This class handles the computation of the shape functions in the physical domain. More...

#include <fe_base.h>

Inheritance diagram for libMesh::FETransformationBase< OutputShape >:

Public Member Functions
	FETransformationBase ()=default

virtual	~FETransformationBase ()=default

virtual void	init_map_phi (const FEGenericBase< OutputShape > &fe) const =0
	Pre-requests any necessary data from FEMap. More...

virtual void	init_map_dphi (const FEGenericBase< OutputShape > &fe) const =0
	Pre-requests any necessary data from FEMap. More...

virtual void	init_map_d2phi (const FEGenericBase< OutputShape > &fe) const =0
	Pre-requests any necessary data from FEMap. More...

virtual void	map_phi (const unsigned int dim, const Elem *const elem, const std::vector< Point > &qp, const FEGenericBase< OutputShape > &fe, std::vector< std::vector< OutputShape >> &phi, bool add_p_level=true) const =0
	Evaluates shape functions in physical coordinates based on proper finite element transformation. More...

virtual void	map_dphi (const unsigned int dim, const Elem *const elem, const std::vector< Point > &qp, const FEGenericBase< OutputShape > &fe, std::vector< std::vector< typename FEGenericBase< OutputShape >::OutputGradient >> &dphi, std::vector< std::vector< OutputShape >> &dphidx, std::vector< std::vector< OutputShape >> &dphidy, std::vector< std::vector< OutputShape >> &dphidz) const =0
	Evaluates shape function gradients in physical coordinates based on proper finite element transformation. More...

virtual void	map_d2phi (const unsigned int dim, const std::vector< Point > &qp, const FEGenericBase< OutputShape > &fe, std::vector< std::vector< typename FEGenericBase< OutputShape >::OutputTensor >> &d2phi, std::vector< std::vector< OutputShape >> &d2phidx2, std::vector< std::vector< OutputShape >> &d2phidxdy, std::vector< std::vector< OutputShape >> &d2phidxdz, std::vector< std::vector< OutputShape >> &d2phidy2, std::vector< std::vector< OutputShape >> &d2phidydz, std::vector< std::vector< OutputShape >> &d2phidz2) const =0
	Evaluates shape function Hessians in physical coordinates based on proper finite element transformation. More...

virtual void	map_curl (const unsigned int dim, const Elem *const elem, const std::vector< Point > &qp, const FEGenericBase< OutputShape > &fe, std::vector< std::vector< OutputShape >> &curl_phi) const =0
	Evaluates the shape function curl in physical coordinates based on proper finite element transformation. More...

virtual void	map_div (const unsigned int dim, const Elem *const elem, const std::vector< Point > &qp, const FEGenericBase< OutputShape > &fe, std::vector< std::vector< typename FEGenericBase< OutputShape >::OutputDivergence >> &div_phi) const =0
	Evaluates the shape function divergence in physical coordinates based on proper finite element transformation. More...

Static Public Member Functions
static std::unique_ptr< FETransformationBase< OutputShape > >	build (const FEType &type)
	Builds an FETransformation object based on the finite element type. More...

Detailed Description

template<typename OutputShape>
class libMesh::FETransformationBase< OutputShape >

This class handles the computation of the shape functions in the physical domain.

Derived classes implement the particular mapping: H1, HCurl, HDiv, or L2. This class assumes the FEGenericBase object has been initialized in the reference domain (i.e. init_shape_functions has been called).

Author: Paul T. Bauman

Date: 2012

Definition at line 54 of file fe_base.h.

Constructor & Destructor Documentation

◆ FETransformationBase()

template<typename OutputShape >

libMesh::FETransformationBase< OutputShape >::FETransformationBase ( )

default

◆ ~FETransformationBase()

template<typename OutputShape >

virtual libMesh::FETransformationBase< OutputShape >::~FETransformationBase ( )

virtualdefault

Member Function Documentation

◆ build()

template<typename OutputShape >

std::unique_ptr< FETransformationBase< OutputShape > > libMesh::FETransformationBase< OutputShape >::build ( const FEType & type )

static

Builds an FETransformation object based on the finite element type.

Definition at line 32 of file fe_transformation_base.C.

