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 and DerivRangeType. More...

enum	{ VALUE, INTEGRAL, H_DIV, H_CURL }
	Enumeration for MapType: defines how reference functions are mapped to physical space. More...

enum	{ NONE, GRAD, DIV, CURL }
	Enumeration for DerivType: defines which derivative method is implemented. More...

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

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

int	GetGeomType () const
	Returns the Geometry::Type of the reference element. More...

int	GetDof () const
	Returns the number of degrees of freedom in the finite element. 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	GetDerivRangeType () const

int	GetMapType () const

int	GetDerivType () const

int	GetDerivMapType () const

virtual void	CalcShape (const IntegrationPoint &ip, Vector &shape) const =0
	Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip. More...

void	CalcPhysShape (ElementTransformation &Trans, Vector &shape) const
	Evaluate the values of all shape functions of a scalar finite element in physical space at the point described by Trans. More...

virtual void	CalcDShape (const IntegrationPoint &ip, DenseMatrix &dshape) const =0
	Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip. More...

void	CalcPhysDShape (ElementTransformation &Trans, DenseMatrix &dshape) const
	Evaluate the gradients of all shape functions of a scalar finite element in physical space at the point described by Trans. More...

const IntegrationRule &	GetNodes () const

virtual void	CalcVShape (const IntegrationPoint &ip, DenseMatrix &shape) const
	Evaluate the values of all shape functions of a vector finite element in reference space at the given point ip. More...

virtual void	CalcVShape (ElementTransformation &Trans, DenseMatrix &shape) const
	Evaluate the values of all shape functions of a vector finite element in physical space at the point described by Trans. More...

void	CalcPhysVShape (ElementTransformation &Trans, DenseMatrix &shape) const
	Equivalent to the CalcVShape() method with the same arguments. More...

virtual void	CalcDivShape (const IntegrationPoint &ip, Vector &divshape) const
	Evaluate the divergence of all shape functions of a vector finite element in reference space at the given point ip. More...

void	CalcPhysDivShape (ElementTransformation &Trans, Vector &divshape) const
	Evaluate the divergence of all shape functions of a vector finite element in physical space at the point described by Trans. More...

virtual void	CalcCurlShape (const IntegrationPoint &ip, DenseMatrix &curl_shape) const
	Evaluate the curl of all shape functions of a vector finite element in reference space at the given point ip. More...

void	CalcPhysCurlShape (ElementTransformation &Trans, DenseMatrix &curl_shape) const
	Evaluate the curl of all shape functions of a vector finite element in physical space at the point described by Trans. More...

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 ()

Static Public Member Functions
static int	VerifyClosed (int pt_type)

static int	VerifyOpen (int pt_type)

Protected Attributes
int	Dim
	Dimension of reference space. More...

int	GeomType
	Geometry::Type of the reference element. More...

int	Dof
	Number of degrees of freedom. More...

int	Order
	Order/degree of the shape functions. More...

int	FuncSpace

int	RangeType

int	MapType

int	DerivType

int	DerivRangeType

int	DerivMapType

IntegrationRule	Nodes

DenseMatrix	vshape

Detailed Description

Abstract class for Finite Elements.

Definition at line 46 of file fe.hpp.

Member Enumeration Documentation

anonymous enum

Enumeration for RangeType and DerivRangeType.

Enumerator
SCALAR
VECTOR

Definition at line 62 of file fe.hpp.

anonymous enum

Enumeration for MapType: defines how reference functions are mapped to physical space.

A reference function, uh(xh), can be mapped to a function, u(x), on a general physical element in following ways:

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	For scalar fields; preserves point values.
INTEGRAL	For scalar fields; preserves volume integrals.
H_DIV	For vector fields; preserves surface integrals of the normal component
H_CURL	For vector fields; preserves line integrals of the tangential component

Definition at line 84 of file fe.hpp.

anonymous enum

Enumeration for DerivType: defines which derivative method is implemented.

Each FiniteElement class implements only one type of derivative. The value returned by GetDerivType() indicates which derivative method is implemented.

Enumerator
NONE	No derivatives implemented.
GRAD	Implements CalcDShape methods.
DIV	Implements CalcDivShape methods.
CURL	Implements CalcCurlShape methods.

Definition at line 99 of file fe.hpp.

Constructor & Destructor Documentation

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

Construct FiniteElement with given

Parameters

D	Reference space dimension
G	Geometry type (of type Geometry::Type)
Do	Number of degrees of freedom in the FiniteElement
O	Order/degree of the FiniteElement
F	FunctionSpace type of the FiniteElement

Definition at line 24 of file fe.cpp.

virtual mfem::FiniteElement::~FiniteElement ( )

inlinevirtual

Definition at line 278 of file fe.hpp.

Member Function Documentation

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

virtual

Evaluate the curl of all shape functions of a vector finite element in reference space at the given point ip.

