libMesh::FEMap Class Reference

Class contained in FE that encapsulates mapping (i.e. More...

#include <fe_map.h>

Inheritance diagram for libMesh::FEMap:

Public Member Functions
	FEMap (Real jtol=0)
virtual	~FEMap ()
template<unsigned int Dim>
void	init_reference_to_physical_map (const std::vector< Point > &qp, const Elem *elem)
void	compute_single_point_map (const unsigned int dim, const std::vector< Real > &qw, const Elem *elem, unsigned int p, const std::vector< const Node *> &elem_nodes, bool compute_second_derivatives)
	Compute the jacobian and some other additional data fields at the single point with index p. More...
virtual void	compute_affine_map (const unsigned int dim, const std::vector< Real > &qw, const Elem *elem)
	Compute the jacobian and some other additional data fields. More...
virtual void	compute_null_map (const unsigned int dim, const std::vector< Real > &qw)
	Assign a fake jacobian and some other additional data fields. More...
virtual void	compute_map (const unsigned int dim, const std::vector< Real > &qw, const Elem *elem, bool calculate_d2phi)
	Compute the jacobian and some other additional data fields. More...
virtual void	compute_face_map (int dim, const std::vector< Real > &qw, const Elem *side)
	Same as compute_map, but for a side. More...
void	compute_edge_map (int dim, const std::vector< Real > &qw, const Elem *side)
	Same as before, but for an edge. More...
template<unsigned int Dim>
void	init_face_shape_functions (const std::vector< Point > &qp, const Elem *side)
	Initializes the reference to physical element map for a side. More...
template<unsigned int Dim>
void	init_edge_shape_functions (const std::vector< Point > &qp, const Elem *edge)
	Same as before, but for an edge. More...
const std::vector< Point > &	get_xyz () const
const std::vector< Real > &	get_jacobian () const
const std::vector< Real > &	get_JxW () const
const std::vector< RealGradient > &	get_dxyzdxi () const
const std::vector< RealGradient > &	get_dxyzdeta () const
const std::vector< RealGradient > &	get_dxyzdzeta () const
const std::vector< RealGradient > &	get_d2xyzdxi2 () const
const std::vector< RealGradient > &	get_d2xyzdeta2 () const
const std::vector< RealGradient > &	get_d2xyzdzeta2 () const
const std::vector< RealGradient > &	get_d2xyzdxideta () const
const std::vector< RealGradient > &	get_d2xyzdxidzeta () const
const std::vector< RealGradient > &	get_d2xyzdetadzeta () const
const std::vector< Real > &	get_dxidx () const
const std::vector< Real > &	get_dxidy () const
const std::vector< Real > &	get_dxidz () const
const std::vector< Real > &	get_detadx () const
const std::vector< Real > &	get_detady () const
const std::vector< Real > &	get_detadz () const
const std::vector< Real > &	get_dzetadx () const
const std::vector< Real > &	get_dzetady () const
const std::vector< Real > &	get_dzetadz () const
const std::vector< std::vector< Real > > &	get_d2xidxyz2 () const
	Second derivatives of "xi" reference coordinate wrt physical coordinates. More...
const std::vector< std::vector< Real > > &	get_d2etadxyz2 () const
	Second derivatives of "eta" reference coordinate wrt physical coordinates. More...
const std::vector< std::vector< Real > > &	get_d2zetadxyz2 () const
	Second derivatives of "zeta" reference coordinate wrt physical coordinates. More...
const std::vector< std::vector< Real > > &	get_psi () const
const std::vector< std::vector< Real > > &	get_phi_map () const
const std::vector< std::vector< Real > > &	get_dphidxi_map () const
const std::vector< std::vector< Real > > &	get_dphideta_map () const
const std::vector< std::vector< Real > > &	get_dphidzeta_map () const
const std::vector< std::vector< Point > > &	get_tangents () const
const std::vector< Point > &	get_normals () const
const std::vector< Real > &	get_curvatures () const
void	print_JxW (std::ostream &os) const
	Prints the Jacobian times the weight for each quadrature point. More...
void	print_xyz (std::ostream &os) const
	Prints the spatial location of each quadrature point (on the physical element). More...
std::vector< std::vector< Real > > &	get_psi ()
std::vector< std::vector< Real > > &	get_dpsidxi ()
const std::vector< std::vector< Real > > &	get_dpsidxi () const
std::vector< std::vector< Real > > &	get_dpsideta ()
const std::vector< std::vector< Real > > &	get_dpsideta () const
std::vector< std::vector< Real > > &	get_d2psidxi2 ()
const std::vector< std::vector< Real > > &	get_d2psidxi2 () const
std::vector< std::vector< Real > > &	get_d2psidxideta ()
const std::vector< std::vector< Real > > &	get_d2psidxideta () const
std::vector< std::vector< Real > > &	get_d2psideta2 ()
const std::vector< std::vector< Real > > &	get_d2psideta2 () const
std::vector< std::vector< Real > > &	get_phi_map ()
std::vector< std::vector< Real > > &	get_dphidxi_map ()
std::vector< std::vector< Real > > &	get_dphideta_map ()
std::vector< std::vector< Real > > &	get_dphidzeta_map ()
std::vector< std::vector< Real > > &	get_d2phidxi2_map ()
std::vector< std::vector< Real > > &	get_d2phidxideta_map ()
std::vector< std::vector< Real > > &	get_d2phidxidzeta_map ()
std::vector< std::vector< Real > > &	get_d2phideta2_map ()
std::vector< std::vector< Real > > &	get_d2phidetadzeta_map ()
std::vector< std::vector< Real > > &	get_d2phidzeta2_map ()
std::vector< Real > &	get_JxW ()
void	set_jacobian_tolerance (Real tol)
	Set the Jacobian tolerance used for determining when the mapping fails. More...

Static Public Member Functions
static std::unique_ptr< FEMap >	build (FEType fe_type)

Protected Member Functions
void	determine_calculations ()
	Determine which values are to be calculated. More...
void	resize_quadrature_map_vectors (const unsigned int dim, unsigned int n_qp)
	A utility function for use by compute_*_map. More...
Real	dxdxi_map (const unsigned int p) const
	Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected. More...
Real	dydxi_map (const unsigned int p) const
	Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected. More...
Real	dzdxi_map (const unsigned int p) const
	Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected. More...
Real	dxdeta_map (const unsigned int p) const
	Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected. More...
Real	dydeta_map (const unsigned int p) const
	Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected. More...
Real	dzdeta_map (const unsigned int p) const
	Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected. More...
Real	dxdzeta_map (const unsigned int p) const
	Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected. More...
Real	dydzeta_map (const unsigned int p) const
	Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected. More...
Real	dzdzeta_map (const unsigned int p) const
	Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected. More...