References libMesh::BERNSTEIN, libMesh::CLOUGH, libMesh::Utility::enum_to_string(), libMesh::FEType::family, libMesh::HERMITE, libMesh::HIERARCHIC, libMesh::HIERARCHIC_VEC, libMesh::JACOBI_20_00, libMesh::JACOBI_30_00, libMesh::L2_HIERARCHIC, libMesh::L2_HIERARCHIC_VEC, libMesh::L2_LAGRANGE, libMesh::L2_LAGRANGE_VEC, libMesh::L2_RAVIART_THOMAS, libMesh::LAGRANGE, libMesh::LAGRANGE_VEC, libMesh::MONOMIAL, libMesh::MONOMIAL_VEC, libMesh::NEDELEC_ONE, libMesh::RATIONAL_BERNSTEIN, libMesh::RAVIART_THOMAS, libMesh::SCALAR, libMesh::SIDE_HIERARCHIC, libMesh::SUBDIVISION, libMesh::SZABAB, and libMesh::XYZ.

 {
   switch (fe_type.family)
     {
       // H1 Conforming Elements
     case LAGRANGE:
     case HIERARCHIC:
     case BERNSTEIN:
     case SZABAB:
     case CLOUGH: // PB: Really H2
     case HERMITE: // PB: Really H2
     case SUBDIVISION:
     case LAGRANGE_VEC:
     case HIERARCHIC_VEC:
     case MONOMIAL: // PB: Shouldn't this be L2 conforming?
     case MONOMIAL_VEC: // PB: Shouldn't this be L2 conforming?
     case XYZ: // PB: Shouldn't this be L2 conforming?
     case RATIONAL_BERNSTEIN:
     case L2_HIERARCHIC:
     case L2_HIERARCHIC_VEC:
     case SIDE_HIERARCHIC:
     case L2_LAGRANGE: // PB: Shouldn't this be L2 conforming?
     case L2_LAGRANGE_VEC: // PB: Shouldn't this be L2 conforming?
     case JACOBI_20_00: // PB: For infinite elements...
     case JACOBI_30_00: // PB: For infinite elements...
       return std::make_unique<H1FETransformation<OutputShape>>();
 
       // HCurl Conforming Elements
     case NEDELEC_ONE:
       return std::make_unique<HCurlFETransformation<OutputShape>>();
 
       // HDiv Conforming Elements
     case RAVIART_THOMAS:
     case L2_RAVIART_THOMAS:
       return std::make_unique<HDivFETransformation<OutputShape>>();
 
       // L2 Conforming Elements
 
       // Other...
     case SCALAR:
       // Should never need this for SCALARs
       return std::make_unique<H1FETransformation<OutputShape>>();
 
     default:
       libmesh_error_msg("Unknown family = " << Utility::enum_to_string(fe_type.family));
     }
 }

◆ init_map_d2phi()

template<typename OutputShape >

virtual void libMesh::FETransformationBase< OutputShape >::init_map_d2phi ( const FEGenericBase< OutputShape > & fe ) const

pure virtual

Pre-requests any necessary data from FEMap.

Implemented in libMesh::H1FETransformation< OutputShape >, libMesh::HCurlFETransformation< OutputShape >, and libMesh::HDivFETransformation< OutputShape >.

◆ init_map_dphi()

template<typename OutputShape >

virtual void libMesh::FETransformationBase< OutputShape >::init_map_dphi ( const FEGenericBase< OutputShape > & fe ) const

pure virtual

Pre-requests any necessary data from FEMap.

Implemented in libMesh::H1FETransformation< OutputShape >, libMesh::HCurlFETransformation< OutputShape >, and libMesh::HDivFETransformation< OutputShape >.

◆ init_map_phi()

template<typename OutputShape >

virtual void libMesh::FETransformationBase< OutputShape >::init_map_phi ( const FEGenericBase< OutputShape > & fe ) const

pure virtual

Pre-requests any necessary data from FEMap.

Implemented in libMesh::H1FETransformation< OutputShape >, libMesh::HCurlFETransformation< OutputShape >, and libMesh::HDivFETransformation< OutputShape >.

