradient(0., -105525.*xi/512. + 204225.*(eta + 1.)*(xi + 1.)/512. - 612675.*(eta + 1.)*(xi + 1.)*(xi + 1.)/256. + 4288725.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/1024. - 1429575.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/512. + 2573235.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. - 174825.*(xi + 1.)*(eta + 1.)*(eta + 1.)/1024. - 105525./512. + 524475.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/512. - 3671325.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 1223775.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/1024. - 2202795.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8192. + 316575.*((xi + 1.)*(xi + 1.))/256. - 2216025.*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. + 738675.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 1329615.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4096.);
                      case 7:
                        return sign * RealGradient(0., 5775.*xi/32. - 14175.*(eta + 1.)*(xi + 1.)/32. + 42525.*(eta + 1.)*((xi + 1.)*(xi + 1.))/16. - 297675.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 99225.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. - 178605.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/256. + 14175.*(xi + 1.)*((eta + 1.)*(eta + 1.))/64. + 5775./32. - 42525.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/32. + 297675.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/128. - 99225.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 178605.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 17325.*(xi + 1.)*(xi + 1.)/16. + 121275.*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 40425.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 72765.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/256.);
                      case 8:
                        return sign * RealGradient(0., -46725.*xi/512. + 145425.*(eta + 1.)*(xi + 1.)/512. - 436275.*(eta + 1.)*(xi + 1.)*(xi + 1.)/256. + 3053925.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/1024. - 1017975.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/512. + 1832355.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. - 174825.*(xi + 1.)*(eta + 1.)*(eta + 1.)/1024. - 46725./512. + 524475.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/512. - 3671325.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 1223775.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/1024. - 2202795.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8192. + 140175.*((xi + 1.)*(xi + 1.))/256. - 981225.*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. + 327075.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 588735.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4096.);
                      case 9:
                        return sign * RealGradient(0., 1575.*xi/4. - 1050.*(eta + 1.)*(xi + 1.) + 6300.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 11025.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 7350.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)) - 6615.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 4725.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 1575./4. - 14175.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/4. + 99225.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 33075.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. + 59535.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 4725.*(xi + 1.)*(xi + 1.)/2. + 33075.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 11025.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 19845.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 10:
                        return sign * RealGradient(-1575.*eta/4. - 900.*xi + 4725.*(eta + 1.)*(xi + 1.) - 99225.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 11025.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 99225.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. - 6300.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 4725.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/2. - 4875./4. + 525.*((eta + 1.)*(eta + 1.)) + 33075.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. - 14700.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 33075.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8. + 4725.*((xi + 1.)*(xi + 1.))/2. - 99225.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 11025.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. - 2100.*(xi + 1.)*(xi + 1.)*(xi + 1.) + 4725.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8., 0.);
                      case 11:
                        return sign * RealGradient(26775.*eta/512. + 10575.*xi/64. - 222075.*(eta + 1.)*(xi + 1.)/256. + 2943675.*(eta + 1.)*((xi + 1.)*(xi + 1.))/1024. - 3053925.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. + 3671325.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. + 74025.*(xi + 1.)*((eta + 1.)*(eta + 1.))/64. - 222075.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. + 106275./512. - 8925.*(eta + 1.)*(eta + 1.)/128. - 981225.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/256. + 1017975.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/256. - 1223775.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. - 140175.*(xi + 1.)*(xi + 1.)/256. + 2943675.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/2048. + 26775.*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 3053925.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 3671325.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8192. + 145425.*((xi + 1.)*(xi + 1.)*(xi + 1.))/256. - 174825.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024., 0.);
                      case 12:
                        return sign * RealGradient(-4725.*eta/32. - 1575.*xi/4. + 33075.*(eta + 1.)*(xi + 1.)/16. - 363825.*(eta + 1.)*(xi + 1.)*(xi + 1.)/64. + 297675.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 297675.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/256. - 11025.*(xi + 1.)*(eta + 1.)*(eta + 1.)/4. + 33075.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/32. - 16425./32. + 1575.*((eta + 1.)*(eta + 1.))/8. + 121275.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/16. - 99225.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 99225.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64. + 17325.*((xi + 1.)*(xi + 1.))/16. - 363825.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/128. - 4725.*(eta + 1.)*(eta + 1.)*(eta + 1.)/64. + 297675.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/128. - 297675.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/512. - 14175.*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 14175.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64., 0.);
                      case 13:
                        return sign * RealGradient(152775.*eta/512. + 42975.*xi/64. - 902475.*(eta + 1.)*(xi + 1.)/256. + 6648075.*(eta + 1.)*((xi + 1.)*(xi + 1.))/1024. - 4288725.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. + 3671325.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. + 300825.*(xi + 1.)*((eta + 1.)*(eta + 1.))/64. - 902475.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/512. + 467475./512. - 50925.*(eta + 1.)*(eta + 1.)/128. - 2216025.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/256. + 1429575.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/256. - 1223775.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. - 316575.*(xi + 1.)*(xi + 1.)/256. + 6648075.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/2048. + 152775.*((eta + 1.)*(eta + 1.)*(eta + 1.))/1024. - 4288725.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 3671325.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8192. + 204225.*((xi + 1.)*(xi + 1.)*(xi + 1.))/256. - 174825.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024., 0.);
                      case 14:
                        return sign * RealGradient(-7875.*eta/4. - 2250.*xi + 23625.*(eta + 1.)*(xi + 1.)/2. - 165375.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 55125.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 99225.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. - 15750.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 23625.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 15375./4. + 2625.*((eta + 1.)*(eta + 1.)) + 55125.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. - 18375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 33075.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8. + 7875.*((xi + 1.)*(xi + 1.))/2. - 165375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 7875.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 55125.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. - 2625.*(xi + 1.)*(xi + 1.)*(xi + 1.) + 4725.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8., 0.);
                      case 15:
                        return sign * RealGradient(0., 420.*eta + 7875.*xi/4. - 5250.*(eta + 1.)*(xi + 1.) + 15750.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 18375.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 18375.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 6615.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 23625.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 8925./4. - 945.*(eta + 1.)*(eta + 1.)/4. - 70875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 165375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 59535.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 23625.*(xi + 1.)*(xi + 1.)/4. + 55125.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 55125.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 19845.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 16:
                        return sign * RealGradient(0., -29085.*eta/256. - 233625.*xi/512. + 727125.*(eta + 1.)*(xi + 1.)/512. - 2181375.*(eta + 1.)*(xi + 1.)*(xi + 1.)/512. + 5089875.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/1024. - 5089875.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 1832355.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. - 874125.*(xi + 1.)*(eta + 1.)*(eta + 1.)/1024. - 273105./512. + 34965.*((eta + 1.)*(eta + 1.))/512. + 2622375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/1024. - 6118875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 6118875.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. - 2202795.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8192. + 700875.*((xi + 1.)*(xi + 1.))/512. - 1635375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. + 1635375.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/2048. - 588735.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4096.);
                      case 17:
                        return sign * RealGradient(0., 2835.*eta/16. + 28875.*xi/32. - 70875.*(eta + 1.)*(xi + 1.)/32. + 212625.*(eta + 1.)*((xi + 1.)*(xi + 1.))/32. - 496125.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 496125.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/128. - 178605.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/256. + 70875.*(xi + 1.)*((eta + 1.)*(eta + 1.))/64. + 32235./32. - 2835.*(eta + 1.)*(eta + 1.)/32. - 212625.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/64. + 496125.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/128. - 496125.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/256. + 178605.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/512. - 86625.*(xi + 1.)*(xi + 1.)/32. + 202125.*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 202125.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/128. + 72765.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/256.);
                      case 18:
                        return sign * RealGradient(0., -40845.*eta/256. - 527625.*xi/512. + 1021125.*(eta + 1.)*(xi + 1.)/512. - 3063375.*(eta + 1.)*(xi + 1.)*(xi + 1.)/512. + 7147875.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/1024. - 7147875.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 2573235.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. - 874125.*(xi + 1.)*(eta + 1.)*(eta + 1.)/1024. - 567105./512. + 34965.*((eta + 1.)*(eta + 1.))/512. + 2622375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/1024. - 6118875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2048. + 6118875.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4096. - 2202795.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8192. + 1582875.*((xi + 1.)*(xi + 1.))/512. - 3693375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/1024. + 3693375.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/2048. - 1329615.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4096.);
                      case 19:
                        return sign * RealGradient(0., 525.*eta + 13125.*xi/4. - 13125.*(eta + 1.)*(xi + 1.)/2. + 39375.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. - 91875.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 91875.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 33075.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 23625.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 14175./4. - 945.*(eta + 1.)*(eta + 1.)/4. - 70875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 165375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 59535.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 39375.*(xi + 1.)*(xi + 1.)/4. + 91875.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 91875.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 33075.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 20:
                        return RealGradient(0., 20475.*xi/8. - 20475.*(eta + 1.)*(xi + 1.)/4. + 74025.*(eta + 1.)*((xi + 1.)*(xi + 1.))/4. - 362775.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 91875.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 33075.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 36855.*(xi + 1.)*((eta + 1.)*(eta + 1.))/16. + 20475./8. - 133245.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/16. + 652995.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 165375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 59535.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 74025.*(xi + 1.)*(xi + 1.)/8. + 362775.*((xi + 1.)*(xi + 1.)*(xi + 1.))/32. - 91875.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 33075.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 21:
                        return RealGradient(0., -525.*xi + 1050.*(eta + 1.)*(xi + 1.) - 58275.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. + 215775.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 18375.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 33075.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 945.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. - 525. + 104895.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/32. - 388395.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 33075.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 59535.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 58275.*((xi + 1.)*(xi + 1.))/16. - 215775.*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 18375.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 33075.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32.);
                      case 22:
                        return RealGradient(0., 4725.*xi/4. - 4725.*(eta + 1.)*(xi + 1.)/2. + 23625.*(eta + 1.)*((xi + 1.)*(xi + 1.))/8. - 14175.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 8505.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 4725./4. - 42525.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/32. + 25515.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 23625.*(xi + 1.)*(xi + 1.)/16. + 14175.*((xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 23:
                        return RealGradient(0., -4725.*xi/8. + 4725.*(eta + 1.)*(xi + 1.)/4. - 4725.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 14175.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 8505.*(xi + 1.)*(eta + 1.)*(eta + 1.)/16. - 4725./8. + 8505.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. - 25515.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 4725.*((xi + 1.)*(xi + 1.))/4. - 14175.*(xi + 1.)*(xi + 1.)*(xi + 1.)/32.);
                      case 24:
                        return RealGradient(-51825.*eta/16. - 10575.*xi/2. + 155475.*(eta + 1.)*(xi + 1.)/8. - 1088325.*(eta + 1.)*(xi + 1.)*(xi + 1.)/32. + 362775.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 652995.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/128. - 39375.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. + 23625.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 122325./16. + 13125.*((eta + 1.)*(eta + 1.))/4. + 275625.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. - 91875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. + 74025.*((xi + 1.)*(xi + 1.))/8. - 165375.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 7875.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 55125.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. - 24675.*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 44415.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32., 0.);
                      case 25:
                        return RealGradient(30825.*eta/16. + 8325.*xi/4. - 92475.*(eta + 1.)*(xi + 1.)/8. + 647325.*(eta + 1.)*((xi + 1.)*(xi + 1.))/32. - 215775.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 388395.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/128. + 15750.*(xi + 1.)*((eta + 1.)*(eta + 1.)) - 23625.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 58575./16. - 2625.*(eta + 1.)*(eta + 1.) - 55125.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 18375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 33075.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. - 58275.*(xi + 1.)*(xi + 1.)/16. + 165375.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. + 7875.*((eta + 1.)*(eta + 1.)*(eta + 1.))/8. - 55125.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64. + 19425.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 34965.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64., 0.);
                      case 26:
                        return RealGradient(-2025.*eta/16. - 3375.*xi/4. + 6075.*(eta + 1.)*(xi + 1.)/8. - 42525.*(eta + 1.)*(xi + 1.)*(xi + 1.)/32. + 14175.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/16. - 25515.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/128. - 13275./16. + 23625.*((xi + 1.)*(xi + 1.))/16. - 7875.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. + 14175.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64., 0.);
                      case 27:
                        return RealGradient(2025.*eta/16. + 675.*xi - 6075.*(eta + 1.)*(xi + 1.)/8. + 42525.*(eta + 1.)*((xi + 1.)*(xi + 1.))/32. - 14175.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 25515.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/128. + 11025./16. - 4725.*(xi + 1.)*(xi + 1.)/4. + 1575.*((xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 2835.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16., 0.);
                      case 28:
                        return RealGradient(-10365.*eta/16. - 2115.*xi + 31095.*(eta + 1.)*(xi + 1.)/4. - 652995.*(eta + 1.)*(xi + 1.)*(xi + 1.)/32. + 72555.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 652995.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/128. - 7875.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 4725.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/2. - 41385./16. + 2625.*((eta + 1.)*(eta + 1.))/4. + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. - 18375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 165375.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. + 44415.*((xi + 1.)*(xi + 1.))/8. - 99225.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 1575.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8. + 11025.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 99225.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. - 4935.*(xi + 1.)*(xi + 1.)*(xi + 1.) + 44415.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32., 0.);
                      case 29:
                        return RealGradient(6165.*eta/16. + 1665.*xi/2. - 18495.*(eta + 1.)*(xi + 1.)/4. + 388395.*(eta + 1.)*((xi + 1.)*(xi + 1.))/32. - 43155.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 388395.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/128. + 6300.*(xi + 1.)*((eta + 1.)*(eta + 1.)) - 4725.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 18375./16. - 525.*(eta + 1.)*(eta + 1.) - 33075.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 14700.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 33075.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. - 34965.*(xi + 1.)*(xi + 1.)/16. + 99225.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. + 1575.*((eta + 1.)*(eta + 1.)*(eta + 1.))/8. - 11025.*(eta + 1.)*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 99225.*((eta + 1.)*(eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64. + 3885.*((xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 34965.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64., 0.);
                      case 30:
                        return RealGradient(-405.*eta/16. - 675.*xi/2. + 1215.*(eta + 1.)*(xi + 1.)/4. - 25515.*(eta + 1.)*(xi + 1.)*(xi + 1.)/32. + 2835.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 25515.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/128. - 5355./16. + 14175.*((xi + 1.)*(xi + 1.))/16. - 1575.*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 14175.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64., 0.);
                      case 31:
                        return RealGradient(405.*eta/16. + 270.*xi - 1215.*(eta + 1.)*(xi + 1.)/4. + 25515.*(eta + 1.)*((xi + 1.)*(xi + 1.))/32. - 2835.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 25515.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/128. + 4365./16. - 2835.*(xi + 1.)*(xi + 1.)/4. + 630.*((xi + 1.)*(xi + 1.)*(xi + 1.)) - 2835.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16., 0.);
                      case 32:
                        return RealGradient(0., 12285.*xi/8. - 4095.*(eta + 1.)*(xi + 1.) + 14805.*(eta + 1.)*((xi + 1.)*(xi + 1.)) - 72555.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 18375.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/2. - 6615.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 36855.*(xi + 1.)*((eta + 1.)*(eta + 1.))/16. + 12285./8. - 133245.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/16. + 652995.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 165375.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 59535.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 44415.*(xi + 1.)*(xi + 1.)/8. + 217665.*((xi + 1.)*(xi + 1.)*(xi + 1.))/32. - 55125.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 19845.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 33:
                        return RealGradient(0., -315.*xi + 840.*(eta + 1.)*(xi + 1.) - 11655.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. + 43155.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 7350.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.) + 6615.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 945.*(xi + 1.)*(eta + 1.)*(eta + 1.)/2. - 315. + 104895.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/32. - 388395.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 33075.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/8. - 59535.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 34965.*((xi + 1.)*(xi + 1.))/16. - 129465.*(xi + 1.)*(xi + 1.)*(xi + 1.)/32. + 11025.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 19845.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32.);
                      case 34:
                        return RealGradient(0., 2835.*xi/4. - 1890.*(eta + 1.)*(xi + 1.) + 4725.*(eta + 1.)*((xi + 1.)*(xi + 1.))/2. - 2835.*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/4. + 8505.*(xi + 1.)*((eta + 1.)*(eta + 1.))/8. + 2835./4. - 42525.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/32. + 25515.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.)*(xi + 1.))/64. - 14175.*(xi + 1.)*(xi + 1.)/16. + 8505.*((xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 35:
                        return RealGradient(0., -2835.*xi/8. + 945.*(eta + 1.)*(xi + 1.) - 1890.*(eta + 1.)*(xi + 1.)*(xi + 1.) + 2835.*(eta + 1.)*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 8505.*(xi + 1.)*(eta + 1.)*(eta + 1.)/16. - 2835./8. + 8505.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/8. - 25515.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64. + 2835.*((xi + 1.)*(xi + 1.))/4. - 8505.*(xi + 1.)*(xi + 1.)*(xi + 1.)/32.);
                      case 36:
                        return RealGradient(2295.*eta/2. + 594.*xi - 2295.*(eta + 1.)*(xi + 1.) + 3825.*(eta + 1.)*((xi + 1.)*(xi + 1.))/4. + 4725.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. - 2835.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/4. + 2889./2. - 4725.*(eta + 1.)*(eta + 1.)/4. - 7875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 495.*(xi + 1.)*(xi + 1.)/2. + 4725.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. + 2835.*((eta + 1.)*(eta + 1.)*(eta + 1.))/8., 0.);
                      case 37:
                        return RealGradient(765.*eta/2. + 396.*xi - 1530.*(eta + 1.)*(xi + 1.) + 3825.*(eta + 1.)*((xi + 1.)*(xi + 1.))/4. + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.)) - 945.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/2. + 1359./2. - 1575.*(eta + 1.)*(eta + 1.)/4. - 7875.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 495.*(xi + 1.)*(xi + 1.)/2. + 4725.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. + 945.*((eta + 1.)*(eta + 1.)*(eta + 1.))/8., 0.);
                      case 38:
                        return RealGradient(-765.*eta/4. - 495.*xi/2. + 3825.*(eta + 1.)*(xi + 1.)/4. - 3825.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 7875.*(xi + 1.)*(eta + 1.)*(eta + 1.)/8. + 4725.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/16. - 1557./4. + 1575.*((eta + 1.)*(eta + 1.))/8. + 7875.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/16. + 495.*((xi + 1.)*(xi + 1.))/4. - 4725.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/32. - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)/16., 0.);
                      case 39:
                        return RealGradient(0., 60.*xi + 60. - 495.*(xi + 1.)*(xi + 1.)/2. + 1275.*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 2625.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 40:
                        return RealGradient(0., 60.*xi + 60. - 495.*(xi + 1.)*(xi + 1.)/2. + 1275.*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 2625.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/16. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32.);
                      case 41:
                        return RealGradient(0., -30.*xi - 30. + 495.*((xi + 1.)*(xi + 1.))/4. - 1275.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. + 2625.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/32. - 945.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/64.);
                      case 42:
                        return RealGradient(0., -15.*xi/2. - 15./2. + 90.*((xi + 1.)*(xi + 1.)) - 375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 525.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 945.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32.);
                      case 43:
                        return RealGradient(0., -15.*xi/2. - 15./2. + 90.*((xi + 1.)*(xi + 1.)) - 375.*(xi + 1.)*(xi + 1.)*(xi + 1.)/2. + 525.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 945.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/32.);
                      case 44:
                        return RealGradient(0., 15.*xi/4. + 15./4. - 45.*(xi + 1.)*(xi + 1.) + 375.*((xi + 1.)*(xi + 1.)*(xi + 1.))/4. - 525.*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)/8. + 945.*((xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.)*(xi + 1.))/64.);
                      case 45:
                        return RealGradient(-675.*eta - 216.*xi + 1350.*(eta + 1.)*(xi + 1.) - 1125.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. - 1890.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 2835.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/4. - 783. + 945.*((eta + 1.)*(eta + 1.)) + 1575.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. + 90.*((xi + 1.)*(xi + 1.)) - 4725.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 2835.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 46:
                        return RealGradient(-225.*eta - 144.*xi + 900.*(eta + 1.)*(xi + 1.) - 1125.*(eta + 1.)*(xi + 1.)*(xi + 1.)/2. - 1260.*(xi + 1.)*(eta + 1.)*(eta + 1.) + 945.*(xi + 1.)*((eta + 1.)*(eta + 1.)*(eta + 1.))/2. - 333. + 315.*((eta + 1.)*(eta + 1.)) + 1575.*((eta + 1.)*(eta + 1.))*((xi + 1.)*(xi + 1.))/2. + 90.*((xi + 1.)*(xi + 1.)) - 4725.*(xi + 1.)*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. - 945.*(eta + 1.)*(eta + 1.)*(eta + 1.)/8., 0.);
                      case 47:
                        return RealGradient(225.*eta/2. + 90.*xi - 1125.*(eta + 1.)*(xi + 1.)/2. + 1125.*(eta + 1.)*((xi + 1.)*(xi + 1.))/4. + 1575.*(xi + 1.)*((eta + 1.)*(eta + 1.))/2. - 4725.*(xi + 1.)*(eta + 1.)*(eta + 1.)*(eta + 1.)/16. + 369./2. - 315.*(eta + 1.)*(eta + 1.)/2. - 1575.*(eta + 1.)*(eta + 1.)*(xi + 1.)*(xi + 1.)/4. - 45.*(xi + 1.)*(xi + 1.) + 4725.*((xi + 1.)*(xi + 1.))*((eta + 1.)*(eta + 1.)*(eta + 1.))/32. + 945.*((eta + 1.)*(eta + 1.)*(eta + 1.))/16., 0.);
                      case 48:
                        return RealGradient(0., 30.*xi + 30. - 135.*(xi + 1.)*(xi + 1.)/4. + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 49:
                        return RealGradient(0., -15.*xi/2. - 15./2. + 45.*((xi + 1.)*(xi + 1.))/2. - 75.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8.);
                      case 50:
                        return RealGradient(-135.*eta/4. - 81.*xi + 135.*(eta + 1.)*(xi + 1.)/2. - 225.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 297./4. + 135.*((xi + 1.)*(xi + 1.))/4., 0.);
                      case 51:
                        return RealGradient(135.*eta/4. + 54.*xi - 135.*(eta + 1.)*(xi + 1.)/2. + 225.*(eta + 1.)*((xi + 1.)*(xi + 1.))/8. + 243./4. - 45.*(xi + 1.)*(xi + 1.)/2., 0.);
                      case 52:
                        return RealGradient(-45.*eta/4. - 54.*xi + 45.*(eta + 1.)*(xi + 1.) - 225.*(eta + 1.)*(xi + 1.)*(xi + 1.)/8. - 207./4. + 135.*((xi + 1.)*(xi + 1.))/4., 0.);
                      case 53:
                        return RealGradient(45.*eta/4. + 36.*xi - 45.*(eta + 1.)*(xi + 1.) + 225.*(eta + 1.)*((xi + 1.)*(xi + 1.))/8. + 153./4. - 45.*(xi + 1.)*(xi + 1.)/2., 0.);
                      case 54:
                        return RealGradient(0., 30.*xi + 30. - 135.*(xi + 1.)*(xi + 1.)/4. + 75.*((xi + 1.)*(xi + 1.)*(xi + 1.))/8.);
                      case 55:
                        return RealGradient(0., -15.*xi/2. - 15./2. + 45.*((xi + 1.)*(xi + 1.))/2. - 75.*(xi + 1.)*(xi + 1.)*(xi + 1.)/8.);
                      case 56:
                        return RealGradient(15.*eta/4. - 3./4., 0.);
                      case 57:
                        return RealGradient(0., 0.);
                      case 58:
                        return RealGradient(0., 0.);
                      case 59:
                        return RealGradient(-15.*eta/4. - 3./4., 0.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          case TRI6:
          case TRI7:
            {
              switch (j)
                {
                  // d^2()/dxi^2
                case 0:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(30240.*eta*xi - 12600.*eta - 12600.*eta*xi*xi - 8400.*xi - 25200.*xi*eta*eta + 2100. + 22680.*(eta*eta) + 7560.*(xi*xi) - 12600.*eta*eta*eta, -45360.*eta*xi + 8400.*eta + 50400.*eta*(xi*xi) + 12600.*xi + 37800.*xi*(eta*eta) - 1400. - 15120.*eta*eta - 30240.*xi*xi + 8400.*(eta*eta*eta) + 21000.*(xi*xi*xi));
                      case 1:
                        return sign * RealGradient(-20475.*eta*xi/2. + 136185.*eta/32. + 58275.*eta*(xi*xi)/16. + 40845.*xi/16. + 146475.*xi*(eta*eta)/16. - 21105./32. - 240975.*eta*eta/32. - 34965.*xi*xi/16. + 127575.*(eta*eta*eta)/32., 252315.*eta*xi/16. - 39375.*eta/16. - 146475.*eta*xi*xi/8. - 125265.*xi/32. - 382725.*xi*eta*eta/32. + 1715./4. + 25515.*(eta*eta)/8. + 145845.*(xi*xi)/16. - 14175.*eta*eta*eta/16. - 97125.*xi*xi*xi/16.);
                      case 2:
                        return sign * RealGradient(7560.*eta*xi - 3255.*eta/2. - 4725.*eta*xi*xi - 2835.*xi - 4725.*xi*eta*eta + 1155./2. + 945.*(eta*eta)/2. + 2835.*(xi*xi) + 1575.*(eta*eta*eta)/2., -4725.*eta*xi + 105.*eta + 9450.*eta*(xi*xi) + 7455.*xi/2. - 4725.*xi*eta*eta/2. - 315. + 1890.*(eta*eta) - 10395.*xi*xi - 1575.*eta*eta*eta + 7875.*(xi*xi*xi));
                      case 3:
                        return sign * RealGradient(-2835.*eta*xi/2. - 16695.*eta/32. + 58275.*eta*(xi*xi)/16. + 29085.*xi/16. - 29925.*xi*eta*eta/16. - 9345./32. + 76545.*(eta*eta)/32. - 34965.*xi*xi/16. - 48825.*eta*eta*eta/32., -65205.*eta*xi/16. + 9345.*eta/16. + 29925.*eta*(xi*xi)/8. - 66465.*xi/32. + 146475.*xi*(eta*eta)/32. + 595./4. - 4725.*eta*eta/8. + 110565.*(xi*xi)/16. - 5775.*eta*eta*eta/16. - 97125.*xi*xi*xi/16.);
                      case 4:
                        return sign * RealGradient(10080.*eta*xi - 1680.*eta - 12600.*eta*xi*xi - 6720.*xi + 1260. + 7560.*(xi*xi), 8400.*xi - 700. - 25200.*xi*xi + 21000.*(xi*xi*xi));
                      case 5:
                        return sign * RealGradient(840.*eta*(12.*xi - 2. - 15.*xi*xi), 8400.*xi - 700. - 25200.*xi*xi + 21000.*(xi*xi*xi));
                      case 6:
                        return sign * RealGradient(2835.*eta*(-120.*eta*xi + 54.*eta + 60.*xi - 16. - 30.*eta*eta - 45.*xi*xi)/32., -127575.*eta*xi/8. + 2205.*eta + 42525.*eta*(xi*xi)/2. + 8505.*xi/2. + 127575.*xi*(eta*eta)/16. - 1785./4. - 31185.*eta*eta/16. - 161595.*xi*xi/16. + 1575.*(eta*eta*eta)/4. + 212625.*(xi*xi*xi)/32.);
                      case 7:
                        return sign * RealGradient(105.*eta*(-60.*eta*xi + 45.*eta + 18.*xi - 8. - 45.*eta*eta - 15.*xi*xi/2.), -13230.*eta*xi + 2520.*eta + 12600.*eta*(xi*xi) + 1680.*xi + 14175.*xi*(eta*eta) - 245. - 4725.*eta*eta - 2835.*xi*xi + 2100.*(eta*eta*eta) + 2625.*(xi*xi*xi)/2.);
                      case 8:
                        return sign * RealGradient(105.*eta*(-360.*eta*xi + 594.*eta + 84.*xi - 80. - 810.*eta*eta - 15.*xi*xi)/32., -36855.*eta*xi/8. + 1575.*eta + 4725.*eta*(xi*xi)/2. + 735.*xi/2. + 127575.*xi*(eta*eta)/16. - 385./4. - 76545.*eta*eta/16. - 5355.*xi*xi/16. + 14175.*(eta*eta*eta)/4. + 2625.*(xi*xi*xi)/32.);
                      case 9:
                        return sign * RealGradient(0., 0.);
                      case 10:
                        return sign * RealGradient(0., 0.);
                      case 11:
                        return sign * RealGradient(105.*eta*(330.*eta*xi + 180.*eta - 54.*xi - 11. - 465.*eta*eta - 15.*xi*xi)/32., 945.*eta*xi/8. + 1155.*eta/2. - 17325.*eta*xi*xi/8. - 1785.*xi/32. + 146475.*xi*(eta*eta)/32. - 595./32. - 76545.*eta*eta/32. + 2835.*(xi*xi)/32. + 9975.*(eta*eta*eta)/16. + 2625.*(xi*xi*xi)/32.);
                      case 12:
                        return sign * RealGradient(105.*eta*(45.*eta*xi - 18.*eta - 3.*xi + 5./2. + 15.*(eta*eta)/2. - 15.*xi*xi/2.), 9450.*eta*xi - 1680.*eta - 9450.*eta*xi*xi - 105.*xi/2. - 4725.*xi*eta*eta/2. + 175./2. - 945.*eta*eta/2. - 2205.*xi*xi/2. + 1575.*(eta*eta*eta) + 2625.*(xi*xi*xi)/2.);
                      case 13:
                        return sign * RealGradient(2835.*eta*(30.*eta*xi - 36.*eta + 30.*xi - 1. + 45.*(eta*eta) - 45.*xi*xi)/32., 76545.*eta*xi/8. - 7245.*eta/2. - 42525.*eta*xi*xi/8. + 127575.*xi/32. - 382725.*xi*eta*eta/32. - 11235./32. + 240975.*(eta*eta)/32. - 314685.*xi*xi/32. - 48825.*eta*eta*eta/16. + 212625.*(xi*xi*xi)/32.);
                      case 14:
                        return sign * RealGradient(840.*eta*(-30.*eta*xi + 18.*eta + 18.*xi - 5. - 15.*eta*eta - 15.*xi*xi), -60480.*eta*xi + 16800.*eta + 50400.*eta*(xi*xi) + 21000.*xi + 37800.*xi*(eta*eta) - 3500. - 22680.*eta*eta - 37800.*xi*xi + 8400.*(eta*eta*eta) + 21000.*(xi*xi*xi));
                      case 15:
                        return RealGradient(10080.*eta*(20.*eta*xi - 21.*eta - 14.*xi + 7. + 15.*(eta*eta) + 5.*(xi*xi)), 423360.*eta*xi - 94080.*eta - 403200.*eta*xi*xi - 70560.*xi - 453600.*xi*eta*eta + 9800. + 211680.*(eta*eta) + 141120.*(xi*xi) - 134400.*eta*eta*eta - 84000.*xi*xi*xi);
                      case 16:
                        return RealGradient(10080.*eta*(-40.*eta*xi + 21.*eta + 28.*xi - 7. - 15.*eta*eta - 25.*xi*xi), -846720.*eta*xi + 188160.*eta + 806400.*eta*(xi*xi) + 352800.*xi + 453600.*xi*(eta*eta) - 49000. - 211680.*eta*eta - 705600.*xi*xi + 67200.*(eta*eta*eta) + 420000.*(xi*xi*xi));
                      case 17:
                        return RealGradient(20160.*eta*(-10.*eta*xi + 3.*eta + 13.*xi - 3. - 10.*xi*xi), -241920.*eta*xi + 26880.*eta + 403200.*eta*(xi*xi) + 161280.*xi - 14560. - 443520.*xi*xi + 336000.*(xi*xi*xi));
                      case 18:
                        return RealGradient(10080.*eta*(10.*eta*xi - 3.*eta - 22.*xi + 4. + 25.*(xi*xi)), 120960.*eta*xi - 13440.*eta - 201600.*eta*xi*xi - 201600.*xi + 18200. + 554400.*(xi*xi) - 420000.*xi*xi*xi);
                      case 19:
                        return RealGradient(0., 6720.*eta - 280. - 30240.*eta*eta + 33600.*(eta*eta*eta));
                      case 20:
                        return RealGradient(0., -13440.*eta + 560. + 60480.*(eta*eta) - 67200.*eta*eta*eta);
                      case 21:
                        return RealGradient(8960.*eta*(-65.*eta*xi/3. + 14.*eta + 35.*xi/3. - 4. - 10.*eta*eta - 20.*xi*xi/3.), -340480.*eta*xi + 56000.*eta + 1164800.*eta*(xi*xi)/3. + 71680.*xi + 268800.*xi*(eta*eta) - 24920./3. - 81760.*eta*eta - 474880.*xi*xi/3. + 280000.*(eta*eta*eta)/9. + 896000.*(xi*xi*xi)/9.);
                      case 22:
                        return RealGradient(2240.*eta*(280.*eta*xi/3. - 49.*eta - 136.*xi/3. + 13. + 35.*(eta*eta) + 100.*(xi*xi)/3.), 371840.*eta*xi - 62720.*eta - 1254400.*eta*xi*xi/3. - 91840.*xi - 235200.*xi*eta*eta + 32480./3. + 76160.*(eta*eta) + 600320.*(xi*xi)/3. - 224000.*eta*eta*eta/9. - 1120000.*xi*xi*xi/9.);
                      case 23:
                        return RealGradient(2240.*eta*(-100.*eta*xi/3. + 34.*eta + 31.*xi/3. - 6. - 35.*eta*eta - 10.*xi*xi/3.), -183680.*eta*xi + 44800.*eta + 448000.*eta*(xi*xi)/3. + 20160.*xi + 235200.*xi*(eta*eta) - 10640./3. - 109760.*eta*eta - 89600.*xi*xi/3. + 627200.*(eta*eta*eta)/9. + 112000.*(xi*xi*xi)/9.);
                      case 24:
                        return RealGradient(1120.*eta*(250.*eta*xi/3. - 73.*eta - 70.*xi/3. + 12. + 80.*(eta*eta) + 25.*(xi*xi)/3.), 232960.*eta*xi - 58240.*eta - 560000.*eta*xi*xi/3. - 26880.*xi - 268800.*xi*eta*eta + 14840./3. + 125440.*(eta*eta) + 115360.*(xi*xi)/3. - 582400.*eta*eta*eta/9. - 140000.*xi*xi*xi/9.);
                      case 25:
                        return RealGradient(2240.*eta*(20.*eta*xi/3. - eta - 44.*xi/3. + 5. - 5.*eta*eta + 20.*(xi*xi)/3.), 4480.*eta*xi + 15680.*eta/3. - 89600.*eta*xi*xi/3. - 11200.*xi + 33600.*xi*(eta*eta) + 6440./9. - 25760.*eta*eta + 98560.*(xi*xi)/3. + 190400.*(eta*eta*eta)/9. - 224000.*xi*xi*xi/9.);
                      case 26:
                        return RealGradient(2240.*eta*(80.*eta*xi/3. - 23.*eta + 64.*xi/3. - 1. + 25.*(eta*eta) - 100.*xi*xi/3.), 165760.*eta*xi - 138880.*eta/3. - 358400.*eta*xi*xi/3. + 64960.*xi - 168000.*xi*eta*eta - 48160./9. + 80640.*(eta*eta) - 519680.*xi*xi/3. - 246400.*eta*eta*eta/9. + 1120000.*(xi*xi*xi)/9.);
                      case 27:
                        return RealGradient(1120.*eta*(-40.*eta*xi/3. + 11.*eta - 2.*xi/3. - 1. - 5.*eta*eta + 5.*(xi*xi)/3.), -24640.*eta*xi + 4480.*eta/3. + 89600.*eta*(xi*xi)/3. + 1120.*xi + 16800.*xi*(eta*eta) - 1400./9. + 5600.*(eta*eta) + 2240.*(xi*xi)/3. - 89600.*eta*eta*eta/9. - 28000.*xi*xi*xi/9.);
                      case 28:
                        return RealGradient(1120.*eta*(200.*eta*xi/3. - 17.*eta - 20.*xi/3. + 3. - 5.*eta*eta - 25.*xi*xi/3.), 116480.*eta*xi - 35840.*eta/3. - 448000.*eta*xi*xi/3. - 3360.*xi + 16800.*xi*(eta*eta) + 8680./9. - 30240.*eta*eta - 24640.*xi*xi/3. + 246400.*(eta*eta*eta)/9. + 140000.*(xi*xi*xi)/9.);
                      case 29:
                        return RealGradient(2240.*eta*(-110.*eta*xi/3. + 36.*eta + 71.*xi/3. - 12. - 25.*eta*eta - 20.*xi*xi/3.), -165760.*eta*xi + 89600.*eta/3. + 492800.*eta*(xi*xi)/3. + 24640.*xi + 168000.*xi*(eta*eta) - 29680./9. - 51520.*eta*eta - 138880.*xi*xi/3. + 179200.*(eta*eta*eta)/9. + 224000.*(xi*xi*xi)/9.);
                      case 30:
                        return RealGradient(1120.*eta*(170.*eta*xi/3. - 23.*eta - 134.*xi/3. + 10. + 10.*(eta*eta) + 125.*(xi*xi)/3.), 103040.*eta*xi - 31360.*eta/3. - 380800.*eta*xi*xi/3. - 56000.*xi - 33600.*xi*eta*eta + 51800./9. - 2240.*eta*eta + 375200.*(xi*xi)/3. + 44800.*(eta*eta*eta)/9. - 700000.*xi*xi*xi/9.);
                      case 31:
                        return RealGradient(1120.*eta*(220.*eta*xi/3. - 27.*eta - 178.*xi/3. + 17. + 5.*(eta*eta) + 85.*(xi*xi)/3.), 105280.*eta*xi - 22400.*eta/3. - 492800.*eta*xi*xi/3. - 32480.*xi - 16800.*xi*eta*eta + 27160./9. - 19040.*eta*eta + 239680.*(xi*xi)/3. + 224000.*(eta*eta*eta)/9. - 476000.*xi*xi*xi/9.);
                      case 32:
                        return RealGradient(1120.*eta*(-80.*eta*xi/3. + 5.*eta + 116.*xi/3. - 7. + 5.*(eta*eta) - 125.*xi*xi/3.), -22400.*eta*xi - 8960.*eta/3. + 179200.*eta*(xi*xi)/3. + 39200.*xi - 16800.*xi*eta*eta - 26600./9. + 12320.*(eta*eta) - 324800.*xi*xi/3. - 44800.*eta*eta*eta/9. + 700000.*(xi*xi*xi)/9.);
                      case 33:
                        return RealGradient(1120.*eta*(20.*eta*xi - 17.*eta - 8.*xi + 3. + 15.*(eta*eta) + 5.*(xi*xi)), 47040.*eta*xi - 29120.*eta/3. - 44800.*eta*xi*xi - 7840.*xi - 50400.*xi*eta*eta + 9520./9. + 20160.*(eta*eta) + 15680.*(xi*xi) - 11200.*eta*eta*eta - 28000.*xi*xi*xi/3.);
                      case 34:
                        return RealGradient(3360.*eta*(-10.*eta*xi + 6.*eta + 2.*xi - 1. - 5.*eta*eta), -67200.*eta*xi + 38080.*eta/3. + 67200.*eta*(xi*xi) + 3360.*xi + 50400.*xi*(eta*eta) - 5600./9. - 19040.*eta*eta - 3360.*xi*xi + 22400.*(eta*eta*eta)/3.);
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 0
 