Protected Attributes
std::vector< Point >	xyz
	The spatial locations of the quadrature points. More...
std::vector< RealGradient >	dxyzdxi_map
	Vector of partial derivatives: d(x)/d(xi), d(y)/d(xi), d(z)/d(xi) More...
std::vector< RealGradient >	dxyzdeta_map
	Vector of partial derivatives: d(x)/d(eta), d(y)/d(eta), d(z)/d(eta) More...
std::vector< RealGradient >	dxyzdzeta_map
	Vector of partial derivatives: d(x)/d(zeta), d(y)/d(zeta), d(z)/d(zeta) More...
std::vector< RealGradient >	d2xyzdxi2_map
	Vector of second partial derivatives in xi: d^2(x)/d(xi)^2, d^2(y)/d(xi)^2, d^2(z)/d(xi)^2. More...
std::vector< RealGradient >	d2xyzdxideta_map
	Vector of mixed second partial derivatives in xi-eta: d^2(x)/d(xi)d(eta) d^2(y)/d(xi)d(eta) d^2(z)/d(xi)d(eta) More...
std::vector< RealGradient >	d2xyzdeta2_map
	Vector of second partial derivatives in eta: d^2(x)/d(eta)^2. More...
std::vector< RealGradient >	d2xyzdxidzeta_map
	Vector of second partial derivatives in xi-zeta: d^2(x)/d(xi)d(zeta), d^2(y)/d(xi)d(zeta), d^2(z)/d(xi)d(zeta) More...
std::vector< RealGradient >	d2xyzdetadzeta_map
	Vector of mixed second partial derivatives in eta-zeta: d^2(x)/d(eta)d(zeta) d^2(y)/d(eta)d(zeta) d^2(z)/d(eta)d(zeta) More...
std::vector< RealGradient >	d2xyzdzeta2_map
	Vector of second partial derivatives in zeta: d^2(x)/d(zeta)^2. More...
std::vector< Real >	dxidx_map
	Map for partial derivatives: d(xi)/d(x). More...
std::vector< Real >	dxidy_map
	Map for partial derivatives: d(xi)/d(y). More...
std::vector< Real >	dxidz_map
	Map for partial derivatives: d(xi)/d(z). More...
std::vector< Real >	detadx_map
	Map for partial derivatives: d(eta)/d(x). More...
std::vector< Real >	detady_map
	Map for partial derivatives: d(eta)/d(y). More...
std::vector< Real >	detadz_map
	Map for partial derivatives: d(eta)/d(z). More...
std::vector< Real >	dzetadx_map
	Map for partial derivatives: d(zeta)/d(x). More...
std::vector< Real >	dzetady_map
	Map for partial derivatives: d(zeta)/d(y). More...
std::vector< Real >	dzetadz_map
	Map for partial derivatives: d(zeta)/d(z). More...
std::vector< std::vector< Real > >	d2xidxyz2_map
	Second derivatives of "xi" reference coordinate wrt physical coordinates. More...
std::vector< std::vector< Real > >	d2etadxyz2_map
	Second derivatives of "eta" reference coordinate wrt physical coordinates. More...
std::vector< std::vector< Real > >	d2zetadxyz2_map
	Second derivatives of "zeta" reference coordinate wrt physical coordinates. More...
std::vector< std::vector< Real > >	phi_map
	Map for the shape function phi. More...
std::vector< std::vector< Real > >	dphidxi_map
	Map for the derivative, d(phi)/d(xi). More...
std::vector< std::vector< Real > >	dphideta_map
	Map for the derivative, d(phi)/d(eta). More...
std::vector< std::vector< Real > >	dphidzeta_map
	Map for the derivative, d(phi)/d(zeta). More...
std::vector< std::vector< Real > >	d2phidxi2_map
	Map for the second derivative, d^2(phi)/d(xi)^2. More...
std::vector< std::vector< Real > >	d2phidxideta_map
	Map for the second derivative, d^2(phi)/d(xi)d(eta). More...
std::vector< std::vector< Real > >	d2phidxidzeta_map
	Map for the second derivative, d^2(phi)/d(xi)d(zeta). More...
std::vector< std::vector< Real > >	d2phideta2_map
	Map for the second derivative, d^2(phi)/d(eta)^2. More...
std::vector< std::vector< Real > >	d2phidetadzeta_map
	Map for the second derivative, d^2(phi)/d(eta)d(zeta). More...
std::vector< std::vector< Real > >	d2phidzeta2_map
	Map for the second derivative, d^2(phi)/d(zeta)^2. More...
std::vector< std::vector< Real > >	psi_map
	Map for the side shape functions, psi. More...
std::vector< std::vector< Real > >	dpsidxi_map
	Map for the derivative of the side functions, d(psi)/d(xi). More...
std::vector< std::vector< Real > >	dpsideta_map
	Map for the derivative of the side function, d(psi)/d(eta). More...
std::vector< std::vector< Real > >	d2psidxi2_map
	Map for the second derivatives (in xi) of the side shape functions. More...
std::vector< std::vector< Real > >	d2psidxideta_map
	Map for the second (cross) derivatives in xi, eta of the side shape functions. More...
std::vector< std::vector< Real > >	d2psideta2_map
	Map for the second derivatives (in eta) of the side shape functions. More...
std::vector< std::vector< Point > >	tangents
	Tangent vectors on boundary at quadrature points. More...
std::vector< Point >	normals
	Normal vectors on boundary at quadrature points. More...
std::vector< Real >	curvatures
	The mean curvature (= one half the sum of the principal curvatures) on the boundary at the quadrature points. More...
std::vector< Real >	jac
	Jacobian values at quadrature points. More...
std::vector< Real >	JxW
	Jacobian*Weight values at quadrature points. More...
bool	calculations_started
	Have calculations with this object already been started? Then all get_* functions should already have been called. More...
bool	calculate_xyz
	Should we calculate physical point locations? More...
bool	calculate_dxyz
	Should we calculate mapping gradients? More...
bool	calculate_d2xyz
	Should we calculate mapping hessians? More...
Real	jacobian_tolerance
	The Jacobian tolerance used for determining when the mapping fails. More...