◆ map_curl()

template<typename OutputShape >

virtual void libMesh::FETransformationBase< OutputShape >::map_curl	(	const unsigned int	dim,
		const Elem *const	elem,
		const std::vector< Point > &	qp,
		const FEGenericBase< OutputShape > &	fe,
		std::vector< std::vector< OutputShape >> &	curl_phi
	)		const

pure virtual

Evaluates the shape function curl in physical coordinates based on proper finite element transformation.

Implemented in libMesh::HCurlFETransformation< OutputShape >, libMesh::HDivFETransformation< OutputShape >, and libMesh::H1FETransformation< OutputShape >.

◆ map_d2phi()

template<typename OutputShape >

virtual void libMesh::FETransformationBase< OutputShape >::map_d2phi	(	const unsigned int	dim,
		const std::vector< Point > &	qp,
		const FEGenericBase< OutputShape > &	fe,
		std::vector< std::vector< typename FEGenericBase< OutputShape >::OutputTensor >> &	d2phi,
		std::vector< std::vector< OutputShape >> &	d2phidx2,
		std::vector< std::vector< OutputShape >> &	d2phidxdy,
		std::vector< std::vector< OutputShape >> &	d2phidxdz,
		std::vector< std::vector< OutputShape >> &	d2phidy2,
		std::vector< std::vector< OutputShape >> &	d2phidydz,
		std::vector< std::vector< OutputShape >> &	d2phidz2
	)		const

pure virtual

Evaluates shape function Hessians in physical coordinates based on proper finite element transformation.

Implemented in libMesh::HCurlFETransformation< OutputShape >, libMesh::HDivFETransformation< OutputShape >, and libMesh::H1FETransformation< OutputShape >.

◆ map_div()

template<typename OutputShape >

virtual void libMesh::FETransformationBase< OutputShape >::map_div	(	const unsigned int	dim,
		const Elem *const	elem,
		const std::vector< Point > &	qp,
		const FEGenericBase< OutputShape > &	fe,
		std::vector< std::vector< typename FEGenericBase< OutputShape >::OutputDivergence >> &	div_phi
	)		const

pure virtual

Evaluates the shape function divergence in physical coordinates based on proper finite element transformation.

Implemented in libMesh::HDivFETransformation< OutputShape >, libMesh::HCurlFETransformation< OutputShape >, and libMesh::H1FETransformation< OutputShape >.

◆ map_dphi()

template<typename OutputShape >

virtual void libMesh::FETransformationBase< OutputShape >::map_dphi	(	const unsigned int	dim,
		const Elem *const	elem,
		const std::vector< Point > &	qp,
		const FEGenericBase< OutputShape > &	fe,
		std::vector< std::vector< typename FEGenericBase< OutputShape >::OutputGradient >> &	dphi,
		std::vector< std::vector< OutputShape >> &	dphidx,
		std::vector< std::vector< OutputShape >> &	dphidy,
		std::vector< std::vector< OutputShape >> &	dphidz
	)		const

pure virtual

Evaluates shape function gradients in physical coordinates based on proper finite element transformation.

Implemented in libMesh::H1FETransformation< OutputShape >, libMesh::HCurlFETransformation< OutputShape >, and libMesh::HDivFETransformation< OutputShape >.

◆ map_phi()

template<typename OutputShape >

virtual void libMesh::FETransformationBase< OutputShape >::map_phi	(	const unsigned int	dim,
		const Elem *const	elem,
		const std::vector< Point > &	qp,
		const FEGenericBase< OutputShape > &	fe,
		std::vector< std::vector< OutputShape >> &	phi,
		bool	add_p_level = `true`
	)		const

pure virtual

Evaluates shape functions in physical coordinates based on proper finite element transformation.

Implemented in libMesh::H1FETransformation< OutputShape >, libMesh::HCurlFETransformation< OutputShape >, and libMesh::HDivFETransformation< OutputShape >.

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Member Functions

Detailed Description

template<typename OutputShape> class libMesh::FETransformationBase< OutputShape >

Constructor & Destructor Documentation

◆ FETransformationBase()

◆ ~FETransformationBase()

Member Function Documentation

◆ build()

◆ init_map_d2phi()

◆ init_map_dphi()

◆ init_map_phi()

◆ map_curl()

◆ map_d2phi()

◆ map_div()

◆ map_dphi()

◆ map_phi()

template<typename OutputShape>
class libMesh::FETransformationBase< OutputShape >