                  // d^2()/dxideta
                case 1:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(45360.*eta*xi - 16800.*eta - 25200.*eta*xi*xi - 12600.*xi - 37800.*xi*eta*eta + 2800. + 30240.*(eta*eta) + 15120.*(xi*xi) - 16800.*eta*eta*eta - 4200.*xi*xi*xi, -30240.*eta*xi + 4200.*eta + 37800.*eta*(xi*xi) + 8400.*xi + 25200.*xi*(eta*eta) - 700. - 7560.*eta*eta - 22680.*xi*xi + 4200.*(eta*eta*eta) + 16800.*(xi*xi*xi));
                      case 1:
                        return sign * RealGradient(-240975.*eta*xi/16. + 7245.*eta/2. + 146475.*eta*(xi*xi)/16. + 136185.*xi/32. + 382725.*xi*(eta*eta)/32. - 12145./16. - 76545.*eta*eta/16. - 20475.*xi*xi/4. + 14175.*(eta*eta*eta)/8. + 19425.*(xi*xi*xi)/16., 25515.*eta*xi/4. + 2835.*eta/32. - 382725.*eta*xi*xi/32. - 39375.*xi/16. - 42525.*xi*eta*eta/16. + 3045./32. - 42525.*eta*eta/32. + 252315.*(xi*xi)/32. + 42525.*(eta*eta*eta)/32. - 48825.*xi*xi*xi/8.);
                      case 2:
                        return sign * RealGradient(945.*eta*xi + 1680.*eta - 4725.*eta*xi*xi - 3255.*xi/2. + 4725.*xi*(eta*eta)/2. - 4725.*eta*eta + 3780.*(xi*xi) + 3150.*(eta*eta*eta) - 1575.*xi*xi*xi, 3780.*eta*xi - 525.*eta/2. - 4725.*eta*xi*xi/2. + 105.*xi - 4725.*xi*eta*eta + 35./2. + 315.*(eta*eta)/2. - 4725.*xi*xi/2. + 525.*(eta*eta*eta)/2. + 3150.*(xi*xi*xi));
                      case 3:
                        return sign * RealGradient(76545.*eta*xi/16. - 1155.*eta/2. - 29925.*eta*xi*xi/16. - 16695.*xi/32. - 146475.*xi*eta*eta/32. + 1855./16. - 945.*eta*eta/16. - 2835.*xi*xi/4. + 5775.*(eta*eta*eta)/8. + 19425.*(xi*xi*xi)/16., -4725.*eta*xi/4. + 1155.*eta/32. + 146475.*eta*(xi*xi)/32. + 9345.*xi/16. - 17325.*xi*eta*eta/16. - 875./32. + 2835.*(eta*eta)/32. - 65205.*xi*xi/32. + 525.*(eta*eta*eta)/32. + 9975.*(xi*xi*xi)/8.);
                      case 4:
                        return sign * RealGradient(-1680.*xi + 140. + 5040.*(xi*xi) - 4200.*xi*xi*xi, 0.);
                      case 5:
                        return sign * RealGradient(-1680.*xi + 140. + 5040.*(xi*xi) - 4200.*xi*xi*xi, 0.);
                      case 6:
                        return sign * RealGradient(76545.*eta*xi/8. - 1575.*eta - 42525.*eta*xi*xi/4. - 2835.*xi/2. - 127575.*xi*eta*eta/16. + 735./4. + 36855.*(eta*eta)/16. + 42525.*(xi*xi)/16. - 1575.*eta*eta*eta/2. - 42525.*xi*xi*xi/32., -31185.*eta*xi/8. + 525.*eta/2. + 127575.*eta*(xi*xi)/16. + 2205.*xi + 4725.*xi*(eta*eta)/4. - 455./4. - 2205.*eta*eta/16. - 127575.*xi*xi/16. + 525.*(eta*eta*eta)/32. + 14175.*(xi*xi*xi)/2.);
                      case 7:
                        return sign * RealGradient(9450.*eta*xi - 2520.*eta - 6300.*eta*xi*xi - 840.*xi - 14175.*xi*eta*eta + 175. + 6615.*(eta*eta) + 945.*(xi*xi) - 4200.*eta*eta*eta - 525.*xi*xi*xi/2., -9450.*eta*xi + 840.*eta + 14175.*eta*(xi*xi) + 2520.*xi + 6300.*xi*(eta*eta) - 175. - 945.*eta*eta - 6615.*xi*xi + 525.*(eta*eta*eta)/2. + 4200.*(xi*xi*xi));
                      case 8:
                        return sign * RealGradient(31185.*eta*xi/8. - 2205.*eta - 4725.*eta*xi*xi/4. - 525.*xi/2. - 127575.*xi*eta*eta/16. + 455./4. + 127575.*(eta*eta)/16. + 2205.*(xi*xi)/16. - 14175.*eta*eta*eta/2. - 525.*xi*xi*xi/32., -76545.*eta*xi/8. + 2835.*eta/2. + 127575.*eta*(xi*xi)/16. + 1575.*xi + 42525.*xi*(eta*eta)/4. - 735./4. - 42525.*eta*eta/16. - 36855.*xi*xi/16. + 42525.*(eta*eta*eta)/32. + 1575.*(xi*xi*xi)/2.);
                      case 9:
                        return sign * RealGradient(0., 1680.*eta - 140. - 5040.*eta*eta + 4200.*(eta*eta*eta));
                      case 10:
                        return sign * RealGradient(0., 1680.*eta - 140. - 5040.*eta*eta + 4200.*(eta*eta*eta));
                      case 11:
                        return sign * RealGradient(4725.*eta*xi/4. - 9345.*eta/16. + 17325.*eta*(xi*xi)/16. - 1155.*xi/32. - 146475.*xi*eta*eta/32. + 875./32. + 65205.*(eta*eta)/32. - 2835.*xi*xi/32. - 9975.*eta*eta*eta/8. - 525.*xi*xi*xi/32., -76545.*eta*xi/16. + 16695.*eta/32. + 146475.*eta*(xi*xi)/32. + 1155.*xi/2. + 29925.*xi*(eta*eta)/16. - 1855./16. + 2835.*(eta*eta)/4. + 945.*(xi*xi)/16. - 19425.*eta*eta*eta/16. - 5775.*xi*xi*xi/8.);
                      case 12:
                        return sign * RealGradient(-3780.*eta*xi - 105.*eta + 4725.*eta*(xi*xi) + 525.*xi/2. + 4725.*xi*(eta*eta)/2. - 35./2. + 4725.*(eta*eta)/2. - 315.*xi*xi/2. - 3150.*eta*eta*eta - 525.*xi*xi*xi/2., -945.*eta*xi + 3255.*eta/2. - 4725.*eta*xi*xi/2. - 1680.*xi + 4725.*xi*(eta*eta) - 3780.*eta*eta + 4725.*(xi*xi) + 1575.*(eta*eta*eta) - 3150.*xi*xi*xi);
                      case 13:
                        return sign * RealGradient(-25515.*eta*xi/4. + 39375.*eta/16. + 42525.*eta*(xi*xi)/16. - 2835.*xi/32. + 382725.*xi*(eta*eta)/32. - 3045./32. - 252315.*eta*eta/32. + 42525.*(xi*xi)/32. + 48825.*(eta*eta*eta)/8. - 42525.*xi*xi*xi/32., 240975.*eta*xi/16. - 136185.*eta/32. - 382725.*eta*xi*xi/32. - 7245.*xi/2. - 146475.*xi*eta*eta/16. + 12145./16. + 20475.*(eta*eta)/4. + 76545.*(xi*xi)/16. - 19425.*eta*eta*eta/16. - 14175.*xi*xi*xi/8.);
                      case 14:
                        return sign * RealGradient(30240.*eta*xi - 8400.*eta - 25200.*eta*xi*xi - 4200.*xi - 37800.*xi*eta*eta + 700. + 22680.*(eta*eta) + 7560.*(xi*xi) - 16800.*eta*eta*eta - 4200.*xi*xi*xi, -45360.*eta*xi + 12600.*eta + 37800.*eta*(xi*xi) + 16800.*xi + 25200.*xi*(eta*eta) - 2800. - 15120.*eta*eta - 30240.*xi*xi + 4200.*(eta*eta*eta) + 16800.*(xi*xi*xi));
                      case 15:
                        return RealGradient(-423360.*eta*xi + 188160.*eta + 201600.*eta*(xi*xi) + 70560.*xi + 453600.*xi*(eta*eta) - 19600. - 423360.*eta*eta - 70560.*xi*xi + 268800.*(eta*eta*eta) + 16800.*(xi*xi*xi), 423360.*eta*xi - 70560.*eta - 453600.*eta*xi*xi - 94080.*xi - 403200.*xi*eta*eta + 9800. + 141120.*(eta*eta) + 211680.*(xi*xi) - 84000.*eta*eta*eta - 134400.*xi*xi*xi);
                      case 16:
                        return RealGradient(423360.*eta*xi - 94080.*eta - 403200.*eta*xi*xi - 70560.*xi - 453600.*xi*eta*eta + 9800. + 211680.*(eta*eta) + 141120.*(xi*xi) - 134400.*eta*eta*eta - 84000.*xi*xi*xi, -423360.*eta*xi + 70560.*eta + 453600.*eta*(xi*xi) + 188160.*xi + 201600.*xi*(eta*eta) - 19600. - 70560.*eta*eta - 423360.*xi*xi + 16800.*(eta*eta*eta) + 268800.*(xi*xi*xi));
                      case 17:
                        return RealGradient(120960.*eta*xi - 13440.*eta - 201600.*eta*xi*xi - 60480.*xi + 6440. + 131040.*(xi*xi) - 67200.*xi*xi*xi, 26880.*xi - 1120. - 120960.*xi*xi + 134400.*(xi*xi*xi));
                      case 18:
                        return RealGradient(-60480.*eta*xi + 6720.*eta + 100800.*eta*(xi*xi) + 40320.*xi - 3640. - 110880.*xi*xi + 84000.*(xi*xi*xi), -13440.*xi + 560. + 60480.*(xi*xi) - 67200.*xi*xi*xi);
                      case 19:
                        return RealGradient(-13440.*eta + 560. + 60480.*(eta*eta) - 67200.*eta*eta*eta, -60480.*eta*xi + 40320.*eta + 6720.*xi + 100800.*xi*(eta*eta) - 3640. - 110880.*eta*eta + 84000.*(eta*eta*eta));
                      case 20:
                        return RealGradient(26880.*eta - 1120. - 120960.*eta*eta + 134400.*(eta*eta*eta), 120960.*eta*xi - 60480.*eta - 13440.*xi - 201600.*xi*eta*eta + 6440. + 131040.*(eta*eta) - 67200.*eta*eta*eta);
                      case 21:
                        return RealGradient(250880.*eta*xi - 58240.*eta - 582400.*eta*xi*xi/3. - 35840.*xi - 268800.*xi*eta*eta + 17920./3. + 116480.*(eta*eta) + 156800.*(xi*xi)/3. - 560000.*eta*eta*eta/9. - 179200.*xi*xi*xi/9., -163520.*eta*xi + 13440.*eta + 268800.*eta*(xi*xi) + 56000.*xi + 280000.*xi*(eta*eta)/3. - 10360./3. - 39200.*eta*eta/3. - 170240.*xi*xi + 28000.*(eta*eta*eta)/9. + 1164800.*(xi*xi*xi)/9.);
                      case 22:
                        return RealGradient(-219520.*eta*xi + 44800.*eta + 627200.*eta*(xi*xi)/3. + 29120.*xi + 235200.*xi*(eta*eta) - 12880./3. - 91840.*eta*eta - 152320.*xi*xi/3. + 448000.*(eta*eta*eta)/9. + 224000.*(xi*xi*xi)/9., 152320.*eta*xi - 13440.*eta - 235200.*eta*xi*xi - 62720.*xi - 224000.*xi*eta*eta/3. + 12040./3. + 34720.*(eta*eta)/3. + 185920.*(xi*xi) - 22400.*eta*eta*eta/9. - 1254400.*xi*xi*xi/9.);
                      case 23:
                        return RealGradient(152320.*eta*xi - 62720.*eta - 224000.*eta*xi*xi/3. - 13440.*xi - 235200.*xi*eta*eta + 12040./3. + 185920.*(eta*eta) + 34720.*(xi*xi)/3. - 1254400.*eta*eta*eta/9. - 22400.*xi*xi*xi/9., -219520.*eta*xi + 29120.*eta + 235200.*eta*(xi*xi) + 44800.*xi + 627200.*xi*(eta*eta)/3. - 12880./3. - 152320.*eta*eta/3. - 91840.*xi*xi + 224000.*(eta*eta*eta)/9. + 448000.*(xi*xi*xi)/9.);
                      case 24:
                        return RealGradient(-163520.*eta*xi + 56000.*eta + 280000.*eta*(xi*xi)/3. + 13440.*xi + 268800.*xi*(eta*eta) - 10360./3. - 170240.*eta*eta - 39200.*xi*xi/3. + 1164800.*(eta*eta*eta)/9. + 28000.*(xi*xi*xi)/9., 250880.*eta*xi - 35840.*eta - 268800.*eta*xi*xi - 58240.*xi - 582400.*xi*eta*eta/3. + 17920./3. + 156800.*(eta*eta)/3. + 116480.*(xi*xi) - 179200.*eta*eta*eta/9. - 560000.*xi*xi*xi/9.);
                      case 25:
                        return RealGradient(-4480.*eta*xi - 31360.*eta/3. + 44800.*eta*(xi*xi)/3. + 11200.*xi - 33600.*xi*eta*eta - 12880./9. + 51520.*(eta*eta) - 49280.*xi*xi/3. - 380800.*eta*eta*eta/9. + 44800.*(xi*xi*xi)/9., -51520.*eta*xi + 11200.*eta + 33600.*eta*(xi*xi) + 15680.*xi/3. + 190400.*xi*(eta*eta)/3. - 10360./9. - 75040.*eta*eta/3. + 2240.*(xi*xi) + 140000.*(eta*eta*eta)/9. - 89600.*xi*xi*xi/9.);
                      case 26:
                        return RealGradient(-103040.*eta*xi + 89600.*eta/3. + 179200.*eta*(xi*xi)/3. - 2240.*xi + 168000.*xi*(eta*eta) - 9520./9. - 82880.*eta*eta + 71680.*(xi*xi)/3. + 492800.*(eta*eta*eta)/9. - 224000.*xi*xi*xi/9., 161280.*eta*xi - 26880.*eta - 168000.*eta*xi*xi - 138880.*xi/3. - 246400.*xi*eta*eta/3. + 51800./9. + 79520.*(eta*eta)/3. + 82880.*(xi*xi) - 44800.*eta*eta*eta/9. - 358400.*xi*xi*xi/9.);
                      case 27:
                        return RealGradient(24640.*eta*xi - 8960.*eta/3. - 44800.*eta*xi*xi/3. - 1120.*xi - 16800.*xi*eta*eta + 2800./9. - 11200.*eta*eta - 1120.*xi*xi/3. + 179200.*(eta*eta*eta)/9. + 5600.*(xi*xi*xi)/9., 11200.*eta*xi - 7840.*eta + 16800.*eta*(xi*xi) + 4480.*xi/3. - 89600.*xi*eta*eta/3. + 5320./9. + 64960.*(eta*eta)/3. - 12320.*xi*xi - 140000.*eta*eta*eta/9. + 89600.*(xi*xi*xi)/9.);
                      case 28:
                        return RealGradient(-38080.*eta*xi - 22400.*eta/3. + 224000.*eta*(xi*xi)/3. + 3360.*xi - 16800.*xi*eta*eta + 280./9. + 52640.*(eta*eta) - 11200.*xi*xi/3. - 492800.*eta*eta*eta/9. - 28000.*xi*xi*xi/9., -60480.*eta*xi + 19040.*eta + 16800.*eta*(xi*xi) - 35840.*xi/3. + 246400.*xi*(eta*eta)/3. - 8960./9. - 99680.*eta*eta/3. + 58240.*(xi*xi) + 95200.*(eta*eta*eta)/9. - 448000.*xi*xi*xi/9.);
                      case 29:
                        return RealGradient(161280.*eta*xi - 138880.*eta/3. - 246400.*eta*xi*xi/3. - 26880.*xi - 168000.*xi*eta*eta + 51800./9. + 82880.*(eta*eta) + 79520.*(xi*xi)/3. - 358400.*eta*eta*eta/9. - 44800.*xi*xi*xi/9., -103040.*eta*xi - 2240.*eta + 168000.*eta*(xi*xi) + 89600.*xi/3. + 179200.*xi*(eta*eta)/3. - 9520./9. + 71680.*(eta*eta)/3. - 82880.*xi*xi - 224000.*eta*eta*eta/9. + 492800.*(xi*xi*xi)/9.);
                      case 30:
                        return RealGradient(-51520.*eta*xi + 15680.*eta/3. + 190400.*eta*(xi*xi)/3. + 11200.*xi + 33600.*xi*(eta*eta) - 10360./9. + 2240.*(eta*eta) - 75040.*xi*xi/3. - 89600.*eta*eta*eta/9. + 140000.*(xi*xi*xi)/9., -4480.*eta*xi + 11200.*eta - 33600.*eta*xi*xi - 31360.*xi/3. + 44800.*xi*(eta*eta)/3. - 12880./9. - 49280.*eta*eta/3. + 51520.*(xi*xi) + 44800.*(eta*eta*eta)/9. - 380800.*xi*xi*xi/9.);
                      case 31:
                        return RealGradient(-60480.*eta*xi - 35840.*eta/3. + 246400.*eta*(xi*xi)/3. + 19040.*xi + 16800.*xi*(eta*eta) - 8960./9. + 58240.*(eta*eta) - 99680.*xi*xi/3. - 448000.*eta*eta*eta/9. + 95200.*(xi*xi*xi)/9., -38080.*eta*xi + 3360.*eta - 16800.*eta*xi*xi - 22400.*xi/3. + 224000.*xi*(eta*eta)/3. + 280./9. - 11200.*eta*eta/3. + 52640.*(xi*xi) - 28000.*eta*eta*eta/9. - 492800.*xi*xi*xi/9.);
                      case 32:
                        return RealGradient(11200.*eta*xi + 4480.*eta/3. - 89600.*eta*xi*xi/3. - 7840.*xi + 16800.*xi*(eta*eta) + 5320./9. - 12320.*eta*eta + 64960.*(xi*xi)/3. + 89600.*(eta*eta*eta)/9. - 140000.*xi*xi*xi/9., 24640.*eta*xi - 1120.*eta - 16800.*eta*xi*xi - 8960.*xi/3. - 44800.*xi*eta*eta/3. + 2800./9. - 1120.*eta*eta/3. - 11200.*xi*xi + 5600.*(eta*eta*eta)/9. + 179200.*(xi*xi*xi)/9.);
                      case 33:
                        return RealGradient(-38080.*eta*xi + 38080.*eta/3. + 22400.*eta*(xi*xi) + 3360.*xi + 50400.*xi*(eta*eta) - 6440./9. - 33600.*eta*eta - 4480.*xi*xi + 22400.*(eta*eta*eta) + 5600.*(xi*xi*xi)/3., 40320.*eta*xi - 3360.*eta - 50400.*eta*xi*xi - 29120.*xi/3. - 33600.*xi*eta*eta + 6160./9. + 3360.*(eta*eta) + 23520.*(xi*xi) - 44800.*xi*xi*xi/3.);
                      case 34:
                        return RealGradient(40320.*eta*xi - 29120.*eta/3. - 33600.*eta*xi*xi - 3360.*xi - 50400.*xi*eta*eta + 6160./9. + 23520.*(eta*eta) + 3360.*(xi*xi) - 44800.*eta*eta*eta/3., -38080.*eta*xi + 3360.*eta + 50400.*eta*(xi*xi) + 38080.*xi/3. + 22400.*xi*(eta*eta) - 6440./9. - 4480.*eta*eta - 33600.*xi*xi + 5600.*(eta*eta*eta)/3. + 22400.*(xi*xi*xi));
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 1
 