Private Member Functions
void	compute_inverse_map_second_derivs (unsigned p)
	A helper function used by FEMap::compute_single_point_map() to compute second derivatives of the inverse map. More...

Private Attributes
std::vector< const Node * >	_elem_nodes
	Work vector for compute_affine_map() More...

Friends
template<unsigned int Dim, FEFamily T>
class	FE
	FE classes should be able to reset calculations_started in a few special cases. More...

Detailed Description

Class contained in FE that encapsulates mapping (i.e.

from physical space to reference space and vice-versa) quantities and operations.

Author

Paul Bauman

Date

2012 Computes finite element mapping function values, gradients, etc.

Definition at line 48 of file fe_map.h.

Constructor & Destructor Documentation

FEMap()

libMesh::FEMap::FEMap

(

Real

jtol = 0

)

~FEMap()

virtual libMesh::FEMap::~FEMap ( )

virtual

Definition at line 53 of file fe_map.h.

{}

Member Function Documentation

build()

static std::unique_ptr<FEMap> libMesh::FEMap::build ( FEType  fe_type )

static

compute_affine_map()

virtual void libMesh::FEMap::compute_affine_map ( const unsigned int  dim, const std::vector< Real > &  qw, const Elem *  elem  )

virtual

Compute the jacobian and some other additional data fields.

Takes the integration weights as input, along with a pointer to the element. The element is assumed to have a constant Jacobian

compute_edge_map()

void libMesh::FEMap::compute_edge_map	(	int	dim,
		const std::vector< Real > &	qw,
		const Elem *	side
	)

Same as before, but for an edge.

Useful for some projections.

compute_face_map()

virtual void libMesh::FEMap::compute_face_map ( int  dim, const std::vector< Real > &  qw, const Elem *  side  )

virtual

Same as compute_map, but for a side.

Useful for boundary integration.

Reimplemented in libMesh::FEXYZMap.

compute_inverse_map_second_derivs()

void libMesh::FEMap::compute_inverse_map_second_derivs ( unsigned  p )

private

A helper function used by FEMap::compute_single_point_map() to compute second derivatives of the inverse map.

compute_map()

virtual void libMesh::FEMap::compute_map ( const unsigned int  dim, const std::vector< Real > &  qw, const Elem *  elem, bool  calculate_d2phi  )

virtual

Compute the jacobian and some other additional data fields.

Takes the integration weights as input, along with a pointer to the element. Also takes a boolean parameter indicating whether second derivatives need to be calculated, allowing us to potentially skip unnecessary, expensive computations.

compute_null_map()

virtual void libMesh::FEMap::compute_null_map ( const unsigned int  dim, const std::vector< Real > &  qw  )

virtual

Assign a fake jacobian and some other additional data fields.

Takes the integration weights as input. For use on non-element evaluations.

compute_single_point_map()

void libMesh::FEMap::compute_single_point_map	(	const unsigned int	dim,
		const std::vector< Real > &	qw,
		const Elem *	elem,
		unsigned int	p,
		const std::vector< const Node *> &	elem_nodes,
		bool	compute_second_derivatives
	)

Compute the jacobian and some other additional data fields at the single point with index p.

Takes the integration weights as input, along with a pointer to the element and a list of points that contribute to the element. Also takes a boolean flag telling whether second derivatives should actually be computed.

determine_calculations()

void libMesh::FEMap::determine_calculations ( )

protected

Determine which values are to be calculated.

Definition at line 567 of file fe_map.h.

References calculate_d2xyz, calculate_dxyz, and calculations_started.

                                {
    calculations_started = true;

#ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
    // Second derivative calculations currently have first derivative
    // calculations as a prerequisite
    if (calculate_d2xyz)
      calculate_dxyz = true;
#endif
  }

dxdeta_map()

Real libMesh::FEMap::dxdeta_map ( const unsigned int  p ) const

protected

Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected.

Returns

The x value of the pth entry of the dxzydeta_map.

Definition at line 613 of file fe_map.h.

References dxyzdeta_map.

{ return dxyzdeta_map[p](0); }

dxdxi_map()

Real libMesh::FEMap::dxdxi_map ( const unsigned int  p ) const

protected

Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected.

Returns

The x value of the pth entry of the dxzydxi_map.

Definition at line 589 of file fe_map.h.

References dxyzdxi_map.

{ return dxyzdxi_map[p](0); }

dxdzeta_map()

Real libMesh::FEMap::dxdzeta_map ( const unsigned int  p ) const

protected

Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected.

Returns

The x value of the pth entry of the dxzydzeta_map.

Definition at line 637 of file fe_map.h.

References dxyzdzeta_map.

{ return dxyzdzeta_map[p](0); }

dydeta_map()

Real libMesh::FEMap::dydeta_map ( const unsigned int  p ) const

protected

Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected.

Returns

The y value of the pth entry of the dxzydeta_map.

Definition at line 621 of file fe_map.h.

References dxyzdeta_map.

{ return dxyzdeta_map[p](1); }

dydxi_map()

Real libMesh::FEMap::dydxi_map ( const unsigned int  p ) const

protected

Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected.

Returns

The y value of the pth entry of the dxzydxi_map.

Definition at line 597 of file fe_map.h.

References dxyzdxi_map.

{ return dxyzdxi_map[p](1); }

dydzeta_map()

Real libMesh::FEMap::dydzeta_map ( const unsigned int  p ) const

protected

Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected.

Returns

The y value of the pth entry of the dxzydzeta_map.

Definition at line 645 of file fe_map.h.

References dxyzdzeta_map.

{ return dxyzdzeta_map[p](1); }

dzdeta_map()

Real libMesh::FEMap::dzdeta_map ( const unsigned int  p ) const

protected

Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected.

Returns

The z value of the pth entry of the dxzydeta_map.

Definition at line 629 of file fe_map.h.

References dxyzdeta_map.

{ return dxyzdeta_map[p](2); }

dzdxi_map()

Real libMesh::FEMap::dzdxi_map ( const unsigned int  p ) const

protected

Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected.

Returns

The z value of the pth entry of the dxzydxi_map.

Definition at line 605 of file fe_map.h.

References dxyzdxi_map.

