Abstract class for Finite Elements. More...

#include <fe.hpp>

Inheritance diagram for mfem::FiniteElement:

Collaboration diagram for mfem::FiniteElement:

Public Types
enum	{ SCALAR, VECTOR }
	Enumeration for RangeType. More...

enum	{ VALUE, INTEGRAL, H_DIV, H_CURL }

Public Member Functions
	FiniteElement (int D, int G, int Do, int O, int F=FunctionSpace::Pk)

int	GetDim () const
	Returns the space dimension for the finite element. More...

int	GetGeomType () const
	Returns the geometry type: More...

int	GetDof () const
	Returns the degrees of freedom in the FE space. More...

int	GetOrder () const
	Returns the order of the finite element. More...

int	Space () const
	Returns the type of space on each element. More...

int	GetRangeType () const

int	GetMapType () const

virtual void	CalcShape (const IntegrationPoint &ip, Vector &shape) const =0

virtual void	CalcDShape (const IntegrationPoint &ip, DenseMatrix &dshape) const =0

const IntegrationRule &	GetNodes () const

virtual void	CalcVShape (const IntegrationPoint &ip, DenseMatrix &shape) const

virtual void	CalcVShape (ElementTransformation &Trans, DenseMatrix &shape) const

virtual void	CalcDivShape (const IntegrationPoint &ip, Vector &divshape) const

virtual void	CalcCurlShape (const IntegrationPoint &ip, DenseMatrix &curl_shape) const

virtual void	GetFaceDofs (int face, int *dofs, int ndofs) const

virtual void	CalcHessian (const IntegrationPoint &ip, DenseMatrix &h) const

virtual void	GetLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I) const

virtual void	Project (Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const

virtual void	Project (VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const

virtual void	ProjectDelta (int vertex, Vector &dofs) const

virtual void	Project (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const

virtual void	ProjectGrad (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const

virtual void	ProjectCurl (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const

virtual void	ProjectDiv (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const

virtual	~FiniteElement ()

Protected Attributes
int	Dim

int	GeomType

int	Dof

int	Order

int	FuncSpace

int	RangeType

int	MapType

IntegrationRule	Nodes

Detailed Description

Abstract class for Finite Elements.

Definition at line 44 of file fe.hpp.

Member Enumeration Documentation

anonymous enum

Enumeration for RangeType.

Enumerator
SCALAR
VECTOR

Definition at line 52 of file fe.hpp.

anonymous enum

Enumeration for MapType: defines how reference functions, uh(xh), are mapped to functions on a general element, u(x):

VALUE u(x) = uh(xh) INTEGRAL u(x) = (1/w) * uh(xh) H_DIV u(x) = (J/w) * uh(xh) H_CURL u(x) = J^{-t} * uh(xh) (square J) H_CURL u(x) = J*(J^t*J)^{-1} * uh(xh) (general J)

where

x = T(xh) is the image of the reference point xh ("x hat"), J = J(xh) is the Jacobian matrix of the transformation T, and w = w(xh) = / det(J), for square J, . \ det(J^t*J)^{1/2}, for general J, is the transformation weight factor.

Enumerator
VALUE
INTEGRAL
H_DIV
H_CURL

Definition at line 71 of file fe.hpp.

Constructor & Destructor Documentation

mfem::FiniteElement::FiniteElement	(	int	D,
		int	G,
		int	Do,
		int	O,
		int	F = `FunctionSpace::Pk`
	)

Construct Finite Element with given (D)im - space dimension, (G)eomType - geometry type (of type Geometry::Type), (Do)f - degrees of freedom in the FE space, and (O)rder - order of the FE space (F)uncSpace- type of space on each element

Definition at line 22 of file fe.cpp.

virtual mfem::FiniteElement::~FiniteElement ( )

inlinevirtual

Definition at line 196 of file fe.hpp.

Member Function Documentation

void mfem::FiniteElement::CalcCurlShape	(	const IntegrationPoint &	ip,
		DenseMatrix &	curl_shape
	)		const

virtual

pure virtual function which evaluates the values of the curl all shape functions at a given point ip and stores them in the matrix curl_shape (Dof x Dim) so that each row contains the curl of one shape function

Reimplemented in mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::Nedelec1TetFiniteElement, and mfem::Nedelec1HexFiniteElement.