                  // d^2()/deta^2
                case 2:
                  {
                    switch(ii)
                      {
                      case 0:
                        return sign * RealGradient(60480.*eta*xi - 21000.*eta - 37800.*eta*xi*xi - 16800.*xi - 50400.*xi*eta*eta + 3500. + 37800.*(eta*eta) + 22680.*(xi*xi) - 21000.*eta*eta*eta - 8400.*xi*xi*xi, 840.*xi*(30.*eta*xi - 18.*eta - 18.*xi + 5. + 15.*(eta*eta) + 15.*(xi*xi)));
                      case 1:
                        return sign * RealGradient(-76545.*eta*xi/8. - 127575.*eta/32. + 382725.*eta*(xi*xi)/32. + 7245.*xi/2. + 42525.*xi*(eta*eta)/8. + 11235./32. + 314685.*(eta*eta)/32. - 240975.*xi*xi/32. - 212625.*eta*eta*eta/32. + 48825.*(xi*xi*xi)/16., 2835.*xi*(-30.*eta*xi - 30.*eta + 36.*xi + 1. + 45.*(eta*eta) - 45.*xi*xi)/32.);
                      case 2:
                        return sign * RealGradient(-9450.*eta*xi + 105.*eta/2. + 4725.*eta*(xi*xi)/2. + 1680.*xi + 9450.*xi*(eta*eta) - 175./2. + 2205.*(eta*eta)/2. + 945.*(xi*xi)/2. - 2625.*eta*eta*eta/2. - 1575.*xi*xi*xi, 105.*xi*(-45.*eta*xi + 3.*eta + 18.*xi - 5./2. + 15.*(eta*eta)/2. - 15.*xi*xi/2.));
                      case 3:
                        return sign * RealGradient(-945.*eta*xi/8. + 1785.*eta/32. - 146475.*eta*xi*xi/32. - 1155.*xi/2. + 17325.*xi*(eta*eta)/8. + 595./32. - 2835.*eta*eta/32. + 76545.*(xi*xi)/32. - 2625.*eta*eta*eta/32. - 9975.*xi*xi*xi/16., 105.*xi*(-330.*eta*xi + 54.*eta - 180.*xi + 11. + 15.*(eta*eta) + 465.*(xi*xi))/32.);
                      case 4:
                        return sign * RealGradient(0., 0.);
                      case 5:
                        return sign * RealGradient(0., 0.);
                      case 6:
                        return sign * RealGradient(36855.*eta*xi/8. - 735.*eta/2. - 127575.*eta*xi*xi/16. - 1575.*xi - 4725.*xi*eta*eta/2. + 385./4. + 5355.*(eta*eta)/16. + 76545.*(xi*xi)/16. - 2625.*eta*eta*eta/32. - 14175.*xi*xi*xi/4., 105.*xi*(360.*eta*xi - 84.*eta - 594.*xi + 80. + 15.*(eta*eta) + 810.*(xi*xi))/32.);
                      case 7:
                        return sign * RealGradient(13230.*eta*xi - 1680.*eta - 14175.*eta*xi*xi - 2520.*xi - 12600.*xi*eta*eta + 245. + 2835.*(eta*eta) + 4725.*(xi*xi) - 2625.*eta*eta*eta/2. - 2100.*xi*xi*xi, 105.*xi*(60.*eta*xi - 18.*eta - 45.*xi + 8. + 15.*(eta*eta)/2. + 45.*(xi*xi)));
                      case 8:
                        return sign * RealGradient(127575.*eta*xi/8. - 8505.*eta/2. - 127575.*eta*xi*xi/16. - 2205.*xi - 42525.*xi*eta*eta/2. + 1785./4. + 161595.*(eta*eta)/16. + 31185.*(xi*xi)/16. - 212625.*eta*eta*eta/32. - 1575.*xi*xi*xi/4., 2835.*xi*(120.*eta*xi - 60.*eta - 54.*xi + 16. + 45.*(eta*eta) + 30.*(xi*xi))/32.);
                      case 9:
                        return sign * RealGradient(-8400.*eta + 700. + 25200.*(eta*eta) - 21000.*eta*eta*eta, 840.*xi*(-12.*eta + 2. + 15.*(eta*eta)));
                      case 10:
                        return sign * RealGradient(-8400.*eta + 700. + 25200.*(eta*eta) - 21000.*eta*eta*eta, -10080.*eta*xi + 6720.*eta + 1680.*xi + 12600.*xi*(eta*eta) - 1260. - 7560.*eta*eta);
                      case 11:
                        return sign * RealGradient(65205.*eta*xi/16. + 66465.*eta/32. - 146475.*eta*xi*xi/32. - 9345.*xi/16. - 29925.*xi*eta*eta/8. - 595./4. - 110565.*eta*eta/16. + 4725.*(xi*xi)/8. + 97125.*(eta*eta*eta)/16. + 5775.*(xi*xi*xi)/16., 2835.*eta*xi/2. - 29085.*eta/16. + 29925.*eta*(xi*xi)/16. + 16695.*xi/32. - 58275.*xi*eta*eta/16. + 9345./32. + 34965.*(eta*eta)/16. - 76545.*xi*xi/32. + 48825.*(xi*xi*xi)/32.);
                      case 12:
                        return sign * RealGradient(4725.*eta*xi - 7455.*eta/2. + 4725.*eta*(xi*xi)/2. - 105.*xi - 9450.*xi*eta*eta + 315. + 10395.*(eta*eta) - 1890.*xi*xi - 7875.*eta*eta*eta + 1575.*(xi*xi*xi), -7560.*eta*xi + 2835.*eta + 4725.*eta*(xi*xi) + 3255.*xi/2. + 4725.*xi*(eta*eta) - 1155./2. - 2835.*eta*eta - 945.*xi*xi/2. - 1575.*xi*xi*xi/2.);
                      case 13:
                        return sign * RealGradient(-252315.*eta*xi/16. + 125265.*eta/32. + 382725.*eta*(xi*xi)/32. + 39375.*xi/16. + 146475.*xi*(eta*eta)/8. - 1715./4. - 145845.*eta*eta/16. - 25515.*xi*xi/8. + 97125.*(eta*eta*eta)/16. + 14175.*(xi*xi*xi)/16., 20475.*eta*xi/2. - 40845.*eta/16. - 146475.*eta*xi*xi/16. - 136185.*xi/32. - 58275.*xi*eta*eta/16. + 21105./32. + 34965.*(eta*eta)/16. + 240975.*(xi*xi)/32. - 127575.*xi*xi*xi/32.);
                      case 14:
                        return sign * RealGradient(45360.*eta*xi - 12600.*eta - 37800.*eta*xi*xi - 8400.*xi - 50400.*xi*eta*eta + 1400. + 30240.*(eta*eta) + 15120.*(xi*xi) - 21000.*eta*eta*eta - 8400.*xi*xi*xi, -30240.*eta*xi + 8400.*eta + 25200.*eta*(xi*xi) + 12600.*xi + 12600.*xi*(eta*eta) - 2100. - 7560.*eta*eta - 22680.*xi*xi + 12600.*(xi*xi*xi));
                      case 15:
                        return RealGradient(-846720.*eta*xi + 352800.*eta + 453600.*eta*(xi*xi) + 188160.*xi + 806400.*xi*(eta*eta) - 49000. - 705600.*eta*eta - 211680.*xi*xi + 420000.*(eta*eta*eta) + 67200.*(xi*xi*xi), 10080.*xi*(-40.*eta*xi + 28.*eta + 21.*xi - 7. - 25.*eta*eta - 15.*xi*xi));
                      case 16:
                        return RealGradient(423360.*eta*xi - 70560.*eta - 453600.*eta*xi*xi - 94080.*xi - 403200.*xi*eta*eta + 9800. + 141120.*(eta*eta) + 211680.*(xi*xi) - 84000.*eta*eta*eta - 134400.*xi*xi*xi, 10080.*xi*(20.*eta*xi - 14.*eta - 21.*xi + 7. + 5.*(eta*eta) + 15.*(xi*xi)));
                      case 17:
                        return RealGradient(-13440.*xi + 560. + 60480.*(xi*xi) - 67200.*xi*xi*xi, 0.);
                      case 18:
                        return RealGradient(6720.*xi - 280. - 30240.*xi*xi + 33600.*(xi*xi*xi), 0.);
                      case 19:
                        return RealGradient(120960.*eta*xi - 201600.*eta - 13440.*xi - 201600.*xi*eta*eta + 18200. + 554400.*(eta*eta) - 420000.*eta*eta*eta, 10080.*xi*(10.*eta*xi - 22.*eta - 3.*xi + 4. + 25.*(eta*eta)));
                      case 20:
                        return RealGradient(-241920.*eta*xi + 161280.*eta + 26880.*xi + 403200.*xi*(eta*eta) - 14560. - 443520.*eta*eta + 336000.*(eta*eta*eta), 20160.*xi*(-10.*eta*xi + 13.*eta + 3.*xi - 3. - 10.*eta*eta));
                      case 21:
                        return RealGradient(232960.*eta*xi - 26880.*eta - 268800.*eta*xi*xi - 58240.*xi - 560000.*xi*eta*eta/3. + 14840./3. + 115360.*(eta*eta)/3. + 125440.*(xi*xi) - 140000.*eta*eta*eta/9. - 582400.*xi*xi*xi/9., 1120.*xi*(250.*eta*xi/3. - 70.*eta/3. - 73.*xi + 12. + 25.*(eta*eta)/3. + 80.*(xi*xi)));
                      case 22:
                        return RealGradient(-183680.*eta*xi + 20160.*eta + 235200.*eta*(xi*xi) + 44800.*xi + 448000.*xi*(eta*eta)/3. - 10640./3. - 89600.*eta*eta/3. - 109760.*xi*xi + 112000.*(eta*eta*eta)/9. + 627200.*(xi*xi*xi)/9., 2240.*xi*(-100.*eta*xi/3. + 31.*eta/3. + 34.*xi - 6. - 10.*eta*eta/3. - 35.*xi*xi));
                      case 23:
                        return RealGradient(371840.*eta*xi - 91840.*eta - 235200.*eta*xi*xi - 62720.*xi - 1254400.*xi*eta*eta/3. + 32480./3. + 600320.*(eta*eta)/3. + 76160.*(xi*xi) - 1120000.*eta*eta*eta/9. - 224000.*xi*xi*xi/9., 2240.*xi*(280.*eta*xi/3. - 136.*eta/3. - 49.*xi + 13. + 100.*(eta*eta)/3. + 35.*(xi*xi)));
                      case 24:
                        return RealGradient(-340480.*eta*xi + 71680.*eta + 268800.*eta*(xi*xi) + 56000.*xi + 1164800.*xi*(eta*eta)/3. - 24920./3. - 474880.*eta*eta/3. - 81760.*xi*xi + 896000.*(eta*eta*eta)/9. + 280000.*(xi*xi*xi)/9., 8960.*xi*(-65.*eta*xi/3. + 35.*eta/3. + 14.*xi - 4. - 20.*eta*eta/3. - 10.*xi*xi));
                      case 25:
                        return RealGradient(103040.*eta*xi - 56000.*eta - 33600.*eta*xi*xi - 31360.*xi/3. - 380800.*xi*eta*eta/3. + 51800./9. + 375200.*(eta*eta)/3. - 2240.*xi*xi - 700000.*eta*eta*eta/9. + 44800.*(xi*xi*xi)/9., 1120.*xi*(170.*eta*xi/3. - 134.*eta/3. - 23.*xi + 10. + 125.*(eta*eta)/3. + 10.*(xi*xi)));
                      case 26:
                        return RealGradient(-165760.*eta*xi + 24640.*eta + 168000.*eta*(xi*xi) + 89600.*xi/3. + 492800.*xi*(eta*eta)/3. - 29680./9. - 138880.*eta*eta/3. - 51520.*xi*xi + 224000.*(eta*eta*eta)/9. + 179200.*(xi*xi*xi)/9., 2240.*xi*(-110.*eta*xi/3. + 71.*eta/3. + 36.*xi - 12. - 20.*eta*eta/3. - 25.*xi*xi));
                      case 27:
                        return RealGradient(-22400.*eta*xi + 39200.*eta - 16800.*eta*xi*xi - 8960.*xi/3. + 179200.*xi*(eta*eta)/3. - 26600./9. - 324800.*eta*eta/3. + 12320.*(xi*xi) + 700000.*(eta*eta*eta)/9. - 44800.*xi*xi*xi/9., 1120.*xi*(-80.*eta*xi/3. + 116.*eta/3. + 5.*xi - 7. - 125.*eta*eta/3. + 5.*(xi*xi)));
                      case 28:
                        return RealGradient(105280.*eta*xi - 32480.*eta - 16800.*eta*xi*xi - 22400.*xi/3. - 492800.*xi*eta*eta/3. + 27160./9. + 239680.*(eta*eta)/3. - 19040.*xi*xi - 476000.*eta*eta*eta/9. + 224000.*(xi*xi*xi)/9., 1120.*xi*(220.*eta*xi/3. - 178.*eta/3. - 27.*xi + 17. + 85.*(eta*eta)/3. + 5.*(xi*xi)));
                      case 29:
                        return RealGradient(165760.*eta*xi + 64960.*eta - 168000.*eta*xi*xi - 138880.*xi/3. - 358400.*xi*eta*eta/3. - 48160./9. - 519680.*eta*eta/3. + 80640.*(xi*xi) + 1120000.*(eta*eta*eta)/9. - 246400.*xi*xi*xi/9., 2240.*xi*(80.*eta*xi/3. + 64.*eta/3. - 23.*xi - 1. - 100.*eta*eta/3. + 25.*(xi*xi)));
                      case 30:
                        return RealGradient(4480.*eta*xi - 11200.*eta + 33600.*eta*(xi*xi) + 15680.*xi/3. - 89600.*xi*eta*eta/3. + 6440./9. + 98560.*(eta*eta)/3. - 25760.*xi*xi - 224000.*eta*eta*eta/9. + 190400.*(xi*xi*xi)/9., 2240.*xi*(20.*eta*xi/3. - 44.*eta/3. - xi + 5. + 20.*(eta*eta)/3. - 5.*xi*xi));
                      case 31:
                        return RealGradient(116480.*eta*xi - 3360.*eta + 16800.*eta*(xi*xi) - 35840.*xi/3. - 448000.*xi*eta*eta/3. + 8680./9. - 24640.*eta*eta/3. - 30240.*xi*xi + 140000.*(eta*eta*eta)/9. + 246400.*(xi*xi*xi)/9., 1120.*xi*(200.*eta*xi/3. - 20.*eta/3. - 17.*xi + 3. - 25.*eta*eta/3. - 5.*xi*xi));
                      case 32:
                        return RealGradient(-24640.*eta*xi + 1120.*eta + 16800.*eta*(xi*xi) + 4480.*xi/3. + 89600.*xi*(eta*eta)/3. - 1400./9. + 2240.*(eta*eta)/3. + 5600.*(xi*xi) - 28000.*eta*eta*eta/9. - 89600.*xi*xi*xi/9., 1120.*xi*(-40.*eta*xi/3. - 2.*eta/3. + 11.*xi - 1. + 5.*(eta*eta)/3. - 5.*xi*xi));
                      case 33:
                        return RealGradient(-67200.*eta*xi + 3360.*eta + 50400.*eta*(xi*xi) + 38080.*xi/3. + 67200.*xi*(eta*eta) - 5600./9. - 3360.*eta*eta - 19040.*xi*xi + 22400.*(xi*xi*xi)/3., 3360.*xi*(-10.*eta*xi + 2.*eta + 6.*xi - 1. - 5.*xi*xi));
                      case 34:
                        return RealGradient(47040.*eta*xi - 7840.*eta - 50400.*eta*xi*xi - 29120.*xi/3. - 44800.*xi*eta*eta + 9520./9. + 15680.*(eta*eta) + 20160.*(xi*xi) - 28000.*eta*eta*eta/3. - 11200.*xi*xi*xi, 1120.*xi*(20.*eta*xi - 8.*eta - 17.*xi + 3. + 5.*(eta*eta) + 15.*(xi*xi)));
                      default:
                        libmesh_error_msg("Invalid i = " << i);
                      }
                  } // j = 2
 