{ return dxyzdxi_map[p](2); }

dzdzeta_map()

Real libMesh::FEMap::dzdzeta_map ( const unsigned int  p ) const

protected

Used in FEMap::compute_map(), which should be be usable in derived classes, and therefore protected.

Returns

The z value of the pth entry of the dxzydzeta_map.

Definition at line 653 of file fe_map.h.

References dxyzdzeta_map.

{ return dxyzdzeta_map[p](2); }

get_curvatures()

const std::vector<Real>& libMesh::FEMap::get_curvatures

(

)

const

Returns

The curvatures for use in face integration.

Definition at line 378 of file fe_map.h.

References calculate_d2xyz, calculations_started, and curvatures.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return curvatures;}

get_d2etadxyz2()

const std::vector<std::vector<Real> >& libMesh::FEMap::get_d2etadxyz2

(

)

const

Second derivatives of "eta" reference coordinate wrt physical coordinates.

Definition at line 313 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2etadxyz2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2etadxyz2_map; }

get_d2phideta2_map()

std::vector<std::vector<Real> >& libMesh::FEMap::get_d2phideta2_map

(

)

Returns

The reference to physical map 2nd derivative

Definition at line 527 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2phideta2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2phideta2_map; }

get_d2phidetadzeta_map()

std::vector<std::vector<Real> >& libMesh::FEMap::get_d2phidetadzeta_map

(

)

Returns

The reference to physical map 2nd derivative

Definition at line 534 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2phidetadzeta_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2phidetadzeta_map; }

get_d2phidxi2_map()

std::vector<std::vector<Real> >& libMesh::FEMap::get_d2phidxi2_map

(

)

Returns

The reference to physical map 2nd derivative

Definition at line 506 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2phidxi2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2phidxi2_map; }

get_d2phidxideta_map()

std::vector<std::vector<Real> >& libMesh::FEMap::get_d2phidxideta_map

(

)

Returns

The reference to physical map 2nd derivative

Definition at line 513 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2phidxideta_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2phidxideta_map; }

get_d2phidxidzeta_map()

std::vector<std::vector<Real> >& libMesh::FEMap::get_d2phidxidzeta_map

(

)

Returns

The reference to physical map 2nd derivative

Definition at line 520 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2phidxidzeta_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2phidxidzeta_map; }

get_d2phidzeta2_map()

std::vector<std::vector<Real> >& libMesh::FEMap::get_d2phidzeta2_map

(

)

Returns

The reference to physical map 2nd derivative

Definition at line 541 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2phidzeta2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2phidzeta2_map; }

get_d2psideta2() [1/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_d2psideta2

(

)

Returns

The reference to physical map 2nd derivative for the side/edge

Definition at line 460 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2psideta2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2psideta2_map; }

get_d2psideta2() [2/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_d2psideta2

(

)

const

Returns

const reference to physical map 2nd derivative for the side/edge

Definition at line 468 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2psideta2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2psideta2_map; }

get_d2psidxi2() [1/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_d2psidxi2

(

)

Returns

The reference to physical map 2nd derivative for the side/edge

Definition at line 432 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2psidxi2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2psidxi2_map; }

get_d2psidxi2() [2/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_d2psidxi2

(

)

const

Returns

const reference to physical map 2nd derivative for the side/edge

Definition at line 439 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2psidxi2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2psidxi2_map; }

get_d2psidxideta() [1/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_d2psidxideta

(

)

Returns

The reference to physical map 2nd derivative for the side/edge

Definition at line 446 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2psidxideta_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2psidxideta_map; }

get_d2psidxideta() [2/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_d2psidxideta

(

)

const

Returns

const reference to physical map 2nd derivative for the side/edge

Definition at line 453 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2psidxideta_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2psidxideta_map; }

get_d2xidxyz2()

const std::vector<std::vector<Real> >& libMesh::FEMap::get_d2xidxyz2

(

)

const

Second derivatives of "xi" reference coordinate wrt physical coordinates.

Definition at line 306 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2xidxyz2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2xidxyz2_map; }

get_d2xyzdeta2()

const std::vector<RealGradient>& libMesh::FEMap::get_d2xyzdeta2

(

)

const

Returns

The second partial derivatives in eta.

Definition at line 196 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2xyzdeta2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2xyzdeta2_map; }

get_d2xyzdetadzeta()

const std::vector<RealGradient>& libMesh::FEMap::get_d2xyzdetadzeta

(

)

const

Returns

The second partial derivatives in eta-zeta.

Definition at line 224 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2xyzdetadzeta_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2xyzdetadzeta_map; }

get_d2xyzdxi2()

const std::vector<RealGradient>& libMesh::FEMap::get_d2xyzdxi2

(

)

const

Returns

The second partial derivatives in xi.

Definition at line 189 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2xyzdxi2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2xyzdxi2_map; }

get_d2xyzdxideta()

const std::vector<RealGradient>& libMesh::FEMap::get_d2xyzdxideta

(

)

const

Returns

The second partial derivatives in xi-eta.

Definition at line 210 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2xyzdxideta_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2xyzdxideta_map; }

get_d2xyzdxidzeta()

const std::vector<RealGradient>& libMesh::FEMap::get_d2xyzdxidzeta

(

)

const

Returns

The second partial derivatives in xi-zeta.

Definition at line 217 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2xyzdxidzeta_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2xyzdxidzeta_map; }

get_d2xyzdzeta2()

const std::vector<RealGradient>& libMesh::FEMap::get_d2xyzdzeta2

(

)

const

Returns

The second partial derivatives in zeta.

Definition at line 203 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2xyzdzeta2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2xyzdzeta2_map; }

get_d2zetadxyz2()

const std::vector<std::vector<Real> >& libMesh::FEMap::get_d2zetadxyz2

(

)

const

Second derivatives of "zeta" reference coordinate wrt physical coordinates.

Definition at line 320 of file fe_map.h.

References calculate_d2xyz, calculations_started, and d2zetadxyz2_map.

  { libmesh_assert(!calculations_started || calculate_d2xyz);
    calculate_d2xyz = true; return d2zetadxyz2_map; }

get_detadx()

const std::vector<Real>& libMesh::FEMap::get_detadx

(

)

const

Returns

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

Definition at line 258 of file fe_map.h.

References calculate_dxyz, calculations_started, and detadx_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return detadx_map; }

get_detady()

const std::vector<Real>& libMesh::FEMap::get_detady

(

)

const

Returns

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

Definition at line 266 of file fe_map.h.