Definition at line 51 of file fe.cpp.

void mfem::FiniteElement::CalcDivShape	(	const IntegrationPoint &	ip,
		Vector &	divshape
	)		const

virtual

This virtual function evaluates the divergence of all shape functions at the given IntegrationPoint. The result is stored in the Vector divshape (of size Dof).

Reimplemented in mfem::RT_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, mfem::RT0TetFiniteElement, mfem::RT1HexFiniteElement, mfem::RT0HexFiniteElement, mfem::RT2QuadFiniteElement, mfem::RT2TriangleFiniteElement, mfem::RT1QuadFiniteElement, mfem::RT1TriangleFiniteElement, mfem::RT0QuadFiniteElement, and mfem::RT0TriangleFiniteElement.

Definition at line 44 of file fe.cpp.

virtual void mfem::FiniteElement::CalcDShape	(	const IntegrationPoint &	ip,
		DenseMatrix &	dshape
	)		const

pure virtual

pure virtual function which evaluates the values of all partial derivatives of all shape functions at a given point ip and stores them in the matrix dshape (Dof x Dim) so that each row contains the derivatives of one shape function

void mfem::FiniteElement::CalcHessian	(	const IntegrationPoint &	ip,
		DenseMatrix &	h
	)		const

virtual

each row of h contains the upper triangular part of the hessian of one shape function; the order in 2D is {u_xx, u_xy, u_yy}

Reimplemented in mfem::Cubic2DFiniteElement, mfem::BiCubic2DFiniteElement, mfem::Quad2DFiniteElement, and mfem::BiLinear2DFiniteElement.

Definition at line 63 of file fe.cpp.

virtual void mfem::FiniteElement::CalcShape	(	const IntegrationPoint &	ip,
		Vector &	shape
	)		const

pure virtual

pure virtual function which evaluates the values of all shape functions at a given point ip and stores them in the vector shape of dimension Dof

void mfem::FiniteElement::CalcVShape	(	const IntegrationPoint &	ip,
		DenseMatrix &	shape
	)		const

virtual

This virtual function evaluates the values of all components of all shape functions at the given IntegrationPoint. The result is stored in the DenseMatrix shape (Dof x Dim) so that each row contains the components of one shape function.

Definition at line 30 of file fe.cpp.

void mfem::FiniteElement::CalcVShape	(	ElementTransformation &	Trans,
		DenseMatrix &	shape
	)		const

virtual

int mfem::FiniteElement::GetDim ( ) const

inline

Returns the space dimension for the finite element.

Definition at line 82 of file fe.hpp.

int mfem::FiniteElement::GetDof ( ) const

inline

Returns the degrees of freedom in the FE space.

Definition at line 88 of file fe.hpp.

void mfem::FiniteElement::GetFaceDofs	(	int	face,
		int **	dofs,
		int *	ndofs
	)		const

virtual

Reimplemented in mfem::Linear3DFiniteElement.

Definition at line 58 of file fe.cpp.

int mfem::FiniteElement::GetGeomType ( ) const

inline

Returns the geometry type:

Definition at line 85 of file fe.hpp.

void mfem::FiniteElement::GetLocalInterpolation	(	ElementTransformation &	Trans,
		DenseMatrix &	I
	)		const

virtual

Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base geometry under the given transformation.

Reimplemented in mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::RT_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, mfem::RT0TetFiniteElement, mfem::RT1HexFiniteElement, mfem::RT0HexFiniteElement, mfem::Nedelec1TetFiniteElement, mfem::Nedelec1HexFiniteElement, mfem::RT2QuadFiniteElement, mfem::RT1QuadFiniteElement, mfem::RT1TriangleFiniteElement, mfem::RT0QuadFiniteElement, mfem::RT0TriangleFiniteElement, mfem::BiQuadPos2DFiniteElement, and mfem::NodalFiniteElement.

Definition at line 69 of file fe.cpp.

int mfem::FiniteElement::GetMapType ( ) const

inline

Definition at line 98 of file fe.hpp.

const IntegrationRule& mfem::FiniteElement::GetNodes ( ) const

inline

Definition at line 113 of file fe.hpp.

int mfem::FiniteElement::GetOrder ( ) const

inline

Returns the order of the finite element.

Definition at line 91 of file fe.hpp.

int mfem::FiniteElement::GetRangeType ( ) const

inline

Definition at line 96 of file fe.hpp.

void mfem::FiniteElement::Project	(	Coefficient &	coeff,
		ElementTransformation &	Trans,
		Vector &	dofs
	)		const

virtual

Given a coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom.