                default:
                  libmesh_error_msg("Invalid j = " << j);
                }
            }
 
          default:
            libmesh_error_msg("ERROR: Unsupported 2D element type!: " << Utility::enum_to_string(elem->type()));
          } // end switch (type)
      } // end case FIFTH
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 2D FE order!: " << totalorder);
 
    } // end switch (order)
 
#else // LIBMESH_DIM > 1
  libmesh_assert(true || i || j);
  libmesh_ignore(elem, order, add_p_level);
  libmesh_not_implemented();
#endif
}

shape_second_deriv() [79/233]

Real libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 131 of file fe_rational_shape_1D.C.

{
  libmesh_assert(elem);
 
  // FEType object to be passed to various FEInterface functions below.
  FEType underlying_fe_type(order, _underlying_fe_family);
 
  return rational_fe_shape_second_deriv(*elem, underlying_fe_type, i,
                                        j, p, add_p_level);
}

shape_second_deriv() [80/233]

Real libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 130 of file fe_rational_shape_2D.C.

{
  libmesh_assert(elem);
 
  // FEType object to be passed to various FEInterface functions below.
  FEType underlying_fe_type(order, _underlying_fe_family);
 
  return rational_fe_shape_second_deriv(*elem, underlying_fe_type, i,
                                        j, p, add_p_level);
}

shape_second_deriv() [81/233]

Real libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 126 of file fe_rational_shape_3D.C.

{
  libmesh_assert(elem);
 
  // FEType object to be passed to various FEInterface functions below.
  FEType underlying_fe_type(order, _underlying_fe_family);
 
  return rational_fe_shape_second_deriv(*elem, underlying_fe_type, i,
                                        j, p, add_p_level);
}

shape_second_deriv() [82/233]

RealGradient libMesh::FE< 2, RAVIART_THOMAS >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 160 of file fe_raviart_shape_2D.C.

{
  RealGradient ND1 = FE<2,NEDELEC_ONE>::shape_second_deriv(elem, order, i, j, p, add_p_level);
  return RealGradient(-ND1(1), ND1(0));
}

shape_second_deriv() [83/233]

RealGradient libMesh::FE< 2, L2_RAVIART_THOMAS >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 172 of file fe_raviart_shape_2D.C.

{
  return FE<2,RAVIART_THOMAS>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [84/233]

RealGradient libMesh::FE< 3, L2_RAVIART_THOMAS >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 458 of file fe_raviart_shape_3D.C.

{
  return FE<3,RAVIART_THOMAS>::shape_second_deriv(elem, order, i, j, p, add_p_level);
}

shape_second_deriv() [85/233]

Real libMesh::FE< 2, SUBDIVISION >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 846 of file fe_subdivision_2D.C.

{
  libmesh_assert(elem);
  const Order totalorder = order + add_p_level*elem->p_level();
  return FE<2,SUBDIVISION>::shape_second_deriv(elem->type(), totalorder, i, j, p);
}

shape_second_deriv() [86/233]

RealGradient libMesh::FE< 3, RAVIART_THOMAS >::shape_second_deriv ( const Elem *  elem, const Order  order, const unsigned int  libmesh_dbg_vari, const unsigned int  libmesh_dbg_varj, const Point &  , const bool  add_p_level  )

inherited

Definition at line 404 of file fe_raviart_shape_3D.C.

{
#if LIBMESH_DIM == 3
 
  libmesh_assert(elem);
 
  // j = 0 ==> d^2 phi / dxi^2
  // j = 1 ==> d^2 phi / dxi deta
  // j = 2 ==> d^2 phi / deta^2
  // j = 3 ==> d^2 phi / dxi dzeta
  // j = 4 ==> d^2 phi / deta dzeta
  // j = 5 ==> d^2 phi / dzeta^2
  libmesh_assert_less (j, 6);
 
  const Order totalorder = order + add_p_level*elem->p_level();
  libmesh_assert_less(i, n_dofs(elem->type(), totalorder));
 
  switch (totalorder)
    {
      // linear Raviart-Thomas shape function second derivatives
    case FIRST:
      {
        switch (elem->type())
          {
            // All second derivatives for linear hexes and tets are zero.
          case HEX27:
          case TET14:
            return RealGradient();
 
          default:
            libmesh_error_msg("ERROR: Unsupported 3D element type!: " << Utility::enum_to_string(elem->type()));
 
          } //switch(type)
      }
 
      // unsupported order
    default:
      libmesh_error_msg("ERROR: Unsupported 3D FE order!: " << totalorder);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_assert(true || p(0));
  libmesh_ignore(elem, order, i, j, add_p_level);
  libmesh_not_implemented();
#endif
}

shape_second_deriv() [87/233]

Real libMesh::FE< 3, CLOUGH >::shape_second_deriv ( const Elem *  libmesh_dbg_varelem, const Order  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 132 of file fe_clough_shape_3D.C.

{
  libmesh_assert(elem);
  libmesh_not_implemented();
  return 0.;
}

shape_second_deriv() [88/233]

Real libMesh::FE< 1, HIERARCHIC >::shape_second_deriv ( const ElemType  elem_type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 302 of file fe_hierarchic_shape_1D.C.

{
  return fe_hierarchic_1D_shape_second_deriv(elem_type, order, i, j, p);
}

shape_second_deriv() [89/233]

Real libMesh::FE< 1, L2_HIERARCHIC >::shape_second_deriv ( const ElemType  elem_type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 315 of file fe_hierarchic_shape_1D.C.

{
  return fe_hierarchic_1D_shape_second_deriv(elem_type, order, i, j, p);
}

shape_second_deriv() [90/233]

static OutputShape libMesh::FE< Dim, T >::shape_second_deriv ( const ElemType  t, const Order  o, const unsigned int  i, const unsigned int  j, const Point &  p  )

staticinherited

Returns

The second \( j^{th} \) derivative of the \( i^{th} \) shape function at the point p.

Note

Cross-derivatives are indexed according to: j = 0 ==> d^2 phi / dxi^2 j = 1 ==> d^2 phi / dxi deta j = 2 ==> d^2 phi / deta^2 j = 3 ==> d^2 phi / dxi dzeta j = 4 ==> d^2 phi / deta dzeta j = 5 ==> d^2 phi / dzeta^2

Computing second derivatives is not currently supported for all element types: \( C^1 \) (Clough, Hermite and Subdivision), Lagrange, Hierarchic, L2_Hierarchic, and Monomial are supported. All other element types return an error when asked for second derivatives.

On a p-refined element, o should be the total order of the element.

shape_second_deriv() [91/233]

RealGradient libMesh::FE< 0, HIERARCHIC_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 146 of file fe_hierarchic_vec.C.

{
  Real value = FE<0,HIERARCHIC>::shape_second_deriv( type, order, i, j, p );
  return libMesh::RealGradient( value );
}

shape_second_deriv() [92/233]

RealGradient libMesh::FE< 0, L2_HIERARCHIC_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 169 of file fe_hierarchic_vec.C.

{
  return FE<0,HIERARCHIC_VEC>::shape_second_deriv(type, order, i, j, p);
}

shape_second_deriv() [93/233]

RealGradient libMesh::FE< 1, HIERARCHIC_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 192 of file fe_hierarchic_vec.C.

{
  Real value = FE<1,HIERARCHIC>::shape_second_deriv( type, order, i, j, p );
  return libMesh::RealGradient( value );
}

shape_second_deriv() [94/233]

RealGradient libMesh::FE< 1, L2_HIERARCHIC_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 216 of file fe_hierarchic_vec.C.

{
  return FE<1,HIERARCHIC_VEC>::shape_second_deriv(type, order, i, j, p);
}

shape_second_deriv() [95/233]

RealGradient libMesh::FE< 2, HIERARCHIC_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 268 of file fe_hierarchic_vec.C.

{
  Real value = FE<2,HIERARCHIC>::shape_second_deriv( type, order, i/2, j, p );
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_second_deriv() [96/233]

RealGradient libMesh::FE< 2, L2_HIERARCHIC_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 306 of file fe_hierarchic_vec.C.

{
  return FE<2,HIERARCHIC_VEC>::shape_second_deriv(type, order, i, j, p);
}

shape_second_deriv() [97/233]

RealGradient libMesh::FE< 3, HIERARCHIC_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 366 of file fe_hierarchic_vec.C.

{
  Real value = FE<3,HIERARCHIC>::shape_second_deriv( type, order, i/3, j, p );
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_second_deriv() [98/233]

RealGradient libMesh::FE< 3, L2_HIERARCHIC_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 407 of file fe_hierarchic_vec.C.

{
  return FE<3,HIERARCHIC_VEC>::shape_second_deriv(type, order, i, j, p);
}

shape_second_deriv() [99/233]

Real libMesh::FE< 2, LAGRANGE >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 233 of file fe_lagrange_shape_2D.C.

{
  return fe_lagrange_2D_shape_second_deriv<LAGRANGE>(type, nullptr, order, i, j, p);
}

shape_second_deriv() [100/233]

Real libMesh::FE< 2, L2_LAGRANGE >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 245 of file fe_lagrange_shape_2D.C.

{
  return fe_lagrange_2D_shape_second_deriv<L2_LAGRANGE>(type, nullptr, order, i, j, p);
}

shape_second_deriv() [101/233]

Real libMesh::FE< 3, LAGRANGE >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 576 of file fe_lagrange_shape_3D.C.

{
  return fe_lagrange_3D_shape_second_deriv<LAGRANGE>(type, order, nullptr, i, j, p);
}

shape_second_deriv() [102/233]

Real libMesh::FE< 3, L2_LAGRANGE >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 588 of file fe_lagrange_shape_3D.C.

{
  return fe_lagrange_3D_shape_second_deriv<L2_LAGRANGE>(type, order, nullptr, i, j, p);
}

shape_second_deriv() [103/233]

RealGradient libMesh::FE< 0, LAGRANGE_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 686 of file fe_lagrange_vec.C.

{
  Real value = FE<0,LAGRANGE>::shape_second_deriv( type, order, i, j, p );
  return libMesh::RealGradient( value );
}

shape_second_deriv() [104/233]

RealGradient libMesh::FE< 0, L2_LAGRANGE_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 709 of file fe_lagrange_vec.C.

{
  return FE<0,LAGRANGE_VEC>::shape_second_deriv(type, order, i, j, p);
}

shape_second_deriv() [105/233]

RealGradient libMesh::FE< 1, LAGRANGE_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 732 of file fe_lagrange_vec.C.

{
  Real value = FE<1,LAGRANGE>::shape_second_deriv( type, order, i, j, p );
  return libMesh::RealGradient( value );
}

shape_second_deriv() [106/233]

RealGradient libMesh::FE< 1, L2_LAGRANGE_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 756 of file fe_lagrange_vec.C.

{
  return FE<1,LAGRANGE_VEC>::shape_second_deriv(type, order, i, j, p);
}

shape_second_deriv() [107/233]

RealGradient libMesh::FE< 2, LAGRANGE_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 808 of file fe_lagrange_vec.C.

{
  Real value = FE<2,LAGRANGE>::shape_second_deriv( type, order, i/2, j, p );
 
  switch( i%2 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_second_deriv() [108/233]

RealGradient libMesh::FE< 2, L2_LAGRANGE_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 846 of file fe_lagrange_vec.C.

{
  return FE<2,LAGRANGE_VEC>::shape_second_deriv(type, order, i, j, p);
}

shape_second_deriv() [109/233]

RealGradient libMesh::FE< 3, LAGRANGE_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 906 of file fe_lagrange_vec.C.

{
  Real value = FE<3,LAGRANGE>::shape_second_deriv( type, order, i/3, j, p );
 
  switch( i%3 )
    {
    case 0:
      return libMesh::RealGradient( value );
 
    case 1:
      return libMesh::RealGradient( Real(0), value );
 
    case 2:
      return libMesh::RealGradient( Real(0), Real(0), value );
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
    }
 
  //dummy
  return libMesh::RealGradient();
}

shape_second_deriv() [110/233]

RealGradient libMesh::FE< 3, L2_LAGRANGE_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 947 of file fe_lagrange_vec.C.