References calculate_dxyz, calculations_started, and detady_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return detady_map; }

get_detadz()

const std::vector<Real>& libMesh::FEMap::get_detadz

(

)

const

Returns

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

Definition at line 274 of file fe_map.h.

References calculate_dxyz, calculations_started, and detadz_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return detadz_map; }

get_dphideta_map() [1/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_dphideta_map

(

)

const

Returns

The reference to physical map derivative

Definition at line 348 of file fe_map.h.

References calculate_dxyz, calculations_started, and dphideta_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dphideta_map; }

get_dphideta_map() [2/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_dphideta_map

(

)

Returns

The reference to physical map derivative

Definition at line 491 of file fe_map.h.

References calculate_dxyz, calculations_started, and dphideta_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dphideta_map; }

get_dphidxi_map() [1/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_dphidxi_map

(

)

const

Returns

The reference to physical map derivative

Definition at line 341 of file fe_map.h.

References calculate_dxyz, calculations_started, and dphidxi_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dphidxi_map; }

get_dphidxi_map() [2/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_dphidxi_map

(

)

Returns

The reference to physical map derivative

Definition at line 484 of file fe_map.h.

References calculate_dxyz, calculations_started, and dphidxi_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dphidxi_map; }

get_dphidzeta_map() [1/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_dphidzeta_map

(

)

const

Returns

The reference to physical map derivative

Definition at line 355 of file fe_map.h.

References calculate_dxyz, calculations_started, and dphidzeta_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dphidzeta_map; }

get_dphidzeta_map() [2/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_dphidzeta_map

(

)

Returns

The reference to physical map derivative

Definition at line 498 of file fe_map.h.

References calculate_dxyz, calculations_started, and dphidzeta_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dphidzeta_map; }

get_dpsideta() [1/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_dpsideta

(

)

Returns

The reference to physical map derivative for the side/edge

Definition at line 419 of file fe_map.h.

References calculate_dxyz, calculations_started, and dpsideta_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dpsideta_map; }

get_dpsideta() [2/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_dpsideta

(

)

const

Definition at line 423 of file fe_map.h.

References calculate_dxyz, calculations_started, and dpsideta_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dpsideta_map; }

get_dpsidxi() [1/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_dpsidxi

(

)

Returns

The reference to physical map derivative for the side/edge

Definition at line 408 of file fe_map.h.

References calculate_dxyz, calculations_started, and dpsidxi_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dpsidxi_map; }

get_dpsidxi() [2/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_dpsidxi

(

)

const

Definition at line 412 of file fe_map.h.

References calculate_dxyz, calculations_started, and dpsidxi_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dpsidxi_map; }

get_dxidx()

const std::vector<Real>& libMesh::FEMap::get_dxidx

(

)

const

Returns

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

Definition at line 234 of file fe_map.h.

References calculate_dxyz, calculations_started, and dxidx_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dxidx_map; }

get_dxidy()

const std::vector<Real>& libMesh::FEMap::get_dxidy

(

)

const

Returns

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

Definition at line 242 of file fe_map.h.

References calculate_dxyz, calculations_started, and dxidy_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dxidy_map; }

get_dxidz()

const std::vector<Real>& libMesh::FEMap::get_dxidz

(

)

const

Returns

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

Definition at line 250 of file fe_map.h.

References calculate_dxyz, calculations_started, and dxidz_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dxidz_map; }

get_dxyzdeta()

const std::vector<RealGradient>& libMesh::FEMap::get_dxyzdeta

(

)

const

Returns

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

Definition at line 172 of file fe_map.h.

References calculate_dxyz, calculations_started, and dxyzdeta_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dxyzdeta_map; }

get_dxyzdxi()

const std::vector<RealGradient>& libMesh::FEMap::get_dxyzdxi

(

)

const

Returns

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

Definition at line 164 of file fe_map.h.

References calculate_dxyz, calculations_started, and dxyzdxi_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dxyzdxi_map; }

get_dxyzdzeta()

const std::vector<RealGradient>& libMesh::FEMap::get_dxyzdzeta

(

)

const

Returns

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

Definition at line 180 of file fe_map.h.

References calculate_dxyz, calculations_started, and dxyzdzeta_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dxyzdzeta_map; }

get_dzetadx()

const std::vector<Real>& libMesh::FEMap::get_dzetadx

(

)

const

Returns

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

Definition at line 282 of file fe_map.h.

References calculate_dxyz, calculations_started, and dzetadx_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dzetadx_map; }

get_dzetady()

const std::vector<Real>& libMesh::FEMap::get_dzetady

(

)

const

Returns

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

Definition at line 290 of file fe_map.h.

References calculate_dxyz, calculations_started, and dzetady_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dzetady_map; }

get_dzetadz()

const std::vector<Real>& libMesh::FEMap::get_dzetadz

(

)

const

Returns

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

Definition at line 298 of file fe_map.h.

References calculate_dxyz, calculations_started, and dzetadz_map.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return dzetadz_map; }

get_jacobian()

const std::vector<Real>& libMesh::FEMap::get_jacobian

(

)

const

Returns

The element Jacobian for each quadrature point.

Definition at line 148 of file fe_map.h.

References calculate_dxyz, calculations_started, and jac.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return jac; }

get_JxW() [1/2]

const std::vector<Real>& libMesh::FEMap::get_JxW

(

)

const

Returns

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

Definition at line 156 of file fe_map.h.

References calculate_dxyz, calculations_started, and JxW.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return JxW; }

get_JxW() [2/2]

std::vector<Real>& libMesh::FEMap::get_JxW

(

)

Returns

Writable reference to the element Jacobian times the quadrature weight for each quadrature point.

Definition at line 552 of file fe_map.h.

References calculate_dxyz, calculations_started, and JxW.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return JxW; }

get_normals()

const std::vector<Point>& libMesh::FEMap::get_normals

(

)

const

Returns

The outward pointing normal vectors for face integration.

Definition at line 369 of file fe_map.h.

References calculate_dxyz, calculations_started, and normals.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return normals; }

get_phi_map() [1/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_phi_map

(

)

const

Returns

The reference to physical map for the element

Definition at line 334 of file fe_map.h.

References calculate_xyz, calculations_started, and phi_map.

  { libmesh_assert(!calculations_started || calculate_xyz);
    calculate_xyz = true; return phi_map; }

get_phi_map() [2/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_phi_map

(

)

Returns

The reference to physical map for the element

Definition at line 477 of file fe_map.h.