Reimplemented in mfem::BiQuadPos2DFiniteElement, mfem::PositiveFiniteElement, and mfem::NodalFiniteElement.

Definition at line 75 of file fe.cpp.

void mfem::FiniteElement::Project	(	VectorCoefficient &	vc,
		ElementTransformation &	Trans,
		Vector &	dofs
	)		const

virtual

Given a vector coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. (VectorFiniteElements)

Reimplemented in mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::RT_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, mfem::RT0TetFiniteElement, mfem::RT1HexFiniteElement, mfem::RT0HexFiniteElement, mfem::Nedelec1TetFiniteElement, mfem::Nedelec1HexFiniteElement, mfem::RT2QuadFiniteElement, mfem::RT1QuadFiniteElement, mfem::RT1TriangleFiniteElement, mfem::RT0QuadFiniteElement, mfem::RT0TriangleFiniteElement, mfem::BiQuadPos2DFiniteElement, and mfem::NodalFiniteElement.

Definition at line 81 of file fe.cpp.

void mfem::FiniteElement::Project	(	const FiniteElement &	fe,
		ElementTransformation &	Trans,
		DenseMatrix &	I
	)		const

virtual

Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the projection depends on it.

Reimplemented in mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::RT_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, mfem::PositiveFiniteElement, and mfem::NodalFiniteElement.

Definition at line 93 of file fe.cpp.

void mfem::FiniteElement::ProjectCurl	(	const FiniteElement &	fe,
		ElementTransformation &	Trans,
		DenseMatrix &	curl
	)		const

virtual

Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.

Reimplemented in mfem::ND_TetrahedronElement, mfem::ND_HexahedronElement, mfem::RT_TetrahedronElement, mfem::RT_HexahedronElement, mfem::L2_TriangleElement, and mfem::L2_QuadrilateralElement.

Definition at line 108 of file fe.cpp.

void mfem::FiniteElement::ProjectDelta	(	int	vertex,
		Vector &	dofs
	)		const

virtual

Compute a representation (up to multiplicative constant) for the delta function at the vertex with the given index.

Reimplemented in mfem::L2Pos_TetrahedronElement, mfem::L2_TetrahedronElement, mfem::L2Pos_TriangleElement, mfem::L2_TriangleElement, mfem::L2Pos_HexahedronElement, mfem::L2_HexahedronElement, mfem::L2Pos_QuadrilateralElement, mfem::L2_QuadrilateralElement, mfem::L2Pos_SegmentElement, mfem::L2_SegmentElement, mfem::H1Pos_HexahedronElement, mfem::H1Pos_QuadrilateralElement, mfem::H1Pos_SegmentElement, mfem::H1_HexahedronElement, mfem::H1_QuadrilateralElement, mfem::H1_SegmentElement, mfem::P0HexFiniteElement, mfem::P0TetFiniteElement, mfem::CrouzeixRaviartFiniteElement, mfem::TriLinear3DFiniteElement, mfem::Linear3DFiniteElement, mfem::P0QuadFiniteElement, mfem::P0TriangleFiniteElement, mfem::BiQuadPos2DFiniteElement, mfem::BiQuad2DFiniteElement, mfem::Quad2DFiniteElement, mfem::P1OnQuadFiniteElement, mfem::GaussBiLinear2DFiniteElement, mfem::GaussLinear2DFiniteElement, mfem::BiLinear2DFiniteElement, and mfem::Linear2DFiniteElement.

Definition at line 87 of file fe.cpp.

void mfem::FiniteElement::ProjectDiv	(	const FiniteElement &	fe,
		ElementTransformation &	Trans,
		DenseMatrix &	div
	)		const

virtual

Compute the discrete divergence matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.

Reimplemented in mfem::NodalFiniteElement.

Definition at line 116 of file fe.cpp.

void mfem::FiniteElement::ProjectGrad	(	const FiniteElement &	fe,
		ElementTransformation &	Trans,
		DenseMatrix &	grad
	)		const

virtual

Compute the discrete gradient matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it.

Reimplemented in mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::RT_TriangleElement, mfem::RT_QuadrilateralElement, and mfem::NodalFiniteElement.

Definition at line 100 of file fe.cpp.

int mfem::FiniteElement::Space ( ) const

inline

Returns the type of space on each element.

Definition at line 94 of file fe.hpp.