{
  return FE<3,LAGRANGE_VEC>::shape_second_deriv(type, order, i, j, p);
}

shape_second_deriv() [111/233]

RealVectorValue libMesh::FE< 0, MONOMIAL_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 172 of file fe_monomial_vec.C.

{
  Real value = FE<0, MONOMIAL>::shape_second_deriv(type, order, i, j, p);
  return libMesh::RealVectorValue(value);
}

shape_second_deriv() [112/233]

RealVectorValue libMesh::FE< 1, MONOMIAL_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 208 of file fe_monomial_vec.C.

{
  Real value = FE<1, MONOMIAL>::shape_second_deriv(type, order, i, j, p);
  return libMesh::RealVectorValue(value);
}

shape_second_deriv() [113/233]

RealVectorValue libMesh::FE< 2, MONOMIAL_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 274 of file fe_monomial_vec.C.

{
  Real value = FE<2, MONOMIAL>::shape_second_deriv(type, order, i / 2, j, p);
 
  switch (i % 2)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    default:
      libmesh_error_msg("i%2 must be either 0 or 1!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape_second_deriv() [114/233]

RealVectorValue libMesh::FE< 3, MONOMIAL_VEC >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 361 of file fe_monomial_vec.C.

{
  Real value = FE<3, MONOMIAL>::shape_second_deriv(type, order, i / 3, j, p);
 
  switch (i % 3)
  {
    case 0:
      return libMesh::RealVectorValue(value);
 
    case 1:
      return libMesh::RealVectorValue(Real(0), value);
 
    case 2:
      return libMesh::RealVectorValue(Real(0), Real(0), value);
 
    default:
      libmesh_error_msg("i%3 must be 0, 1, or 2!");
  }
 
  // dummy
  return libMesh::RealVectorValue();
}

shape_second_deriv() [115/233]

Real libMesh::FE< 2, SUBDIVISION >::shape_second_deriv ( const ElemType  type, const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 819 of file fe_subdivision_2D.C.

{
  switch (order)
    {
    case FOURTH:
      {
        switch (type)
          {
          case TRI3SUBDIVISION:
            libmesh_assert_less(i, 12);
            return FESubdivision::regular_shape_second_deriv(i,j,p(0),p(1));
          default:
            libmesh_error_msg("ERROR: Unsupported element type == " << Utility::enum_to_string(type));
          }
      }
    default:
      libmesh_error_msg("ERROR: Unsupported polynomial order == " << order);
    }
}

shape_second_deriv() [116/233]

Real libMesh::FE< 2, MONOMIAL >::shape_second_deriv ( const ElemType  , const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 356 of file fe_monomial_shape_2D.C.

{
#if LIBMESH_DIM > 1
 
 
  libmesh_assert_less_equal (j, 2);
 
  libmesh_assert_less (i, (static_cast<unsigned int>(order)+1)*
                       (static_cast<unsigned int>(order)+2)/2);
 
  const Real xi  = p(0);
  const Real eta = p(1);
 
  // monomials. since they are hierarchic we only need one case block.
 
  switch (j)
    {
      // d^2()/dxi^2
    case 0:
      {
        switch (i)
          {
            // constants
          case 0:
            // linears
          case 1:
          case 2:
            return 0.;
 
            // quadratics
          case 3:
            return 2.;
 
          case 4:
          case 5:
            return 0.;
 
            // cubics
          case 6:
            return 6.*xi;
 
          case 7:
            return 2.*eta;
 
          case 8:
          case 9:
            return 0.;
 
            // quartics
          case 10:
            return 12.*xi*xi;
 
          case 11:
            return 6.*xi*eta;
 
          case 12:
            return 2.*eta*eta;
 
          case 13:
          case 14:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            const int ny = i - (o*(o+1)/2);
            const int nx = o - ny;
            Real val = nx * (nx - 1);
            for (int index=2; index < nx; index++)
              val *= xi;
            for (int index=0; index != ny; index++)
              val *= eta;
            return val;
          }
      }
 
      // d^2()/dxideta
    case 1:
      {
        switch (i)
          {
            // constants
          case 0:
 
            // linears
          case 1:
          case 2:
            return 0.;
 
            // quadratics
          case 3:
            return 0.;
 
          case 4:
            return 1.;
 
          case 5:
            return 0.;
 
            // cubics
          case 6:
            return 0.;
          case 7:
            return 2.*xi;
 
          case 8:
            return 2.*eta;
 
          case 9:
            return 0.;
 
            // quartics
          case 10:
            return 0.;
 
          case 11:
            return 3.*xi*xi;
 
          case 12:
            return 4.*xi*eta;
 
          case 13:
            return 3.*eta*eta;
 
          case 14:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            const int ny = i - (o*(o+1)/2);
            const int nx = o - ny;
            Real val = nx * ny;
            for (int index=1; index < nx; index++)
              val *= xi;
            for (int index=1; index < ny; index++)
              val *= eta;
            return val;
          }
      }
 
      // d^2()/deta^2
    case 2:
      {
        switch (i)
          {
            // constants
          case 0:
 
            // linears
          case 1:
          case 2:
            return 0.;
 
            // quadratics
          case 3:
          case 4:
            return 0.;
 
          case 5:
            return 2.;
 
            // cubics
          case 6:
            return 0.;
 
          case 7:
            return 0.;
 
          case 8:
            return 2.*xi;
 
          case 9:
            return 6.*eta;
 
            // quartics
          case 10:
          case 11:
            return 0.;
 
          case 12:
            return 2.*xi*xi;
 
          case 13:
            return 6.*xi*eta;
 
          case 14:
            return 12.*eta*eta;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)/2; o++) { }
            const int ny = i - (o*(o+1)/2);
            const int nx = o - ny;
            Real val = ny * (ny - 1);
            for (int index=0; index != nx; index++)
              val *= xi;
            for (int index=2; index < ny; index++)
              val *= eta;
            return val;
          }
      }
 
    default:
      libmesh_error_msg("Invalid shape function derivative j = " << j);
    }
 
#else // LIBMESH_DIM == 1
  libmesh_assert(order);
  libmesh_ignore(i, j, p);
  libmesh_not_implemented();
#endif
}

shape_second_deriv() [117/233]

Real libMesh::FE< 3, MONOMIAL >::shape_second_deriv ( const ElemType  , const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 690 of file fe_monomial_shape_3D.C.

{
#if LIBMESH_DIM == 3
 
  libmesh_assert_less (j, 6);
 
  libmesh_assert_less (i, (static_cast<unsigned int>(order)+1)*
                       (static_cast<unsigned int>(order)+2)*
                       (static_cast<unsigned int>(order)+3)/6);
 
  const Real xi   = p(0);
  const Real eta  = p(1);
  const Real zeta = p(2);
 
  // monomials. since they are hierarchic we only need one case block.
  switch (j)
    {
      // d^2()/dxi^2
    case 0:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
            return 2.;
 
          case 5:
          case 6:
          case 7:
          case 8:
          case 9:
            return 0.;
 
            // cubic
          case 10:
            return 6.*xi;
 
          case 11:
            return 2.*eta;
 
          case 12:
          case 13:
            return 0.;
 
          case 14:
            return 2.*zeta;
 
          case 15:
          case 16:
          case 17:
          case 18:
          case 19:
            return 0.;
 
            // quartics
          case 20:
            return 12.*xi*xi;
 
          case 21:
            return 6.*xi*eta;
 
          case 22:
            return 2.*eta*eta;
 
          case 23:
          case 24:
            return 0.;
 
          case 25:
            return 6.*xi*zeta;
 
          case 26:
            return 2.*eta*zeta;
 
          case 27:
          case 28:
            return 0.;
 
          case 29:
            return 2.*zeta*zeta;
 
          case 30:
          case 31:
          case 32:
          case 33:
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            const int i2 = i - (o*(o+1)*(o+2)/6);
            int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const int nx = block - i2;
            const int ny = o - nx - nz;
            Real val = nx * (nx - 1);
            for (int index=2; index < nx; index++)
              val *= xi;
            for (int index=0; index != ny; index++)
              val *= eta;
            for (int index=0; index != nz; index++)
              val *= zeta;
            return val;
          }
      }
 
 
      // d^2()/dxideta
    case 1:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
            return 0.;
 
          case 5:
            return 1.;
 
          case 6:
          case 7:
          case 8:
          case 9:
            return 0.;
 
            // cubic
          case 10:
            return 0.;
 
          case 11:
            return 2.*xi;
 
          case 12:
            return 2.*eta;
 
          case 13:
          case 14:
            return 0.;
 
          case 15:
            return zeta;
 
          case 16:
          case 17:
          case 18:
          case 19:
            return 0.;
 
            // quartics
          case 20:
            return 0.;
 
          case 21:
            return 3.*xi*xi;
 
          case 22:
            return 4.*xi*eta;
 
          case 23:
            return 3.*eta*eta;
 
          case 24:
          case 25:
            return 0.;
 
          case 26:
            return 2.*xi*zeta;
 
          case 27:
            return 2.*eta*zeta;
 
          case 28:
          case 29:
            return 0.;
 
          case 30:
            return zeta*zeta;
 
          case 31:
          case 32:
          case 33:
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            const int i2 = i - (o*(o+1)*(o+2)/6);
            int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const int nx = block - i2;
            const int ny = o - nx - nz;
            Real val = nx * ny;
            for (int index=1; index < nx; index++)
              val *= xi;
            for (int index=1; index < ny; index++)
              val *= eta;
            for (int index=0; index != nz; index++)
              val *= zeta;
            return val;
          }
      }
 
 
      // d^2()/deta^2
    case 2:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
          case 5:
            return 0.;
 
          case 6:
            return 2.;
 
          case 7:
          case 8:
          case 9:
            return 0.;
 
            // cubic
          case 10:
          case 11:
            return 0.;
 
          case 12:
            return 2.*xi;
          case 13:
            return 6.*eta;
 
          case 14:
          case 15:
            return 0.;
 
          case 16:
            return 2.*zeta;
 
          case 17:
          case 18:
          case 19:
            return 0.;
 
            // quartics
          case 20:
          case 21:
            return 0.;
 
          case 22:
            return 2.*xi*xi;
 
          case 23:
            return 6.*xi*eta;
 
          case 24:
            return 12.*eta*eta;
 
          case 25:
          case 26:
            return 0.;
 
          case 27:
            return 2.*xi*zeta;
 
          case 28:
            return 6.*eta*zeta;
 
          case 29:
          case 30:
            return 0.;
 
          case 31:
            return 2.*zeta*zeta;
 
          case 32:
          case 33:
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            const int i2 = i - (o*(o+1)*(o+2)/6);
            int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const int nx = block - i2;
            const int ny = o - nx - nz;
            Real val = ny * (ny - 1);
            for (int index=0; index != nx; index++)
              val *= xi;
            for (int index=2; index < ny; index++)
              val *= eta;
            for (int index=0; index != nz; index++)
              val *= zeta;
            return val;
          }
      }
 
 
      // d^2()/dxidzeta
    case 3:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
          case 5:
          case 6:
            return 0.;
 
          case 7:
            return 1.;
 
          case 8:
          case 9:
            return 0.;
 
            // cubic
          case 10:
          case 11:
          case 12:
          case 13:
            return 0.;
 
          case 14:
            return 2.*xi;
 
          case 15:
            return eta;
 
          case 16:
            return 0.;
 
          case 17:
            return 2.*zeta;
 
          case 18:
          case 19:
            return 0.;
 
            // quartics
          case 20:
          case 21:
          case 22:
          case 23:
          case 24:
            return 0.;
 
          case 25:
            return 3.*xi*xi;
 
          case 26:
            return 2.*xi*eta;
 
          case 27:
            return eta*eta;
 
          case 28:
            return 0.;
 
          case 29:
            return 4.*xi*zeta;
 
          case 30:
            return 2.*eta*zeta;
 
          case 31:
            return 0.;
 
          case 32:
            return 3.*zeta*zeta;
 
          case 33:
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            const int i2 = i - (o*(o+1)*(o+2)/6);
            int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const int nx = block - i2;
            const int ny = o - nx - nz;
            Real val = nx * nz;
            for (int index=1; index < nx; index++)
              val *= xi;
            for (int index=0; index != ny; index++)
              val *= eta;
            for (int index=1; index < nz; index++)
              val *= zeta;
            return val;
          }
      }
 
      // d^2()/detadzeta
    case 4:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
          case 5:
          case 6:
          case 7:
            return 0.;
 
          case 8:
            return 1.;
 
          case 9:
            return 0.;
 
            // cubic
          case 10:
          case 11:
          case 12:
          case 13:
          case 14:
            return 0.;
 
          case 15:
            return xi;
 
          case 16:
            return 2.*eta;
 
          case 17:
            return 0.;
 
          case 18:
            return 2.*zeta;
 
          case 19:
            return 0.;
 
            // quartics
          case 20:
          case 21:
          case 22:
          case 23:
          case 24:
          case 25:
            return 0.;
 
          case 26:
            return xi*xi;
 
          case 27:
            return 2.*xi*eta;
 
          case 28:
            return 3.*eta*eta;
 
          case 29:
            return 0.;
 
          case 30:
            return 2.*xi*zeta;
 
          case 31:
            return 4.*eta*zeta;
 
          case 32:
            return 0.;
 
          case 33:
            return 3.*zeta*zeta;
 
          case 34:
            return 0.;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            const int i2 = i - (o*(o+1)*(o+2)/6);
            int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const int nx = block - i2;
            const int ny = o - nx - nz;
            Real val = ny * nz;
            for (int index=0; index != nx; index++)
              val *= xi;
            for (int index=1; index < ny; index++)
              val *= eta;
            for (int index=1; index < nz; index++)
              val *= zeta;
            return val;
          }
      }
 
 
      // d^2()/dzeta^2
    case 5:
      {
        switch (i)
          {
            // constant
          case 0:
 
            // linear
          case 1:
          case 2:
          case 3:
            return 0.;
 
            // quadratic
          case 4:
          case 5:
          case 6:
          case 7:
          case 8:
            return 0.;
 
          case 9:
            return 2.;
 
            // cubic
          case 10:
          case 11:
          case 12:
          case 13:
          case 14:
          case 15:
          case 16:
            return 0.;
 
          case 17:
            return 2.*xi;
 
          case 18:
            return 2.*eta;
 
          case 19:
            return 6.*zeta;
 
            // quartics
          case 20:
          case 21:
          case 22:
          case 23:
          case 24:
          case 25:
          case 26:
          case 27:
          case 28:
            return 0.;
 
          case 29:
            return 2.*xi*xi;
 
          case 30:
            return 2.*xi*eta;
 
          case 31:
            return 2.*eta*eta;
 
          case 32:
            return 6.*xi*zeta;
 
          case 33:
            return 6.*eta*zeta;
 
          case 34:
            return 12.*zeta*zeta;
 
          default:
            unsigned int o = 0;
            for (; i >= (o+1)*(o+2)*(o+3)/6; o++) { }
            const int i2 = i - (o*(o+1)*(o+2)/6);
            int block=o, nz = 0;
            for (; block < i2; block += (o-nz+1)) { nz++; }
            const int nx = block - i2;
            const int ny = o - nx - nz;
            Real val = nz * (nz - 1);
            for (int index=0; index != nx; index++)
              val *= xi;
            for (int index=0; index != ny; index++)
              val *= eta;
            for (int index=2; index < nz; index++)
              val *= zeta;
            return val;
          }
      }
 
    default:
      libmesh_error_msg("Invalid j = " << j);
    }
 
#else // LIBMESH_DIM != 3
  libmesh_assert(order);
  libmesh_ignore(i, j, p);
  libmesh_not_implemented();
#endif
}

shape_second_deriv() [118/233]

Real libMesh::FE< 1, MONOMIAL >::shape_second_deriv ( const ElemType  , const Order  libmesh_dbg_varorder, const unsigned int  i, const unsigned int  libmesh_dbg_varj, const Point &  p  )

inherited

Definition at line 171 of file fe_monomial_shape_1D.C.

{
  // only d()/dxi in 1D!
 
  libmesh_assert_equal_to (j, 0);
 
  const Real xi = p(0);
 
  libmesh_assert_less_equal (i, static_cast<unsigned int>(order));
 
  switch (i)
    {
    case 0:
    case 1:
      return 0.;
 
    case 2:
      return 2.;
 
    case 3:
      return 6.*xi;
 
    case 4:
      return 12.*xi*xi;
 
    default:
      Real val = 2.;
      for (unsigned int index = 2; index != i; ++index)
        val *= (index+1) * xi;
      return val;
    }
}

shape_second_deriv() [119/233]

Real libMesh::FE< 1, LAGRANGE >::shape_second_deriv ( const ElemType  , const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 184 of file fe_lagrange_shape_1D.C.

{
  return fe_lagrange_1D_shape_second_deriv(order, i, j, p(0));
}

shape_second_deriv() [120/233]

Real libMesh::FE< 1, L2_LAGRANGE >::shape_second_deriv ( const ElemType  , const Order  order, const unsigned int  i, const unsigned int  j, const Point &  p  )

inherited

Definition at line 196 of file fe_lagrange_shape_1D.C.

{
  return fe_lagrange_1D_shape_second_deriv(order, i, j, p(0));
}

shape_second_deriv() [121/233]

Real libMesh::FE< 1, BERNSTEIN >::shape_second_deriv ( const ElemType  , const Order  order, const unsigned int  i, const unsigned int  libmesh_dbg_varj, const Point &  p  )

inherited

Definition at line 412 of file fe_bernstein_shape_1D.C.

{
  // only d^2()/dxi^2 in 1D!
 
  libmesh_assert_equal_to (j, 0);
 
  const Real xi = p(0);
 
  using Utility::pow;
 
  switch (order)
    {
    case FIRST:
 
      switch(i)
        {
        case 0:
        case 1:
          return 0;
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case SECOND:
 
      switch(i)
        {
        case 0:
        case 1:
          return .5;
        case 2:
          return -1;
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case THIRD:
 
      switch(i)
        {
        case 0:
          return 0.75*(1.-xi);
        case 1:
          return 0.75*(1.+xi);
        case 2:
          return -.75 + 2.25*xi;
        case 3:
          return -.75 - 2.25*xi;
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case FOURTH:
 
      switch(i)
        {
        case 0:
          return  0.75*pow<2>(1.-xi);
        case 1:
          return  0.75*pow<2>(1.+xi);
        case 2:
          return  3*(xi - pow<2>(xi));
        case 3:
          return  1.5*(3*pow<2>(xi)-1);
        case 4:
          return  -3*xi-3*pow<2>(xi);
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case FIFTH:
 
      switch(i)
        {
        case 0:
          return -(5./8.)*pow<3>(xi-1.);
        case 1:
          return  (5./8.)*pow<3>(xi+1.);
        case 2:
          return -(5./4.)*pow<3>(1.-xi) + (15./8.)*(1.+xi)*pow<2>(1.-xi);
        case 3:
          return -(15./ 4.)*(1.+xi)*pow<2>(1.-xi) + (5./ 8.)*pow<3>(1.-xi)
          + (15./8.)*pow<2>(1.+xi)*(1.-xi);
        case 4:
          return  (5./ 8.)*pow<3>(1.+xi) - (15./ 4.)*pow<2>(1.+xi)*(1.-xi)
          +(15./8.)*(1.+xi)*pow<2>(1.-xi);
        case 5:
          return -(5./ 8.)*pow<3>(1.+xi) + (15./ 8.)*pow<2>(1.+xi)*(1.-xi)
          -(5./8.)*pow<3>(1.+xi);
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
    case SIXTH:
 
      switch(i)
        {
        case 0:
          return  ( 15./32.)*pow<4>(1.-xi);
        case 1:
          return  ( 15./32.)*pow<4>(1.+xi);
        case 2:
          return -( 15./8.)*pow<4>(1.-xi) +
                  ( 15./8.)*(1.+xi)*pow<3>(1.-xi);
        case 3:
          return -(15./4.)*(1.+xi)*pow<3>(1.-xi)
                  + (15./32.)*pow<4>(1.-xi)
                  + (45./16.)*pow<2>(1.+xi)*pow<2>(1.-xi);
        case 4:
          return -(15./ 8.) +(45./4.)*pow<2>(xi) - (75./8.)*pow<4>(xi);
        case 5:
          return -(15./4.)*(1.-xi)*pow<3>(1.+xi)
                  + (15./32.)*pow<4>(1.+xi)
                  + (45./16.)*pow<2>(1.-xi)*pow<2>(1.+xi);
        case 6:
          return -(15./16.)*pow<4>(1.+xi)
                 + (15./8.)*pow<3>(1.+xi)*(1.-xi);
        default:
          libmesh_error_msg("Invalid shape function index i = " << i);
        }
 
 
    default:
      {
        libmesh_assert (order>6);
 
        // Use this for arbitrary orders
        const int p_order = static_cast<int>(order);
        const int m       = p_order-(i-1);
        const int n       = (i-1);
 
        Real binomial_p_i = 1;
 
        // the binomial coefficient (p choose n)
        // Using an unsigned long here will work for any of the orders we support.
        // Explicitly construct a Real to prevent conversion warnings
        if (i>1)
          binomial_p_i = Real(Utility::binomial(static_cast<unsigned long>(p_order),
                                                static_cast<unsigned long>(n)));
 
        switch(i)
          {
          case 0:
            return binomial_p_i * (1./4.) * p_order * (p_order-1) * std::pow((1-xi)/2, p_order-2);
          case 1:
            return binomial_p_i * (1./4.) * p_order * (p_order-1) * std::pow((1+xi)/2, p_order-2);
 
          default:
            {
              Real val = 0;
 
              if (n == 1)
                val +=
                  binomial_p_i * (-1./4. * m * std::pow((1-xi)/2,m-1));
              else
                val +=
                  binomial_p_i * (-1./4. * n * m * std::pow((1+xi)/2,n-1) * std::pow((1-xi)/2,m-1) +
                                  1./4. * n * (n-1) * std::pow((1+xi)/2,n-2) * std::pow((1-xi)/2,m));
 
              if (m == 1)
                val += binomial_p_i * (-1./4. * n * std::pow((1+xi)/2,n-1));
              else
                val +=
                  binomial_p_i * (1./4. * m * (m-1) * std::pow((1+xi)/2,n)   * std::pow((1-xi)/2,m-2)
                                  - 1./4. * m * n * std::pow((1+xi)/2,n-1)   * std::pow((1-xi)/2,m-1));
 
              return val;
            }
          }
      }
 
    }
}

shape_second_deriv() [122/233]

Real libMesh::FE< 0, BERNSTEIN >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 110 of file fe_bernstein_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [123/233]

Real libMesh::FE< 2, BERNSTEIN >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 611 of file fe_bernstein_shape_2D.C.