References calculate_xyz, calculations_started, and phi_map.

  { libmesh_assert(!calculations_started || calculate_xyz);
    calculate_xyz = true; return phi_map; }

get_psi() [1/2]

const std::vector<std::vector<Real> >& libMesh::FEMap::get_psi

(

)

const

Returns

The reference to physical map for the side/edge

Definition at line 328 of file fe_map.h.

References psi_map.

  { return psi_map; }

get_psi() [2/2]

std::vector<std::vector<Real> >& libMesh::FEMap::get_psi

(

)

Returns

The reference to physical map for the side/edge

Definition at line 402 of file fe_map.h.

References psi_map.

  { return psi_map; }

get_tangents()

const std::vector<std::vector<Point> >& libMesh::FEMap::get_tangents

(

)

const

Returns

The tangent vectors for face integration.

Definition at line 362 of file fe_map.h.

References calculate_dxyz, calculations_started, and tangents.

  { libmesh_assert(!calculations_started || calculate_dxyz);
    calculate_dxyz = true; return tangents; }

get_xyz()

const std::vector<Point>& libMesh::FEMap::get_xyz

(

)

const

Returns

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

Definition at line 141 of file fe_map.h.

References calculate_xyz, calculations_started, and xyz.

  { libmesh_assert(!calculations_started || calculate_xyz);
    calculate_xyz = true; return xyz; }

init_edge_shape_functions()

template<unsigned int Dim>

void libMesh::FEMap::init_edge_shape_functions	(	const std::vector< Point > &	qp,
		const Elem *	edge
	)

Same as before, but for an edge.

This is used for some projection operators.

init_face_shape_functions()

template<unsigned int Dim>

void libMesh::FEMap::init_face_shape_functions	(	const std::vector< Point > &	qp,
		const Elem *	side
	)

Initializes the reference to physical element map for a side.

This is used for boundary integration.

init_reference_to_physical_map()

template<unsigned int Dim>

void libMesh::FEMap::init_reference_to_physical_map	(	const std::vector< Point > &	qp,
		const Elem *	elem
	)

print_JxW()

void libMesh::FEMap::print_JxW

(

std::ostream &

os

)

const

Prints the Jacobian times the weight for each quadrature point.

print_xyz()

void libMesh::FEMap::print_xyz

(

std::ostream &

os

)

const

Prints the spatial location of each quadrature point (on the physical element).

resize_quadrature_map_vectors()

void libMesh::FEMap::resize_quadrature_map_vectors ( const unsigned int  dim, unsigned int  n_qp  )

protected

A utility function for use by compute_*_map.

set_jacobian_tolerance()

void libMesh::FEMap::set_jacobian_tolerance

(

Real

tol

)

Set the Jacobian tolerance used for determining when the mapping fails.

The mapping is determined to fail if jac <= jacobian_tolerance.

Definition at line 560 of file fe_map.h.

References jacobian_tolerance.

{ jacobian_tolerance = tol; }

Friends And Related Function Documentation

FE

template<unsigned int Dim, FEFamily T>

friend class FE

friend

FE classes should be able to reset calculations_started in a few special cases.

Definition at line 950 of file fe_map.h.

Member Data Documentation

_elem_nodes

std::vector<const Node *> libMesh::FEMap::_elem_nodes

private

Work vector for compute_affine_map()

Definition at line 969 of file fe_map.h.

calculate_d2xyz

bool libMesh::FEMap::calculate_d2xyz

mutableprotected

Should we calculate mapping hessians?

Definition at line 941 of file fe_map.h.

Referenced by determine_calculations(), get_curvatures(), get_d2etadxyz2(), get_d2phideta2_map(), get_d2phidetadzeta_map(), get_d2phidxi2_map(), get_d2phidxideta_map(), get_d2phidxidzeta_map(), get_d2phidzeta2_map(), get_d2psideta2(), get_d2psidxi2(), get_d2psidxideta(), get_d2xidxyz2(), get_d2xyzdeta2(), get_d2xyzdetadzeta(), get_d2xyzdxi2(), get_d2xyzdxideta(), get_d2xyzdxidzeta(), get_d2xyzdzeta2(), and get_d2zetadxyz2().

calculate_dxyz

bool libMesh::FEMap::calculate_dxyz

mutableprotected

Should we calculate mapping gradients?

Definition at line 934 of file fe_map.h.

Referenced by determine_calculations(), get_detadx(), get_detady(), get_detadz(), get_dphideta_map(), get_dphidxi_map(), get_dphidzeta_map(), get_dpsideta(), get_dpsidxi(), get_dxidx(), get_dxidy(), get_dxidz(), get_dxyzdeta(), get_dxyzdxi(), get_dxyzdzeta(), get_dzetadx(), get_dzetady(), get_dzetadz(), get_jacobian(), get_JxW(), get_normals(), and get_tangents().

calculate_xyz

bool libMesh::FEMap::calculate_xyz

mutableprotected

Should we calculate physical point locations?

Definition at line 929 of file fe_map.h.

Referenced by libMesh::FEXYZMap::FEXYZMap(), get_phi_map(), and get_xyz().

calculations_started

bool libMesh::FEMap::calculations_started

mutableprotected

Have calculations with this object already been started? Then all get_* functions should already have been called.

Definition at line 924 of file fe_map.h.

Referenced by determine_calculations(), get_curvatures(), get_d2etadxyz2(), get_d2phideta2_map(), get_d2phidetadzeta_map(), get_d2phidxi2_map(), get_d2phidxideta_map(), get_d2phidxidzeta_map(), get_d2phidzeta2_map(), get_d2psideta2(), get_d2psidxi2(), get_d2psidxideta(), get_d2xidxyz2(), get_d2xyzdeta2(), get_d2xyzdetadzeta(), get_d2xyzdxi2(), get_d2xyzdxideta(), get_d2xyzdxidzeta(), get_d2xyzdzeta2(), get_d2zetadxyz2(), get_detadx(), get_detady(), get_detadz(), get_dphideta_map(), get_dphidxi_map(), get_dphidzeta_map(), get_dpsideta(), get_dpsidxi(), get_dxidx(), get_dxidy(), get_dxidz(), get_dxyzdeta(), get_dxyzdxi(), get_dxyzdzeta(), get_dzetadx(), get_dzetady(), get_dzetadz(), get_jacobian(), get_JxW(), get_normals(), get_phi_map(), get_tangents(), and get_xyz().

curvatures

std::vector<Real> libMesh::FEMap::curvatures

protected

The mean curvature (= one half the sum of the principal curvatures) on the boundary at the quadrature points.

The mean curvature is a scalar value.

Definition at line 906 of file fe_map.h.

Referenced by get_curvatures().

d2etadxyz2_map

std::vector<std::vector<Real> > libMesh::FEMap::d2etadxyz2_map

protected

Second derivatives of "eta" reference coordinate wrt physical coordinates.

At each qp: (eta_{xx}, eta_{xy}, eta_{xz}, eta_{yy}, eta_{yz}, eta_{zz})

Definition at line 785 of file fe_map.h.

Referenced by get_d2etadxyz2().

d2phideta2_map

std::vector<std::vector<Real> > libMesh::FEMap::d2phideta2_map

protected

Map for the second derivative, d^2(phi)/d(eta)^2.

Definition at line 834 of file fe_map.h.

Referenced by get_d2phideta2_map().

d2phidetadzeta_map

std::vector<std::vector<Real> > libMesh::FEMap::d2phidetadzeta_map

protected

Map for the second derivative, d^2(phi)/d(eta)d(zeta).

Definition at line 839 of file fe_map.h.

Referenced by get_d2phidetadzeta_map().

d2phidxi2_map

std::vector<std::vector<Real> > libMesh::FEMap::d2phidxi2_map

protected

Map for the second derivative, d^2(phi)/d(xi)^2.

Definition at line 819 of file fe_map.h.

Referenced by get_d2phidxi2_map().

d2phidxideta_map

std::vector<std::vector<Real> > libMesh::FEMap::d2phidxideta_map

protected

Map for the second derivative, d^2(phi)/d(xi)d(eta).

Definition at line 824 of file fe_map.h.

Referenced by get_d2phidxideta_map().

d2phidxidzeta_map

std::vector<std::vector<Real> > libMesh::FEMap::d2phidxidzeta_map

protected

Map for the second derivative, d^2(phi)/d(xi)d(zeta).

Definition at line 829 of file fe_map.h.

Referenced by get_d2phidxidzeta_map().

d2phidzeta2_map

std::vector<std::vector<Real> > libMesh::FEMap::d2phidzeta2_map

protected

Map for the second derivative, d^2(phi)/d(zeta)^2.

Definition at line 844 of file fe_map.h.

Referenced by get_d2phidzeta2_map().

d2psideta2_map

std::vector<std::vector<Real> > libMesh::FEMap::d2psideta2_map

protected

Map for the second derivatives (in eta) of the side shape functions.

Useful for computing the curvature at the quadrature points.

Definition at line 886 of file fe_map.h.

Referenced by get_d2psideta2().

d2psidxi2_map

std::vector<std::vector<Real> > libMesh::FEMap::d2psidxi2_map

protected

Map for the second derivatives (in xi) of the side shape functions.

Useful for computing the curvature at the quadrature points.

Definition at line 872 of file fe_map.h.

Referenced by get_d2psidxi2().

d2psidxideta_map

std::vector<std::vector<Real> > libMesh::FEMap::d2psidxideta_map

protected

Map for the second (cross) derivatives in xi, eta of the side shape functions.

Useful for computing the curvature at the quadrature points.

Definition at line 879 of file fe_map.h.

Referenced by get_d2psidxideta().

d2xidxyz2_map

std::vector<std::vector<Real> > libMesh::FEMap::d2xidxyz2_map

protected

Second derivatives of "xi" reference coordinate wrt physical coordinates.

At each qp: (xi_{xx}, xi_{xy}, xi_{xz}, xi_{yy}, xi_{yz}, xi_{zz})

Definition at line 779 of file fe_map.h.

Referenced by get_d2xidxyz2().

d2xyzdeta2_map

std::vector<RealGradient> libMesh::FEMap::d2xyzdeta2_map

protected

Vector of second partial derivatives in eta: d^2(x)/d(eta)^2.

Definition at line 696 of file fe_map.h.

Referenced by get_d2xyzdeta2().

d2xyzdetadzeta_map

std::vector<RealGradient> libMesh::FEMap::d2xyzdetadzeta_map

protected

Vector of mixed second partial derivatives in eta-zeta: d^2(x)/d(eta)d(zeta) d^2(y)/d(eta)d(zeta) d^2(z)/d(eta)d(zeta)

Definition at line 708 of file fe_map.h.

Referenced by get_d2xyzdetadzeta().

d2xyzdxi2_map

std::vector<RealGradient> libMesh::FEMap::d2xyzdxi2_map

protected

Vector of second partial derivatives in xi: d^2(x)/d(xi)^2, d^2(y)/d(xi)^2, d^2(z)/d(xi)^2.

Definition at line 684 of file fe_map.h.

Referenced by get_d2xyzdxi2().

d2xyzdxideta_map

std::vector<RealGradient> libMesh::FEMap::d2xyzdxideta_map

protected

Vector of mixed second partial derivatives in xi-eta: d^2(x)/d(xi)d(eta) d^2(y)/d(xi)d(eta) d^2(z)/d(xi)d(eta)

Definition at line 690 of file fe_map.h.

Referenced by get_d2xyzdxideta().

d2xyzdxidzeta_map

std::vector<RealGradient> libMesh::FEMap::d2xyzdxidzeta_map

protected

Vector of second partial derivatives in xi-zeta: d^2(x)/d(xi)d(zeta), d^2(y)/d(xi)d(zeta), d^2(z)/d(xi)d(zeta)

Definition at line 702 of file fe_map.h.

Referenced by get_d2xyzdxidzeta().

d2xyzdzeta2_map

std::vector<RealGradient> libMesh::FEMap::d2xyzdzeta2_map

protected

Vector of second partial derivatives in zeta: d^2(x)/d(zeta)^2.

Definition at line 714 of file fe_map.h.

Referenced by get_d2xyzdzeta2().

d2zetadxyz2_map

std::vector<std::vector<Real> > libMesh::FEMap::d2zetadxyz2_map

protected

Second derivatives of "zeta" reference coordinate wrt physical coordinates.

At each qp: (zeta_{xx}, zeta_{xy}, zeta_{xz}, zeta_{yy}, zeta_{yz}, zeta_{zz})

Definition at line 791 of file fe_map.h.