{
  libmesh_error_msg("Bernstein polynomials require the element type \nbecause edge orientation is needed.");
  return 0.;
}

shape_second_deriv() [124/233]

Real libMesh::FE< 3, BERNSTEIN >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 2355 of file fe_bernstein_shape_3D.C.

{
  libmesh_error_msg("Bernstein polynomials require the element type \nbecause edge and face orientation is needed.");
  return 0.;
}

shape_second_deriv() [125/233]

Real libMesh::FE< 0, CLOUGH >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 113 of file fe_clough_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [126/233]

Real libMesh::FE< 1, CLOUGH >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 438 of file fe_clough_shape_1D.C.

{
  libmesh_error_msg("Clough-Tocher elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_second_deriv() [127/233]

Real libMesh::FE< 2, CLOUGH >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 2364 of file fe_clough_shape_2D.C.

{
  libmesh_error_msg("Clough-Tocher elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_second_deriv() [128/233]

Real libMesh::FE< 3, CLOUGH >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 120 of file fe_clough_shape_3D.C.

{
  libmesh_error_msg("Clough-Tocher elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_second_deriv() [129/233]

Real libMesh::FE< 0, HERMITE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 114 of file fe_hermite_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [130/233]

Real libMesh::FE< 1, HERMITE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 385 of file fe_hermite_shape_1D.C.

{
  libmesh_error_msg("Hermite elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_second_deriv() [131/233]

Real libMesh::FE< 2, HERMITE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 433 of file fe_hermite_shape_2D.C.

{
  libmesh_error_msg("Hermite elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_second_deriv() [132/233]

Real libMesh::FE< 3, HERMITE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 674 of file fe_hermite_shape_3D.C.

{
  libmesh_error_msg("Hermite elements require the real element \nto construct gradient-based degrees of freedom.");
  return 0.;
}

shape_second_deriv() [133/233]

Real libMesh::FE< 0, HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 271 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [134/233]

Real libMesh::FE< 0, L2_HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 310 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [135/233]

Real libMesh::FE< 0, SIDE_HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 350 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [136/233]

Real libMesh::FE< 1, SIDE_HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 327 of file fe_hierarchic_shape_1D.C.

{
  return 0;
}

shape_second_deriv() [137/233]

Real libMesh::FE< 2, HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 695 of file fe_hierarchic_shape_2D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge orientation.");
  return 0.;
}

shape_second_deriv() [138/233]

Real libMesh::FE< 2, L2_HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 708 of file fe_hierarchic_shape_2D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge orientation.");
  return 0.;
}

shape_second_deriv() [139/233]

Real libMesh::FE< 2, SIDE_HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 721 of file fe_hierarchic_shape_2D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge orientation.");
  return 0.;
}

shape_second_deriv() [140/233]

Real libMesh::FE< 3, HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1768 of file fe_hierarchic_shape_3D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge/face orientation.");
  return 0.;
}

shape_second_deriv() [141/233]

Real libMesh::FE< 3, L2_HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1781 of file fe_hierarchic_shape_3D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge/face orientation.");
  return 0.;
}

shape_second_deriv() [142/233]

Real libMesh::FE< 3, SIDE_HIERARCHIC >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1794 of file fe_hierarchic_shape_3D.C.

{
  libmesh_error_msg("Hierarchic shape functions require an Elem for edge/face orientation.");
  return 0.;
}

shape_second_deriv() [143/233]

Real libMesh::FE< 0, L2_LAGRANGE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 188 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [144/233]

Real libMesh::FE< 0, LAGRANGE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 213 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [145/233]

Real libMesh::FE< 0, MONOMIAL >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 115 of file fe_monomial_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [146/233]

RealGradient libMesh::FE< 0, NEDELEC_ONE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 473 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [147/233]

RealGradient libMesh::FE< 1, NEDELEC_ONE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 500 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [148/233]

RealGradient libMesh::FE< 2, NEDELEC_ONE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 3735 of file fe_nedelec_one_shape_2D.C.

{
  libmesh_error_msg("Nedelec elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape_second_deriv() [149/233]

RealGradient libMesh::FE< 3, NEDELEC_ONE >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 578 of file fe_nedelec_one_shape_3D.C.

{
  libmesh_error_msg("Nedelec elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape_second_deriv() [150/233]

Real libMesh::FE< 0, RATIONAL_BERNSTEIN >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 111 of file fe_rational_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [151/233]

Real libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 149 of file fe_rational_shape_1D.C.

{
  libmesh_error_msg("Rational bases require the real element \nto query nodal weighting.");
  return 0.;
}

shape_second_deriv() [152/233]

Real libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 149 of file fe_rational_shape_2D.C.

{
  libmesh_error_msg("Rational bases require the real element \nto query nodal weighting.");
  return 0.;
}

shape_second_deriv() [153/233]

Real libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 145 of file fe_rational_shape_3D.C.

{
  libmesh_error_msg("Rational bases require the real element \nto query nodal weighting.");
  return 0.;
}

shape_second_deriv() [154/233]

RealGradient libMesh::FE< 0, RAVIART_THOMAS >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 579 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [155/233]

RealGradient libMesh::FE< 0, L2_RAVIART_THOMAS >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 587 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [156/233]

RealGradient libMesh::FE< 1, RAVIART_THOMAS >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 628 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [157/233]

RealGradient libMesh::FE< 1, L2_RAVIART_THOMAS >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 636 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shape_second_deriv() [158/233]

RealGradient libMesh::FE< 2, RAVIART_THOMAS >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 183 of file fe_raviart_shape_2D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape_second_deriv() [159/233]

RealGradient libMesh::FE< 2, L2_RAVIART_THOMAS >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 194 of file fe_raviart_shape_2D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause edge orientation is needed.");
  return RealGradient();
}

shape_second_deriv() [160/233]

RealGradient libMesh::FE< 3, RAVIART_THOMAS >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 470 of file fe_raviart_shape_3D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}

shape_second_deriv() [161/233]

RealGradient libMesh::FE< 3, L2_RAVIART_THOMAS >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 482 of file fe_raviart_shape_3D.C.

{
  libmesh_error_msg("Raviart-Thomas elements require the element type \nbecause face orientation is needed.");
  return RealGradient();
}

shape_second_deriv() [162/233]

Real libMesh::FE< 0, SCALAR >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 99 of file fe_scalar_shape_0D.C.

{
  return 0.;
}

shape_second_deriv() [163/233]

Real libMesh::FE< 1, SCALAR >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 103 of file fe_scalar_shape_1D.C.

{
  return 0.;
}

shape_second_deriv() [164/233]

Real libMesh::FE< 2, SCALAR >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 101 of file fe_scalar_shape_2D.C.

{
  return 0.;
}

shape_second_deriv() [165/233]

Real libMesh::FE< 3, SCALAR >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 100 of file fe_scalar_shape_3D.C.

{
  return 0.;
}

shape_second_deriv() [166/233]

Real libMesh::FE< 0, SZABAB >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 114 of file fe_szabab_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [167/233]

Real libMesh::FE< 1, SZABAB >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 191 of file fe_szabab_shape_1D.C.

{
  static bool warning_given = false;
 
  if (!warning_given)
    libMesh::err << "Second derivatives for Szabab elements "
                 << " are not yet implemented!"
                 << std::endl;
 
  warning_given = true;
  return 0.;
}

shape_second_deriv() [168/233]

Real libMesh::FE< 2, SZABAB >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1049 of file fe_szabab_shape_2D.C.

{
  static bool warning_given = false;
 
  if (!warning_given)
    libMesh::err << "Second derivatives for Szabab elements "
                 << " are not yet implemented!"
                 << std::endl;
 
  warning_given = true;
  return 0.;
}

shape_second_deriv() [169/233]

Real libMesh::FE< 3, SZABAB >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 113 of file fe_szabab_shape_3D.C.

{
  libmesh_error_msg("Szabo-Babuska polynomials are not defined in 3D");
  return 0.;
}

shape_second_deriv() [170/233]

Real libMesh::FE< 0, XYZ >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 115 of file fe_xyz_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [171/233]

Real libMesh::FE< 1, XYZ >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 247 of file fe_xyz_shape_1D.C.

{
  libmesh_error_msg("XYZ polynomials require the element.");
  return 0.;
}

shape_second_deriv() [172/233]

Real libMesh::FE< 2, XYZ >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 634 of file fe_xyz_shape_2D.C.

{
  libmesh_error_msg("XYZ polynomials require the element.");
  return 0.;
}

shape_second_deriv() [173/233]

Real libMesh::FE< 3, XYZ >::shape_second_deriv ( const ElemType  , const Order  , const unsigned int  , const unsigned int  , const Point &    )

inherited

Definition at line 1412 of file fe_xyz_shape_3D.C.

{
  libmesh_error_msg("XYZ polynomials require the element.");
  return 0.;
}

shape_second_deriv() [174/233]

Real libMesh::FE< 1, BERNSTEIN >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 608 of file fe_bernstein_shape_1D.C.

{
  libmesh_assert(elem);
  return FE<1,BERNSTEIN>::shape_second_deriv
    (elem->type(),
     fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [175/233]

Real libMesh::FE< 2, BERNSTEIN >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 623 of file fe_bernstein_shape_2D.C.

{
  libmesh_assert(elem);
  return FE<2,BERNSTEIN>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [176/233]

Real libMesh::FE< 3, BERNSTEIN >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 2367 of file fe_bernstein_shape_3D.C.

{
  return FE<3,BERNSTEIN>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [177/233]

Real libMesh::FE< 1, CLOUGH >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 449 of file fe_clough_shape_1D.C.

{
  return FE<1,CLOUGH>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [178/233]

Real libMesh::FE< 2, CLOUGH >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 2375 of file fe_clough_shape_2D.C.

{
  return FE<2,CLOUGH>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [179/233]

Real libMesh::FE< 1, HERMITE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 396 of file fe_hermite_shape_1D.C.

{
  return FE<1,HERMITE>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [180/233]

Real libMesh::FE< 2, HERMITE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 445 of file fe_hermite_shape_2D.C.

{
  return FE<2,HERMITE>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [181/233]

Real libMesh::FE< 3, HERMITE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 685 of file fe_hermite_shape_3D.C.

{
  return FE<3,HERMITE>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [182/233]

Real libMesh::FE< 1, HIERARCHIC >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 355 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_hierarchic_1D_shape_second_deriv(elem->type(),
                                             fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [183/233]

Real libMesh::FE< 1, L2_HIERARCHIC >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 384 of file fe_hierarchic_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_hierarchic_1D_shape_second_deriv(elem->type(),
                                             fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [184/233]

Real libMesh::FE< 2, HIERARCHIC >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 746 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape_second_deriv<HIERARCHIC>(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [185/233]

Real libMesh::FE< 2, L2_HIERARCHIC >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 770 of file fe_hierarchic_shape_2D.C.

{
  return fe_hierarchic_2D_shape_second_deriv<L2_HIERARCHIC>(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [186/233]

Real libMesh::FE< 2, SIDE_HIERARCHIC >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 895 of file fe_hierarchic_shape_2D.C.

{
  return FE<2,SIDE_HIERARCHIC>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [187/233]

Real libMesh::FE< 3, HIERARCHIC >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1820 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape_second_deriv<HIERARCHIC>(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [188/233]

Real libMesh::FE< 3, L2_HIERARCHIC >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1845 of file fe_hierarchic_shape_3D.C.

{
  return fe_hierarchic_3D_shape_second_deriv<L2_HIERARCHIC>(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [189/233]

Real libMesh::FE< 3, SIDE_HIERARCHIC >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 2080 of file fe_hierarchic_shape_3D.C.

{
  return FE<3,SIDE_HIERARCHIC>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [190/233]

Real libMesh::FE< 1, LAGRANGE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 237 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_1D_shape_second_deriv(fet.order + add_p_level*elem->p_level(), i, j, p(0));
}

shape_second_deriv() [191/233]

Real libMesh::FE< 1, L2_LAGRANGE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 250 of file fe_lagrange_shape_1D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_1D_shape_second_deriv(fet.order + add_p_level*elem->p_level(), i, j, p(0));
}

shape_second_deriv() [192/233]

Real libMesh::FE< 2, LAGRANGE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 288 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_2D_shape_second_deriv<LAGRANGE>(elem->type(), elem, fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [193/233]

Real libMesh::FE< 2, L2_LAGRANGE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 302 of file fe_lagrange_shape_2D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_2D_shape_second_deriv<L2_LAGRANGE>(elem->type(), elem, fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [194/233]

Real libMesh::FE< 3, LAGRANGE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 633 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_3D_shape_second_deriv<LAGRANGE>
    (elem->type(), fet.order + add_p_level*elem->p_level(), elem, i, j, p);
}

shape_second_deriv() [195/233]

Real libMesh::FE< 3, L2_LAGRANGE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 648 of file fe_lagrange_shape_3D.C.

{
  libmesh_assert(elem);
  return fe_lagrange_3D_shape_second_deriv<L2_LAGRANGE>
    (elem->type(), fet.order + add_p_level*elem->p_level(), elem, i, j, p);
}

shape_second_deriv() [196/233]

Real libMesh::FE< 1, MONOMIAL >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 225 of file fe_monomial_shape_1D.C.

{
  libmesh_assert(elem);
  return FE<1,MONOMIAL>::shape_second_deriv(elem->type(), fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [197/233]

Real libMesh::FE< 2, MONOMIAL >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 592 of file fe_monomial_shape_2D.C.

{
  libmesh_assert(elem);
  // by default call the orientation-independent shape functions
  return FE<2,MONOMIAL>::shape_second_deriv(elem->type(), fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [198/233]

Real libMesh::FE< 3, MONOMIAL >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1355 of file fe_monomial_shape_3D.C.

{
  libmesh_assert(elem);
  // by default call the orientation-independent shape functions
  return FE<3,MONOMIAL>::shape_second_deriv(elem->type(), fet.order + add_p_level*elem->p_level(), i, j, p);
}

shape_second_deriv() [199/233]

RealGradient libMesh::FE< 2, NEDELEC_ONE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 3747 of file fe_nedelec_one_shape_2D.C.

{
  return FE<2,NEDELEC_ONE>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [200/233]

RealGradient libMesh::FE< 3, NEDELEC_ONE >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 590 of file fe_nedelec_one_shape_3D.C.

{
  return FE<3,NEDELEC_ONE>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [201/233]

Real libMesh::FE< 1, RATIONAL_BERNSTEIN >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 163 of file fe_rational_shape_1D.C.

{
  libmesh_assert(elem);
  return FE<1,RATIONAL_BERNSTEIN>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [202/233]

Real libMesh::FE< 2, RATIONAL_BERNSTEIN >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 161 of file fe_rational_shape_2D.C.

{
  return FE<2,RATIONAL_BERNSTEIN>::shape_second_deriv
    (elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [203/233]

Real libMesh::FE< 3, RATIONAL_BERNSTEIN >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 157 of file fe_rational_shape_3D.C.

{
  return FE<3,RATIONAL_BERNSTEIN>::shape_second_deriv
    (elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [204/233]

RealGradient libMesh::FE< 2, RAVIART_THOMAS >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 205 of file fe_raviart_shape_2D.C.

{
  return FE<2,RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [205/233]

RealGradient libMesh::FE< 2, L2_RAVIART_THOMAS >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 216 of file fe_raviart_shape_2D.C.

{
  return FE<2,L2_RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [206/233]

RealGradient libMesh::FE< 3, RAVIART_THOMAS >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 494 of file fe_raviart_shape_3D.C.

{
  return FE<3,RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [207/233]

RealGradient libMesh::FE< 3, L2_RAVIART_THOMAS >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 506 of file fe_raviart_shape_3D.C.

{
  return FE<3,L2_RAVIART_THOMAS>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [208/233]

Real libMesh::FE< 2, SUBDIVISION >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 861 of file fe_subdivision_2D.C.

{
  libmesh_assert(elem);
  const Order totalorder = fet.order + add_p_level*elem->p_level();
  return FE<2,SUBDIVISION>::shape_second_deriv(elem->type(), totalorder, i, j, p);
}

shape_second_deriv() [209/233]

Real libMesh::FE< 1, SZABAB >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 231 of file fe_szabab_shape_1D.C.

{
  libmesh_assert(elem);
 
  return FE<1,SZABAB>::shape_second_deriv(elem->type(),
                                          fet.order + add_p_level*elem->p_level(),
                                          i,
                                          j,
                                          p);
}

shape_second_deriv() [210/233]

Real libMesh::FE< 1, XYZ >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 260 of file fe_xyz_shape_1D.C.

{
  return FE<1,XYZ>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [211/233]

Real libMesh::FE< 2, XYZ >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 647 of file fe_xyz_shape_2D.C.

{
  return FE<2,XYZ>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [212/233]

Real libMesh::FE< 3, XYZ >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level  )

inherited

Definition at line 1424 of file fe_xyz_shape_3D.C.

{
  return FE<3,XYZ>::shape_second_deriv(elem, fet.order, i, j, p, add_p_level);
}

shape_second_deriv() [213/233]

static OutputShape libMesh::FE< Dim, T >::shape_second_deriv ( const FEType  fet, const Elem *  elem, const unsigned int  i, const unsigned int  j, const Point &  p, const bool  add_p_level = true  )

staticinherited

Returns

The second \( j^{th} \) derivative of the \( i^{th} \) shape function at the point p.

Note

Cross-derivatives are indexed according to: j = 0 ==> d^2 phi / dxi^2 j = 1 ==> d^2 phi / dxi deta j = 2 ==> d^2 phi / deta^2 j = 3 ==> d^2 phi / dxi dzeta j = 4 ==> d^2 phi / deta dzeta j = 5 ==> d^2 phi / dzeta^2

Computing second derivatives is not currently supported for all element types: \( C^1 \) (Clough, Hermite and Subdivision), Lagrange, Hierarchic, L2_Hierarchic, and Monomial are supported. All other element types return an error when asked for second derivatives.

On a p-refined element, o should be the total order of the element.

shape_second_deriv() [214/233]

Real libMesh::FE< 0, BERNSTEIN >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 136 of file fe_bernstein_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [215/233]

Real libMesh::FE< 0, CLOUGH >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 138 of file fe_clough_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [216/233]

Real libMesh::FE< 0, HERMITE >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 140 of file fe_hermite_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [217/233]

Real libMesh::FE< 0, HIERARCHIC >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 297 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [218/233]

Real libMesh::FE< 0, L2_HIERARCHIC >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 336 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [219/233]

Real libMesh::FE< 0, SIDE_HIERARCHIC >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 377 of file fe_hierarchic_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [220/233]

Real libMesh::FE< 1, SIDE_HIERARCHIC >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 410 of file fe_hierarchic_shape_1D.C.

{
  return 0.;
}

shape_second_deriv() [221/233]

Real libMesh::FE< 0, L2_LAGRANGE >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 239 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [222/233]

Real libMesh::FE< 0, LAGRANGE >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 252 of file fe_lagrange_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [223/233]

Real libMesh::FE< 0, MONOMIAL >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 141 of file fe_monomial_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [224/233]

Real libMesh::FE< 0, RATIONAL_BERNSTEIN >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 138 of file fe_rational_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [225/233]

Real libMesh::FE< 0, SCALAR >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 120 of file fe_scalar_shape_0D.C.

{
  return 0.;
}

shape_second_deriv() [226/233]

Real libMesh::FE< 1, SCALAR >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 125 of file fe_scalar_shape_1D.C.

{
  return 0.;
}

shape_second_deriv() [227/233]

Real libMesh::FE< 2, SCALAR >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 122 of file fe_scalar_shape_2D.C.

{
  return 0.;
}

shape_second_deriv() [228/233]

Real libMesh::FE< 3, SCALAR >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 122 of file fe_scalar_shape_3D.C.

{
  return 0.;
}

shape_second_deriv() [229/233]

Real libMesh::FE< 0, SZABAB >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 141 of file fe_szabab_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [230/233]

Real libMesh::FE< 2, SZABAB >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 1089 of file fe_szabab_shape_2D.C.

{
  static bool warning_given = false;
 
  if (!warning_given)
    libMesh::err << "Second derivatives for Szabab elements "
                 << " are not yet implemented!"
                 << std::endl;
 
  warning_given = true;
  return 0.;
}

shape_second_deriv() [231/233]

Real libMesh::FE< 3, SZABAB >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 139 of file fe_szabab_shape_3D.C.

{
  static bool warning_given = false;
 
  if (!warning_given)
    libMesh::err << "Second derivatives for Szabab elements "
                 << " are not yet implemented!"
                 << std::endl;
 
  warning_given = true;
  return 0.;
}

shape_second_deriv() [232/233]

Real libMesh::FE< 0, XYZ >::shape_second_deriv ( const FEType  , const Elem *  , const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 142 of file fe_xyz_shape_0D.C.

{
  libmesh_error_msg("No spatial derivatives in 0D!");
  return 0.;
}

shape_second_deriv() [233/233]

Real libMesh::FE< 3, CLOUGH >::shape_second_deriv ( const FEType  , const Elem *  libmesh_dbg_varelem, const unsigned int  , const unsigned int  , const Point &  , const bool    )

inherited

Definition at line 145 of file fe_clough_shape_3D.C.