Referenced by get_d2zetadxyz2().

detadx_map

std::vector<Real> libMesh::FEMap::detadx_map

protected

Map for partial derivatives: d(eta)/d(x).

Needed for the Jacobian.

Definition at line 741 of file fe_map.h.

Referenced by get_detadx().

detady_map

std::vector<Real> libMesh::FEMap::detady_map

protected

Map for partial derivatives: d(eta)/d(y).

Needed for the Jacobian.

Definition at line 747 of file fe_map.h.

Referenced by get_detady().

detadz_map

std::vector<Real> libMesh::FEMap::detadz_map

protected

Map for partial derivatives: d(eta)/d(z).

Needed for the Jacobian.

Definition at line 753 of file fe_map.h.

Referenced by get_detadz().

dphideta_map

std::vector<std::vector<Real> > libMesh::FEMap::dphideta_map

protected

Map for the derivative, d(phi)/d(eta).

Definition at line 807 of file fe_map.h.

Referenced by get_dphideta_map().

dphidxi_map

std::vector<std::vector<Real> > libMesh::FEMap::dphidxi_map

protected

Map for the derivative, d(phi)/d(xi).

Definition at line 802 of file fe_map.h.

Referenced by get_dphidxi_map().

dphidzeta_map

std::vector<std::vector<Real> > libMesh::FEMap::dphidzeta_map

protected

Map for the derivative, d(phi)/d(zeta).

Definition at line 812 of file fe_map.h.

Referenced by get_dphidzeta_map().

dpsideta_map

std::vector<std::vector<Real> > libMesh::FEMap::dpsideta_map

protected

Map for the derivative of the side function, d(psi)/d(eta).

Definition at line 863 of file fe_map.h.

Referenced by get_dpsideta().

dpsidxi_map

std::vector<std::vector<Real> > libMesh::FEMap::dpsidxi_map

protected

Map for the derivative of the side functions, d(psi)/d(xi).

Definition at line 857 of file fe_map.h.

Referenced by get_dpsidxi().

dxidx_map

std::vector<Real> libMesh::FEMap::dxidx_map

protected

Map for partial derivatives: d(xi)/d(x).

Needed for the Jacobian.

Definition at line 722 of file fe_map.h.

Referenced by get_dxidx().

dxidy_map

std::vector<Real> libMesh::FEMap::dxidy_map

protected

Map for partial derivatives: d(xi)/d(y).

Needed for the Jacobian.

Definition at line 728 of file fe_map.h.

Referenced by get_dxidy().

dxidz_map

std::vector<Real> libMesh::FEMap::dxidz_map

protected

Map for partial derivatives: d(xi)/d(z).

Needed for the Jacobian.

Definition at line 734 of file fe_map.h.

Referenced by get_dxidz().

dxyzdeta_map

std::vector<RealGradient> libMesh::FEMap::dxyzdeta_map

protected

Vector of partial derivatives: d(x)/d(eta), d(y)/d(eta), d(z)/d(eta)

Definition at line 670 of file fe_map.h.

Referenced by dxdeta_map(), dydeta_map(), dzdeta_map(), and get_dxyzdeta().

dxyzdxi_map

std::vector<RealGradient> libMesh::FEMap::dxyzdxi_map

protected

Vector of partial derivatives: d(x)/d(xi), d(y)/d(xi), d(z)/d(xi)

Definition at line 664 of file fe_map.h.

Referenced by dxdxi_map(), dydxi_map(), dzdxi_map(), and get_dxyzdxi().

dxyzdzeta_map

std::vector<RealGradient> libMesh::FEMap::dxyzdzeta_map

protected

Vector of partial derivatives: d(x)/d(zeta), d(y)/d(zeta), d(z)/d(zeta)

Definition at line 676 of file fe_map.h.

Referenced by dxdzeta_map(), dydzeta_map(), dzdzeta_map(), and get_dxyzdzeta().

dzetadx_map

std::vector<Real> libMesh::FEMap::dzetadx_map

protected

Map for partial derivatives: d(zeta)/d(x).

Needed for the Jacobian.

Definition at line 760 of file fe_map.h.

Referenced by get_dzetadx().

dzetady_map

std::vector<Real> libMesh::FEMap::dzetady_map

protected

Map for partial derivatives: d(zeta)/d(y).

Needed for the Jacobian.

Definition at line 766 of file fe_map.h.

Referenced by get_dzetady().

dzetadz_map

std::vector<Real> libMesh::FEMap::dzetadz_map

protected

Map for partial derivatives: d(zeta)/d(z).

Needed for the Jacobian.

Definition at line 772 of file fe_map.h.

Referenced by get_dzetadz().

jac

std::vector<Real> libMesh::FEMap::jac

protected

Jacobian values at quadrature points.

Definition at line 913 of file fe_map.h.

Referenced by get_jacobian().

jacobian_tolerance

Real libMesh::FEMap::jacobian_tolerance

protected

The Jacobian tolerance used for determining when the mapping fails.

The mapping is determined to fail if jac <= jacobian_tolerance. If not set by the user, this number defaults to 0

Definition at line 957 of file fe_map.h.

Referenced by set_jacobian_tolerance().

JxW

std::vector<Real> libMesh::FEMap::JxW

protected

Jacobian*Weight values at quadrature points.

Definition at line 918 of file fe_map.h.

Referenced by get_JxW().

normals

std::vector<Point> libMesh::FEMap::normals

protected

Normal vectors on boundary at quadrature points.

Definition at line 898 of file fe_map.h.

Referenced by get_normals().

phi_map

std::vector<std::vector<Real> > libMesh::FEMap::phi_map

protected

Map for the shape function phi.

Definition at line 797 of file fe_map.h.

Referenced by get_phi_map().

psi_map

std::vector<std::vector<Real> > libMesh::FEMap::psi_map

protected

Map for the side shape functions, psi.

Definition at line 851 of file fe_map.h.

Referenced by get_psi().

tangents

std::vector<std::vector<Point> > libMesh::FEMap::tangents

protected

Tangent vectors on boundary at quadrature points.

Definition at line 893 of file fe_map.h.

Referenced by get_tangents().

xyz

std::vector<Point> libMesh::FEMap::xyz

protected

The spatial locations of the quadrature points.

Definition at line 658 of file fe_map.h.

Referenced by get_xyz().

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

• include/fe/fe_map.h