{
  libmesh_assert(elem);
  libmesh_not_implemented();
  return 0.;
}

shapes() [1/5]

void libMesh::FE< 3, LAGRANGE >::shapes ( const Elem *  elem, const Order  o, const unsigned int  i, const std::vector< Point > &  p, std::vector< OutputShape > &  v, const bool  add_p_level  )

inherited

Definition at line 211 of file fe_lagrange_shape_3D.C.

{
  FE<3,LAGRANGE>::default_shapes
    (elem,o,i,p,v,add_p_level);
}

shapes() [2/5]

static void libMesh::FE< Dim, T >::shapes ( const Elem *  elem, const Order  o, const unsigned int  i, const std::vector< Point > &  p, std::vector< OutputShape > &  v, const bool  add_p_level = true  )

staticinherited

Fills v with the values of the \( i^{th} \) shape function, evaluated at all points p.

You must specify element order directly. v should already be the appropriate size.

On a p-refined element, o should be the base order of the element if add_p_level is left true, or can be the base order of the element if add_p_level is set to false.

shapes() [3/5]

void libMesh::FE< 1, RATIONAL_BERNSTEIN >::shapes ( const Elem *  elem, const Order  o, const unsigned int  i, const std::vector< Point > &  p, std::vector< OutputShape > &  vi, const bool  add_p_level  )

inherited

Definition at line 179 of file fe_rational_shape_1D.C.

{
  libmesh_assert_equal_to(p.size(), vi.size());
  for (auto j : index_range(vi))
    vi[j] = FE<1,RATIONAL_BERNSTEIN>::shape (elem, o, i, p[j], add_p_level);
}

shapes() [4/5]

void libMesh::FE< 2, RATIONAL_BERNSTEIN >::shapes ( const Elem *  elem, const Order  o, const unsigned int  i, const std::vector< Point > &  p, std::vector< OutputShape > &  vi, const bool  add_p_level  )

inherited

Definition at line 177 of file fe_rational_shape_2D.C.

{
  libmesh_assert_equal_to(p.size(), vi.size());
  for (auto j : index_range(vi))
    vi[j] = FE<2,RATIONAL_BERNSTEIN>::shape (elem, o, i, p[j], add_p_level);
}

shapes() [5/5]

void libMesh::FE< 3, RATIONAL_BERNSTEIN >::shapes ( const Elem *  elem, const Order  o, const unsigned int  i, const std::vector< Point > &  p, std::vector< OutputShape > &  vi, const bool  add_p_level  )

inherited

Definition at line 173 of file fe_rational_shape_3D.C.

{
  libmesh_assert_equal_to(p.size(), vi.size());
  for (auto j : index_range(vi))
    vi[j] = FE<3,RATIONAL_BERNSTEIN>::shape (elem, o, i, p[j], add_p_level);
}

shapes_need_reinit() [1/86]

bool libMesh::FE< 0, BERNSTEIN >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 452 of file fe_bernstein.C.

{ return true; }

shapes_need_reinit() [2/86]

bool libMesh::FE< 1, BERNSTEIN >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 453 of file fe_bernstein.C.

{ return true; }

shapes_need_reinit() [3/86]

bool libMesh::FE< 2, BERNSTEIN >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 454 of file fe_bernstein.C.

{ return true; }

shapes_need_reinit() [4/86]

bool libMesh::FE< 3, BERNSTEIN >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 455 of file fe_bernstein.C.

{ return true; }

shapes_need_reinit() [5/86]

bool libMesh::FE< 0, CLOUGH >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 299 of file fe_clough.C.

{ return true; }

shapes_need_reinit() [6/86]

bool libMesh::FE< 1, CLOUGH >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 300 of file fe_clough.C.

{ return true; }

shapes_need_reinit() [7/86]

bool libMesh::FE< 2, CLOUGH >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 301 of file fe_clough.C.

{ return true; }

shapes_need_reinit() [8/86]

bool libMesh::FE< 3, CLOUGH >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 302 of file fe_clough.C.

{ return true; }

shapes_need_reinit() [9/86]

bool libMesh::FE< 0, HERMITE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 342 of file fe_hermite.C.

{ return true; }

shapes_need_reinit() [10/86]

bool libMesh::FE< 1, HERMITE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 343 of file fe_hermite.C.

{ return true; }

shapes_need_reinit() [11/86]

bool libMesh::FE< 2, HERMITE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 344 of file fe_hermite.C.

{ return true; }

shapes_need_reinit() [12/86]

bool libMesh::FE< 3, HERMITE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 345 of file fe_hermite.C.

{ return true; }

shapes_need_reinit() [13/86]

bool libMesh::FE< 0, HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 505 of file fe_hierarchic.C.

{ return true; }

shapes_need_reinit() [14/86]

bool libMesh::FE< 1, HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 506 of file fe_hierarchic.C.

{ return true; }

shapes_need_reinit() [15/86]

bool libMesh::FE< 2, HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 507 of file fe_hierarchic.C.

{ return true; }

shapes_need_reinit() [16/86]

bool libMesh::FE< 3, HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 508 of file fe_hierarchic.C.

{ return true; }

shapes_need_reinit() [17/86]

bool libMesh::FE< 0, HIERARCHIC_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 795 of file fe_hierarchic_vec.C.

{ return true; }

shapes_need_reinit() [18/86]

bool libMesh::FE< 1, HIERARCHIC_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 796 of file fe_hierarchic_vec.C.

{ return true; }

shapes_need_reinit() [19/86]

bool libMesh::FE< 2, HIERARCHIC_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 797 of file fe_hierarchic_vec.C.

{ return true; }

shapes_need_reinit() [20/86]

bool libMesh::FE< 3, HIERARCHIC_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 798 of file fe_hierarchic_vec.C.

{ return true; }

shapes_need_reinit() [21/86]

bool libMesh::FE< 0, L2_HIERARCHIC_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 799 of file fe_hierarchic_vec.C.

{ return true; }

shapes_need_reinit() [22/86]

bool libMesh::FE< 1, L2_HIERARCHIC_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 800 of file fe_hierarchic_vec.C.

{ return true; }

shapes_need_reinit() [23/86]

bool libMesh::FE< 2, L2_HIERARCHIC_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 801 of file fe_hierarchic_vec.C.

{ return true; }

shapes_need_reinit() [24/86]

bool libMesh::FE< 3, L2_HIERARCHIC_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 802 of file fe_hierarchic_vec.C.

{ return true; }

shapes_need_reinit() [25/86]

bool libMesh::FE< 0, L2_HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 217 of file fe_l2_hierarchic.C.

{ return true; }

shapes_need_reinit() [26/86]

bool libMesh::FE< 1, L2_HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 218 of file fe_l2_hierarchic.C.

{ return true; }

shapes_need_reinit() [27/86]

bool libMesh::FE< 2, L2_HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 219 of file fe_l2_hierarchic.C.

{ return true; }

shapes_need_reinit() [28/86]

bool libMesh::FE< 3, L2_HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 220 of file fe_l2_hierarchic.C.

{ return true; }

shapes_need_reinit() [29/86]

bool libMesh::FE< 0, L2_LAGRANGE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 268 of file fe_l2_lagrange.C.

{ return false; }

shapes_need_reinit() [30/86]

bool libMesh::FE< 1, L2_LAGRANGE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 269 of file fe_l2_lagrange.C.

{ return false; }

shapes_need_reinit() [31/86]

bool libMesh::FE< 2, L2_LAGRANGE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 270 of file fe_l2_lagrange.C.

{ return false; }

shapes_need_reinit() [32/86]

bool libMesh::FE< 3, L2_LAGRANGE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 271 of file fe_l2_lagrange.C.

{ return false; }

shapes_need_reinit() [33/86]

bool libMesh::FE< 0, LAGRANGE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1126 of file fe_lagrange.C.

{ return false; }

shapes_need_reinit() [34/86]

bool libMesh::FE< 1, LAGRANGE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1127 of file fe_lagrange.C.

{ return false; }

shapes_need_reinit() [35/86]

bool libMesh::FE< 2, LAGRANGE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1128 of file fe_lagrange.C.

{ return false; }

shapes_need_reinit() [36/86]

bool libMesh::FE< 3, LAGRANGE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1129 of file fe_lagrange.C.

{ return false; }

shapes_need_reinit() [37/86]

bool libMesh::FE< 0, LAGRANGE_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1364 of file fe_lagrange_vec.C.

{ return false; }

shapes_need_reinit() [38/86]

bool libMesh::FE< 1, LAGRANGE_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1365 of file fe_lagrange_vec.C.

{ return false; }

shapes_need_reinit() [39/86]

bool libMesh::FE< 2, LAGRANGE_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1366 of file fe_lagrange_vec.C.

{ return false; }

shapes_need_reinit() [40/86]

bool libMesh::FE< 3, LAGRANGE_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1367 of file fe_lagrange_vec.C.

{ return false; }

shapes_need_reinit() [41/86]

bool libMesh::FE< 0, L2_LAGRANGE_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1368 of file fe_lagrange_vec.C.

{ return false; }

shapes_need_reinit() [42/86]

bool libMesh::FE< 1, L2_LAGRANGE_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1369 of file fe_lagrange_vec.C.

{ return false; }

shapes_need_reinit() [43/86]

bool libMesh::FE< 2, L2_LAGRANGE_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1370 of file fe_lagrange_vec.C.

{ return false; }

shapes_need_reinit() [44/86]

bool libMesh::FE< 3, L2_LAGRANGE_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1371 of file fe_lagrange_vec.C.

{ return false; }

shapes_need_reinit() [45/86]

bool libMesh::FE< 0, MONOMIAL >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 444 of file fe_monomial.C.

{ return false; }

shapes_need_reinit() [46/86]

bool libMesh::FE< 1, MONOMIAL >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 445 of file fe_monomial.C.

{ return false; }

shapes_need_reinit() [47/86]

bool libMesh::FE< 2, MONOMIAL >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 446 of file fe_monomial.C.

{ return false; }

shapes_need_reinit() [48/86]

bool libMesh::FE< 3, MONOMIAL >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 447 of file fe_monomial.C.

{ return false; }

shapes_need_reinit() [49/86]

bool libMesh::FE< 0, MONOMIAL_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 749 of file fe_monomial_vec.C.

{
  return false;
}

shapes_need_reinit() [50/86]

bool libMesh::FE< 1, MONOMIAL_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 755 of file fe_monomial_vec.C.

{
  return false;
}

shapes_need_reinit() [51/86]

bool libMesh::FE< 2, MONOMIAL_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 761 of file fe_monomial_vec.C.

{
  return false;
}

shapes_need_reinit() [52/86]

bool libMesh::FE< 3, MONOMIAL_VEC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 767 of file fe_monomial_vec.C.

{
  return false;
}

shapes_need_reinit() [53/86]

bool libMesh::FE< 0, NEDELEC_ONE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 420 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shapes_need_reinit() [54/86]

bool libMesh::FE< 1, NEDELEC_ONE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 421 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

shapes_need_reinit() [55/86]

bool libMesh::FE< 2, NEDELEC_ONE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 422 of file fe_nedelec_one.C.

{ return true; }

shapes_need_reinit() [56/86]

bool libMesh::FE< 3, NEDELEC_ONE >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 423 of file fe_nedelec_one.C.

{ return true; }

shapes_need_reinit() [57/86]

bool libMesh::FE< 0, RATIONAL_BERNSTEIN >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 191 of file fe_rational.C.

{ return true; }

shapes_need_reinit() [58/86]

bool libMesh::FE< 1, RATIONAL_BERNSTEIN >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 192 of file fe_rational.C.

{ return true; }

shapes_need_reinit() [59/86]

bool libMesh::FE< 2, RATIONAL_BERNSTEIN >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 193 of file fe_rational.C.

{ return true; }

shapes_need_reinit() [60/86]

bool libMesh::FE< 3, RATIONAL_BERNSTEIN >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 194 of file fe_rational.C.

{ return true; }

shapes_need_reinit() [61/86]

bool libMesh::FE< 0, RAVIART_THOMAS >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 478 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shapes_need_reinit() [62/86]

bool libMesh::FE< 1, RAVIART_THOMAS >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 479 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shapes_need_reinit() [63/86]

bool libMesh::FE< 2, RAVIART_THOMAS >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 480 of file fe_raviart.C.

{ return true; }

shapes_need_reinit() [64/86]

bool libMesh::FE< 3, RAVIART_THOMAS >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 481 of file fe_raviart.C.

{ return true; }

shapes_need_reinit() [65/86]

bool libMesh::FE< 0, L2_RAVIART_THOMAS >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 484 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shapes_need_reinit() [66/86]

bool libMesh::FE< 1, L2_RAVIART_THOMAS >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 485 of file fe_raviart.C.

{ RAVIART_LOW_D_ERROR_MESSAGE }

shapes_need_reinit() [67/86]

bool libMesh::FE< 2, L2_RAVIART_THOMAS >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 486 of file fe_raviart.C.

{ return true; }

shapes_need_reinit() [68/86]

bool libMesh::FE< 3, L2_RAVIART_THOMAS >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 487 of file fe_raviart.C.

{ return true; }

shapes_need_reinit() [69/86]

bool libMesh::FE< 0, SCALAR >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 125 of file fe_scalar.C.

{ return false; }

shapes_need_reinit() [70/86]

bool libMesh::FE< 1, SCALAR >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 126 of file fe_scalar.C.

{ return false; }

shapes_need_reinit() [71/86]

bool libMesh::FE< 2, SCALAR >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 127 of file fe_scalar.C.

{ return false; }

shapes_need_reinit() [72/86]

bool libMesh::FE< 3, SCALAR >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 128 of file fe_scalar.C.

{ return false; }

shapes_need_reinit() [73/86]

bool libMesh::FE< 0, SIDE_HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 356 of file fe_side_hierarchic.C.

{ return true; }

shapes_need_reinit() [74/86]

bool libMesh::FE< 1, SIDE_HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 357 of file fe_side_hierarchic.C.

{ return true; }

shapes_need_reinit() [75/86]

bool libMesh::FE< 2, SIDE_HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 358 of file fe_side_hierarchic.C.

{ return true; }

shapes_need_reinit() [76/86]

bool libMesh::FE< 3, SIDE_HIERARCHIC >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 359 of file fe_side_hierarchic.C.

{ return true; }

shapes_need_reinit() [77/86]

bool libMesh::FE< 2, SUBDIVISION >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 980 of file fe_subdivision_2D.C.

{ return true; }

shapes_need_reinit() [78/86]

bool libMesh::FE< 0, SZABAB >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1355 of file fe_szabab.C.

{ return true; }

shapes_need_reinit() [79/86]

bool libMesh::FE< 1, SZABAB >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1356 of file fe_szabab.C.

{ return true; }

shapes_need_reinit() [80/86]

bool libMesh::FE< 2, SZABAB >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1357 of file fe_szabab.C.

{ return true; }

shapes_need_reinit() [81/86]

bool libMesh::FE< 3, SZABAB >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 1358 of file fe_szabab.C.

{ return true; }

shapes_need_reinit() [82/86]

bool libMesh::FE< 0, XYZ >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 429 of file fe_xyz.C.

{ return true; }

shapes_need_reinit() [83/86]

bool libMesh::FE< 1, XYZ >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 430 of file fe_xyz.C.

{ return true; }

shapes_need_reinit() [84/86]

bool libMesh::FE< 2, XYZ >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 431 of file fe_xyz.C.

{ return true; }

shapes_need_reinit() [85/86]

bool libMesh::FE< 3, XYZ >::shapes_need_reinit ( ) const

virtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

Definition at line 432 of file fe_xyz.C.

{ return true; }

shapes_need_reinit() [86/86]

virtual bool libMesh::FE< Dim, T >::shapes_need_reinit ( ) const

overridevirtualinherited

Returns

true when the shape functions (for this FEFamily) depend on the particular element, and therefore needs to be re-initialized for each new element. false otherwise.

Implements libMesh::FEAbstract.

side_map() [1/2]

void libMesh::FE< 2, SUBDIVISION >::side_map ( const Elem *  , const Elem *  , const unsigned int  , const std::vector< Point > &  , std::vector< Point > &    )

virtualinherited

Computes the reference space quadrature points on the side of an element based on the side quadrature points.

Implements libMesh::FEAbstract.

Definition at line 917 of file fe_subdivision_2D.C.

{
  libmesh_not_implemented();
}

side_map() [2/2]

void libMesh::FE< Dim, T >::side_map ( const Elem *  elem, const Elem *  side, const unsigned int  s, const std::vector< Point > &  reference_side_points, std::vector< Point > &  reference_points  )

overridevirtualinherited

Computes the reference space quadrature points on the side of an element based on the side quadrature points.

Implements libMesh::FEAbstract.

Definition at line 616 of file fe_boundary.C.

{
  // We're calculating mappings - we need at least first order info
  this->calculate_phi = true;
  this->determine_calculations();
 
  unsigned int side_p_level = elem->p_level();
  if (elem->neighbor_ptr(s) != nullptr)
    side_p_level = std::max(side_p_level, elem->neighbor_ptr(s)->p_level());
 
  if (side->type() != last_side           ||
      (elem->runtime_topology() &&
       this->_elem != elem)               ||
      side_p_level != this->_elem_p_level ||
      !this->shapes_on_quadrature)
    {
      // Set the element type
      this->_elem = elem;
      this->_elem_type = elem->type();
      this->_elem_p_level = side_p_level;
      this->_p_level = this->_add_p_level_in_reinit * side_p_level;
 
      // Set the last_side
      last_side = side->type();
 
      // Initialize the face shape functions
      this->_fe_map->template init_face_shape_functions<Dim>(reference_side_points, side);
    }
  else
    this->_elem = elem;
 
  const unsigned int n_points =
    cast_int<unsigned int>(reference_side_points.size());
  reference_points.resize(n_points);
  for (unsigned int i = 0; i < n_points; i++)
    reference_points[i].zero();
 
  std::vector<Point> refspace_nodes;
  this->get_refspace_nodes(elem->type(), refspace_nodes);
 
  const std::vector<std::vector<Real>> & psi_map = this->_fe_map->get_psi();
 
  // sum over the nodes
  for (auto i : index_range(psi_map))
    {
      const Point & side_node = refspace_nodes[elem->local_side_node(s,i)];
      for (unsigned int p=0; p<n_points; p++)
        reference_points[p].add_scaled (side_node, psi_map[i][p]);
    }
}

side_nodal_soln() [1/4]

void libMesh::FE< 1, SIDE_HIERARCHIC >::side_nodal_soln ( const Elem *  , const Order  , const unsigned int  side, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln_on_side, const bool  , const unsigned    )

inherited

Definition at line 246 of file fe_side_hierarchic.C.

{
  libmesh_assert_less(side, 2);
  nodal_soln_on_side.resize(1);
  nodal_soln_on_side[0] = elem_soln[side];
}

side_nodal_soln() [2/4]

static void libMesh::FE< Dim, T >::side_nodal_soln ( const Elem *  elem, const Order  o, const unsigned int  side, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln_on_side, bool  add_p_level = true, const unsigned  vdim = 1  )

staticinherited

Build the nodal soln on one side from the (full) element soln.

This is the solution that will be plotted on side-elements.

On a p-refined element, o should be the base order of the element.

side_nodal_soln() [3/4]

void libMesh::FE< 2, SIDE_HIERARCHIC >::side_nodal_soln ( const Elem *  elem, const Order  o, const unsigned int  side, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln_on_side, const bool  add_p_level, const unsigned    )

inherited

Definition at line 261 of file fe_side_hierarchic.C.

{
  libmesh_assert_equal_to(elem->dim(), 2);
  side_hierarchic_side_nodal_soln(elem, o, side, elem_soln,
                                  nodal_soln_on_side,
                                  add_p_level);
}

side_nodal_soln() [4/4]

void libMesh::FE< 3, SIDE_HIERARCHIC >::side_nodal_soln ( const Elem *  elem, const Order  o, const unsigned int  side, const std::vector< Number > &  elem_soln, std::vector< Number > &  nodal_soln_on_side, const bool  add_p_level, const unsigned    )

inherited

Definition at line 277 of file fe_side_hierarchic.C.

{
  libmesh_assert_equal_to(elem->dim(), 3);
  side_hierarchic_side_nodal_soln(elem, o, side, elem_soln,
                                  nodal_soln_on_side,
                                  add_p_level);
}

Member Data Documentation

_add_p_level_in_reinit

bool libMesh::FEAbstract::_add_p_level_in_reinit

protectedinherited

Whether to add p-refinement levels in init/reinit methods.

Definition at line 787 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::add_p_level_in_reinit(), and libMesh::FEAbstract::add_p_level_in_reinit().

_counts

ReferenceCounter::Counts libMesh::ReferenceCounter::_counts

staticprotectedinherited

Actually holds the data.

Definition at line 124 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::get_info().

_elem

const Elem* libMesh::FEAbstract::_elem

protectedinherited

The element the current data structures were set up for.

Definition at line 740 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::get_elem().

_elem_p_level

unsigned int libMesh::FEAbstract::_elem_p_level

protectedinherited

The element p-refinement level the current data structures are set up for.

Note that this is different from _p_level which is the p-refinement level this finite elment object is operating at, e.g. how many dofs per elem, etc. On the other hand, this data member can indicate things like the order of the quadrature rule. We will use this primarily to determine whether cached data is still valid

Definition at line 751 of file fe_abstract.h.

_elem_type

ElemType libMesh::FEAbstract::_elem_type

protectedinherited

The element type the current data structures were set up for.

Definition at line 735 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::get_type().

_enable_print_counter

bool libMesh::ReferenceCounter::_enable_print_counter = true

staticprotectedinherited

Flag to control whether reference count information is printed when print_info is called.

Definition at line 143 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::disable_print_counter_info(), libMesh::ReferenceCounter::enable_print_counter_info(), and libMesh::ReferenceCounter::print_info().

_fe_map

std::unique_ptr<FEMap> libMesh::FEAbstract::_fe_map

protectedinherited

Definition at line 654 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::get_curvatures(), libMesh::FEAbstract::get_d2xyzdeta2(), libMesh::FEAbstract::get_d2xyzdetadzeta(), libMesh::FEAbstract::get_d2xyzdxi2(), libMesh::FEAbstract::get_d2xyzdxideta(), libMesh::FEAbstract::get_d2xyzdxidzeta(), libMesh::FEAbstract::get_d2xyzdzeta2(), libMesh::FEAbstract::get_detadx(), libMesh::FEAbstract::get_detady(), libMesh::FEAbstract::get_detadz(), libMesh::FEAbstract::get_dxidx(), libMesh::FEAbstract::get_dxidy(), libMesh::FEAbstract::get_dxidz(), libMesh::FEAbstract::get_dxyzdeta(), libMesh::FEAbstract::get_dxyzdxi(), libMesh::FEAbstract::get_dxyzdzeta(), libMesh::FEAbstract::get_dzetadx(), libMesh::FEAbstract::get_dzetady(), libMesh::FEAbstract::get_dzetadz(), libMesh::FEAbstract::get_fe_map(), libMesh::FEAbstract::get_fe_map(), libMesh::FEAbstract::get_JxW(), libMesh::FEAbstract::get_normals(), libMesh::FEAbstract::get_tangents(), libMesh::FEAbstract::get_xyz(), libMesh::FEAbstract::print_JxW(), and libMesh::FEAbstract::print_xyz().

_fe_trans

std::unique_ptr<FETransformationBase<FEOutputType< T >::type > > libMesh::FEGenericBase< FEOutputType< T >::type >::_fe_trans

protectedinherited

Object that handles computing shape function values, gradients, etc in the physical domain.

Definition at line 609 of file fe_base.h.

_mutex

Threads::spin_mutex libMesh::ReferenceCounter::_mutex

staticprotectedinherited

Mutual exclusion object to enable thread-safe reference counting.

Definition at line 137 of file reference_counter.h.

_n_objects

Threads::atomic< unsigned int > libMesh::ReferenceCounter::_n_objects

staticprotectedinherited

The number of objects.

Print the reference count information when the number returns to 0.

Definition at line 132 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::n_objects(), libMesh::ReferenceCounter::ReferenceCounter(), libMesh::ReferenceCounter::ReferenceCounter(), libMesh::ReferenceCounter::ReferenceCounter(), and libMesh::ReferenceCounter::~ReferenceCounter().

_n_total_qp

unsigned int libMesh::FEAbstract::_n_total_qp

protectedinherited

The total number of quadrature points for the current configuration.

Definition at line 774 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::n_quadrature_points(), and libMesh::InfFE< Dim, T_radial, T_map >::n_quadrature_points().

_p_level

unsigned int libMesh::FEAbstract::_p_level

protectedinherited

The p refinement level the current data structures are set up for.

Definition at line 757 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::get_order(), and libMesh::FEAbstract::get_p_level().

cached_edges

std::vector<bool> libMesh::FE< Dim, T >::cached_edges

protectedinherited

Definition at line 797 of file fe.h.

cached_faces

std::vector<bool> libMesh::FE< Dim, T >::cached_faces

protectedinherited

Definition at line 797 of file fe.h.

cached_nodes

std::vector<Point> libMesh::FE< Dim, T >::cached_nodes

protectedinherited

Vectors holding the node locations, edge and face orientations of the last element we cached.

Definition at line 796 of file fe.h.

calculate_curl_phi

bool libMesh::FEAbstract::calculate_curl_phi

mutableprotectedinherited

Should we calculate shape function curls?

Definition at line 712 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::calculating_nothing(), and libMesh::FEGenericBase< OutputType >::get_curl_phi().

calculate_d2phi [1/2]

bool libMesh::FEAbstract::calculate_d2phi

mutableprotectedinherited

Should we calculate shape function hessians?

Definition at line 702 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::calculating_nothing(), libMesh::FEGenericBase< OutputType >::get_d2phi(), libMesh::FEGenericBase< OutputType >::get_d2phideta2(), libMesh::FEGenericBase< OutputType >::get_d2phidetadzeta(), libMesh::FEGenericBase< OutputType >::get_d2phidx2(), libMesh::FEGenericBase< OutputType >::get_d2phidxdy(), libMesh::FEGenericBase< OutputType >::get_d2phidxdz(), libMesh::FEGenericBase< OutputType >::get_d2phidxi2(), libMesh::FEGenericBase< OutputType >::get_d2phidxideta(), libMesh::FEGenericBase< OutputType >::get_d2phidxidzeta(), libMesh::FEGenericBase< OutputType >::get_d2phidy2(), libMesh::FEGenericBase< OutputType >::get_d2phidydz(), libMesh::FEGenericBase< OutputType >::get_d2phidz2(), libMesh::FEGenericBase< OutputType >::get_d2phidzeta2(), and libMesh::FEGenericBase< OutputType >::get_dual_d2phi().

calculate_d2phi [2/2]

const bool libMesh::FEAbstract::calculate_d2phi =false

protectedinherited

Definition at line 705 of file fe_abstract.h.

calculate_default_dual_coeff

bool libMesh::FEAbstract::calculate_default_dual_coeff

mutableprotectedinherited

Are we calculating the coefficient for the dual basis using the default qrule?

Definition at line 676 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::set_calculate_default_dual_coeff().

calculate_div_phi

bool libMesh::FEAbstract::calculate_div_phi

mutableprotectedinherited

Should we calculate shape function divergences?

Definition at line 717 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::calculating_nothing(), and libMesh::FEGenericBase< OutputType >::get_div_phi().

calculate_dphi

bool libMesh::FEAbstract::calculate_dphi

mutableprotectedinherited

Should we calculate shape function gradients?

Definition at line 696 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::calculating_nothing(), libMesh::FEGenericBase< OutputType >::get_dphi(), libMesh::FEGenericBase< OutputType >::get_dphidx(), libMesh::FEGenericBase< OutputType >::get_dphidy(), libMesh::FEGenericBase< OutputType >::get_dphidz(), libMesh::FEGenericBase< OutputType >::get_dual_dphi(), and libMesh::InfFE< Dim, T_radial, T_map >::get_Sobolev_dweight().

calculate_dphiref

bool libMesh::FEAbstract::calculate_dphiref

mutableprotectedinherited

Should we calculate reference shape function gradients?

Definition at line 722 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::get_curl_phi(), libMesh::FEGenericBase< OutputType >::get_d2phi(), libMesh::FEGenericBase< OutputType >::get_d2phideta2(), libMesh::FEGenericBase< OutputType >::get_d2phidetadzeta(), libMesh::FEGenericBase< OutputType >::get_d2phidx2(), libMesh::FEGenericBase< OutputType >::get_d2phidxdy(), libMesh::FEGenericBase< OutputType >::get_d2phidxdz(), libMesh::FEGenericBase< OutputType >::get_d2phidxi2(), libMesh::FEGenericBase< OutputType >::get_d2phidxideta(), libMesh::FEGenericBase< OutputType >::get_d2phidxidzeta(), libMesh::FEGenericBase< OutputType >::get_d2phidy2(), libMesh::FEGenericBase< OutputType >::get_d2phidydz(), libMesh::FEGenericBase< OutputType >::get_d2phidz2(), libMesh::FEGenericBase< OutputType >::get_d2phidzeta2(), libMesh::FEGenericBase< OutputType >::get_div_phi(), libMesh::FEGenericBase< OutputType >::get_dphi(), libMesh::FEGenericBase< OutputType >::get_dphideta(), libMesh::FEGenericBase< OutputType >::get_dphidx(), libMesh::FEGenericBase< OutputType >::get_dphidxi(), libMesh::FEGenericBase< OutputType >::get_dphidy(), libMesh::FEGenericBase< OutputType >::get_dphidz(), libMesh::FEGenericBase< OutputType >::get_dphidzeta(), libMesh::FEGenericBase< OutputType >::get_dual_d2phi(), and libMesh::FEGenericBase< OutputType >::get_dual_dphi().

calculate_dual

bool libMesh::FEAbstract::calculate_dual

mutableprotectedinherited

Are we calculating dual basis?

Definition at line 671 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::get_dual_d2phi(), libMesh::FEGenericBase< OutputType >::get_dual_dphi(), libMesh::FEGenericBase< OutputType >::get_dual_phi(), and libMesh::FEAbstract::set_calculate_dual().

calculate_map

bool libMesh::FEAbstract::calculate_map

mutableprotectedinherited

Are we calculating mapping functions?

Definition at line 686 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::calculating_nothing(), libMesh::FEAbstract::get_curvatures(), libMesh::InfFE< Dim, T_radial, T_map >::get_curvatures(), libMesh::FEAbstract::get_d2xyzdeta2(), libMesh::InfFE< Dim, T_radial, T_map >::get_d2xyzdeta2(), libMesh::FEAbstract::get_d2xyzdetadzeta(), libMesh::InfFE< Dim, T_radial, T_map >::get_d2xyzdetadzeta(), libMesh::FEAbstract::get_d2xyzdxi2(), libMesh::InfFE< Dim, T_radial, T_map >::get_d2xyzdxi2(), libMesh::FEAbstract::get_d2xyzdxideta(), libMesh::InfFE< Dim, T_radial, T_map >::get_d2xyzdxideta(), libMesh::FEAbstract::get_d2xyzdxidzeta(), libMesh::InfFE< Dim, T_radial, T_map >::get_d2xyzdxidzeta(), libMesh::FEAbstract::get_d2xyzdzeta2(), libMesh::InfFE< Dim, T_radial, T_map >::get_d2xyzdzeta2(), libMesh::FEAbstract::get_detadx(), libMesh::InfFE< Dim, T_radial, T_map >::get_detadx(), libMesh::FEAbstract::get_detady(), libMesh::InfFE< Dim, T_radial, T_map >::get_detady(), libMesh::FEAbstract::get_detadz(), libMesh::InfFE< Dim, T_radial, T_map >::get_detadz(), libMesh::FEAbstract::get_dxidx(), libMesh::InfFE< Dim, T_radial, T_map >::get_dxidx(), libMesh::FEAbstract::get_dxidy(), libMesh::InfFE< Dim, T_radial, T_map >::get_dxidy(), libMesh::FEAbstract::get_dxidz(), libMesh::InfFE< Dim, T_radial, T_map >::get_dxidz(), libMesh::FEAbstract::get_dxyzdeta(), libMesh::InfFE< Dim, T_radial, T_map >::get_dxyzdeta(), libMesh::FEAbstract::get_dxyzdxi(), libMesh::InfFE< Dim, T_radial, T_map >::get_dxyzdxi(), libMesh::InfFE< Dim, T_radial, T_map >::get_dxyzdzeta(), libMesh::FEAbstract::get_dzetadx(), libMesh::InfFE< Dim, T_radial, T_map >::get_dzetadx(), libMesh::FEAbstract::get_dzetady(), libMesh::InfFE< Dim, T_radial, T_map >::get_dzetady(), libMesh::FEAbstract::get_dzetadz(), libMesh::InfFE< Dim, T_radial, T_map >::get_dzetadz(), libMesh::FEAbstract::get_JxW(), libMesh::FEAbstract::get_normals(), libMesh::InfFE< Dim, T_radial, T_map >::get_normals(), libMesh::FEAbstract::get_tangents(), libMesh::InfFE< Dim, T_radial, T_map >::get_tangents(), and libMesh::FEAbstract::get_xyz().

calculate_nothing

bool libMesh::FEAbstract::calculate_nothing

mutableprotectedinherited

Are we potentially deliberately calculating nothing?

Definition at line 681 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::calculating_nothing(), and libMesh::FEAbstract::get_nothing().

calculate_phi

bool libMesh::FEAbstract::calculate_phi

mutableprotectedinherited

Should we calculate shape functions?

Definition at line 691 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::calculating_nothing(), libMesh::FEGenericBase< OutputType >::get_phi(), and libMesh::InfFE< Dim, T_radial, T_map >::get_Sobolev_weight().

calculations_started

bool libMesh::FEAbstract::calculations_started

mutableprotectedinherited

Have calculations with this object already been started? Then all get_* functions should already have been called.

Definition at line 666 of file fe_abstract.h.

Referenced by libMesh::FEGenericBase< OutputType >::get_curl_phi(), libMesh::FEGenericBase< OutputType >::get_d2phi(), libMesh::FEGenericBase< OutputType >::get_d2phideta2(), libMesh::FEGenericBase< OutputType >::get_d2phidetadzeta(), libMesh::FEGenericBase< OutputType >::get_d2phidx2(), libMesh::FEGenericBase< OutputType >::get_d2phidxdy(), libMesh::FEGenericBase< OutputType >::get_d2phidxdz(), libMesh::FEGenericBase< OutputType >::get_d2phidxi2(), libMesh::FEGenericBase< OutputType >::get_d2phidxideta(), libMesh::FEGenericBase< OutputType >::get_d2phidxidzeta(), libMesh::FEGenericBase< OutputType >::get_d2phidy2(), libMesh::FEGenericBase< OutputType >::get_d2phidydz(), libMesh::FEGenericBase< OutputType >::get_d2phidz2(), libMesh::FEGenericBase< OutputType >::get_d2phidzeta2(), libMesh::InfFE< Dim, T_radial, T_map >::get_detadx(), libMesh::InfFE< Dim, T_radial, T_map >::get_detady(), libMesh::InfFE< Dim, T_radial, T_map >::get_detadz(), libMesh::FEGenericBase< OutputType >::get_div_phi(), libMesh::FEGenericBase< OutputType >::get_dphi(), libMesh::InfFE< Dim, T_radial, T_map >::get_dphi_over_decay(), libMesh::InfFE< Dim, T_radial, T_map >::get_dphi_over_decayxR(), libMesh::FEGenericBase< OutputType >::get_dphideta(), libMesh::FEGenericBase< OutputType >::get_dphidx(), libMesh::FEGenericBase< OutputType >::get_dphidxi(), libMesh::FEGenericBase< OutputType >::get_dphidy(), libMesh::FEGenericBase< OutputType >::get_dphidz(), libMesh::FEGenericBase< OutputType >::get_dphidzeta(), libMesh::FEGenericBase< OutputType >::get_dual_d2phi(), libMesh::FEGenericBase< OutputType >::get_dual_dphi(), libMesh::FEGenericBase< OutputType >::get_dual_phi(), libMesh::InfFE< Dim, T_radial, T_map >::get_dxidx(), libMesh::InfFE< Dim, T_radial, T_map >::get_dxidy(), libMesh::InfFE< Dim, T_radial, T_map >::get_dxidz(), libMesh::InfFE< Dim, T_radial, T_map >::get_dzetadx(), libMesh::InfFE< Dim, T_radial, T_map >::get_dzetady(), libMesh::InfFE< Dim, T_radial, T_map >::get_dzetadz(), libMesh::InfFE< Dim, T_radial, T_map >::get_JxW(), libMesh::InfFE< Dim, T_radial, T_map >::get_JxWxdecay_sq(), libMesh::InfFE< Dim, T_radial, T_map >::get_normals(), libMesh::FEGenericBase< OutputType >::get_phi(), libMesh::InfFE< Dim, T_radial, T_map >::get_phi_over_decayxR(), libMesh::InfFE< Dim, T_radial, T_map >::get_Sobolev_dweight(), libMesh::InfFE< Dim, T_radial, T_map >::get_Sobolev_dweightxR_sq(), libMesh::InfFE< Dim, T_radial, T_map >::get_Sobolev_weight(), libMesh::InfFE< Dim, T_radial, T_map >::get_Sobolev_weightxR_sq(), libMesh::InfFE< Dim, T_radial, T_map >::get_tangents(), and libMesh::InfFE< Dim, T_radial, T_map >::get_xyz().

curl_phi

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::curl_phi

protectedinherited

Shape function curl values.

Only defined for vector types.

Definition at line 631 of file fe_base.h.

d2phi

std::vector<std::vector<OutputTensor> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phi

protectedinherited

Shape function second derivative values.

Definition at line 674 of file fe_base.h.

d2phideta2

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phideta2

protectedinherited

Shape function second derivatives in the eta direction.

Definition at line 695 of file fe_base.h.

d2phidetadzeta

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidetadzeta

protectedinherited

Shape function second derivatives in the eta-zeta direction.

Definition at line 700 of file fe_base.h.

d2phidx2

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidx2

protectedinherited

Shape function second derivatives in the x direction.

Definition at line 710 of file fe_base.h.

d2phidxdy

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidxdy

protectedinherited

Shape function second derivatives in the x-y direction.

Definition at line 715 of file fe_base.h.

d2phidxdz

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidxdz

protectedinherited

Shape function second derivatives in the x-z direction.

Definition at line 720 of file fe_base.h.

d2phidxi2

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidxi2

protectedinherited

Shape function second derivatives in the xi direction.

Definition at line 680 of file fe_base.h.

d2phidxideta

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidxideta

protectedinherited

Shape function second derivatives in the xi-eta direction.

Definition at line 685 of file fe_base.h.

d2phidxidzeta

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidxidzeta

protectedinherited

Shape function second derivatives in the xi-zeta direction.

Definition at line 690 of file fe_base.h.

d2phidy2

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidy2

protectedinherited

Shape function second derivatives in the y direction.

Definition at line 725 of file fe_base.h.

d2phidydz

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidydz

protectedinherited

Shape function second derivatives in the y-z direction.

Definition at line 730 of file fe_base.h.

d2phidz2

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidz2

protectedinherited

Shape function second derivatives in the z direction.

Definition at line 735 of file fe_base.h.

d2phidzeta2

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::d2phidzeta2

protectedinherited

Shape function second derivatives in the zeta direction.

Definition at line 705 of file fe_base.h.

dim

const unsigned int libMesh::FEAbstract::dim

protectedinherited

The dimensionality of the object.

Definition at line 660 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::build(), and libMesh::FEAbstract::get_dim().

div_phi

std::vector<std::vector<OutputDivergence> > libMesh::FEGenericBase< FEOutputType< T >::type >::div_phi

protectedinherited

Shape function divergence values.

Only defined for vector types.

Definition at line 636 of file fe_base.h.

dphase

std::vector<OutputGradient> libMesh::FEGenericBase< FEOutputType< T >::type >::dphase

protectedinherited

Used for certain infinite element families: the first derivatives of the phase term in global coordinates, over all quadrature points.

Definition at line 753 of file fe_base.h.

dphi

std::vector<std::vector<OutputGradient> > libMesh::FEGenericBase< FEOutputType< T >::type >::dphi

protectedinherited

Shape function derivative values.

Definition at line 620 of file fe_base.h.

dphideta

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::dphideta

protectedinherited

Shape function derivatives in the eta direction.

Definition at line 646 of file fe_base.h.

dphidx

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::dphidx

protectedinherited

Shape function derivatives in the x direction.

Definition at line 656 of file fe_base.h.

dphidxi

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::dphidxi

protectedinherited

Shape function derivatives in the xi direction.

Definition at line 641 of file fe_base.h.

dphidy

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::dphidy

protectedinherited

Shape function derivatives in the y direction.

Definition at line 661 of file fe_base.h.

dphidz

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::dphidz

protectedinherited

Shape function derivatives in the z direction.

Definition at line 666 of file fe_base.h.

dphidzeta

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::dphidzeta

protectedinherited

Shape function derivatives in the zeta direction.

Definition at line 651 of file fe_base.h.

dual_coeff

DenseMatrix<Real> libMesh::FEGenericBase< FEOutputType< T >::type >::dual_coeff

mutableprotectedinherited

Coefficient matrix for the dual basis.

Definition at line 626 of file fe_base.h.

dual_d2phi

std::vector<std::vector<OutputTensor> > libMesh::FEGenericBase< FEOutputType< T >::type >::dual_d2phi

protectedinherited

Definition at line 675 of file fe_base.h.

dual_dphi

std::vector<std::vector<OutputGradient> > libMesh::FEGenericBase< FEOutputType< T >::type >::dual_dphi

protectedinherited

Definition at line 621 of file fe_base.h.

dual_phi

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::dual_phi

protectedinherited

Definition at line 615 of file fe_base.h.

dweight

std::vector<RealGradient> libMesh::FEGenericBase< FEOutputType< T >::type >::dweight

protectedinherited

Used for certain infinite element families: the global derivative of the additional radial weight \( 1/{r^2} \), over all quadrature points.

Definition at line 760 of file fe_base.h.

fe_type

FEType libMesh::FEAbstract::fe_type

protectedinherited

The finite element type for this object.

Note

This should be constant for the object.

Definition at line 730 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::compute_node_constraints(), libMesh::FEAbstract::compute_periodic_node_constraints(), libMesh::FEAbstract::get_family(), libMesh::FEAbstract::get_fe_type(), libMesh::FEAbstract::get_order(), libMesh::InfFE< Dim, T_radial, T_map >::InfFE(), and libMesh::FEAbstract::set_fe_order().

last_edge

ElemType libMesh::FE< Dim, T >::last_edge

protectedinherited

Definition at line 816 of file fe.h.

last_side

ElemType libMesh::FE< Dim, T >::last_side

protectedinherited

The last side and last edge we did a reinit on.

Definition at line 814 of file fe.h.

phi

std::vector<std::vector<OutputShape> > libMesh::FEGenericBase< FEOutputType< T >::type >::phi

protectedinherited

Shape function values.

Definition at line 614 of file fe_base.h.

qrule

QBase* libMesh::FEAbstract::qrule

protectedinherited

A pointer to the quadrature rule employed.

Definition at line 762 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::n_quadrature_points().

shapes_on_quadrature

bool libMesh::FEAbstract::shapes_on_quadrature

protectedinherited

A flag indicating if current data structures correspond to quadrature rule points.

Definition at line 768 of file fe_abstract.h.

Referenced by libMesh::FEAbstract::n_quadrature_points().

weight

std::vector<Real> libMesh::FEGenericBase< FEOutputType< T >::type >::weight

protectedinherited

Used for certain infinite element families: the additional radial weight \( 1/{r^2} \) in local coordinates, over all quadrature points.

Definition at line 767 of file fe_base.h.

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The documentation for this class was generated from the following file:

• include/fe/fe.h