Each row of the result DenseMatrix curl_shape contains the components of the curl of one vector shape function. The size (Dof x CDim) of curl_shape must be set in advance, where CDim = 3 for Dim = 3 and CDim = 1 for Dim = 2.

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

Definition at line 66 of file fe.cpp.

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

virtual

Evaluate the divergence of all shape functions of a vector finite element in reference space at the given point ip.

The size (Dof) of the result Vector divshape must be set in advance.

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 52 of file fe.cpp.

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

pure virtual

Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip.

Each row of the result DenseMatrix dshape contains the derivatives of one shape function. The size (Dof x Dim) of dshape must be set in advance.

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 103 of file fe.cpp.

void mfem::FiniteElement::CalcPhysCurlShape	(	ElementTransformation &	Trans,
		DenseMatrix &	curl_shape
	)		const

Evaluate the curl of all shape functions of a vector finite element in physical space at the point described by Trans.

Each row of the result DenseMatrix curl_shape contains the components of the curl of one vector shape function. The size (Dof x CDim) of curl_shape must be set in advance, where CDim = 3 for Dim = 3 and CDim = 1 for Dim = 2.

Definition at line 73 of file fe.cpp.

void mfem::FiniteElement::CalcPhysDivShape	(	ElementTransformation &	Trans,
		Vector &	divshape
	)		const

Evaluate the divergence of all shape functions of a vector finite element in physical space at the point described by Trans.

The size (Dof) of the result Vector divshape must be set in advance.

Definition at line 59 of file fe.cpp.

void mfem::FiniteElement::CalcPhysDShape	(	ElementTransformation &	Trans,
		DenseMatrix &	dshape
	)		const

Evaluate the gradients of all shape functions of a scalar finite element in physical space at the point described by Trans.

Each row of the result DenseMatrix dshape contains the derivatives of one shape function. The size (Dof x SDim) of dshape must be set in advance, where SDim >= Dim is the physical space dimension as described by Trans.

Definition at line 174 of file fe.cpp.

void mfem::FiniteElement::CalcPhysShape	(	ElementTransformation &	Trans,
		Vector &	shape
	)		const

Evaluate the values of all shape functions of a scalar finite element in physical space at the point described by Trans.

The size (Dof) of the result Vector shape must be set in advance.

Definition at line 164 of file fe.cpp.

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

inline

Equivalent to the CalcVShape() method with the same arguments.

Definition at line 188 of file fe.hpp.

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

pure virtual

Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip.

The size (Dof) of the result Vector shape must be set in advance.

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

virtual

Evaluate the values of all shape functions of a vector finite element in reference space at the given point ip.

Each row of the result DenseMatrix shape contains the components of one vector shape function. The size (Dof x Dim) of shape must be set in advance.

Definition at line 38 of file fe.cpp.

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

virtual

Evaluate the values of all shape functions of a vector finite element in physical space at the point described by Trans.

Each row of the result DenseMatrix shape contains the components of one vector shape function. The size (Dof x SDim) of shape must be set in advance, where SDim >= Dim is the physical space dimension as described by Trans.

Definition at line 45 of file fe.cpp.

int mfem::FiniteElement::GetDerivMapType ( ) const

inline

Definition at line 137 of file fe.hpp.

int mfem::FiniteElement::GetDerivRangeType ( ) const

inline

Definition at line 131 of file fe.hpp.

int mfem::FiniteElement::GetDerivType ( ) const

inline

Definition at line 135 of file fe.hpp.

int mfem::FiniteElement::GetDim ( ) const

inline

Returns the reference space dimension for the finite element.

Definition at line 115 of file fe.hpp.

int mfem::FiniteElement::GetDof ( ) const

inline

Returns the number of degrees of freedom in the finite element.

Definition at line 121 of file fe.hpp.

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

virtual

Reimplemented in mfem::Linear3DFiniteElement.

Definition at line 98 of file fe.cpp.

int mfem::FiniteElement::GetGeomType ( ) const

inline

Returns the Geometry::Type of the reference element.

Definition at line 118 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.

Definition at line 109 of file fe.cpp.

int mfem::FiniteElement::GetMapType ( ) const

inline

Definition at line 133 of file fe.hpp.

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

inline

Definition at line 166 of file fe.hpp.

int mfem::FiniteElement::GetOrder ( ) const

inline

Returns the order of the finite element.

Definition at line 124 of file fe.hpp.

int mfem::FiniteElement::GetRangeType ( ) const

inline

Definition at line 129 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 115 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 121 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 133 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_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, mfem::L2_TriangleElement, and mfem::L2_QuadrilateralElement.

Definition at line 148 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 127 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 156 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 140 of file fe.cpp.

int mfem::FiniteElement::Space ( ) const

inline

Returns the type of space on each element.

Definition at line 127 of file fe.hpp.

static int mfem::FiniteElement::VerifyClosed ( int pt_type )

inlinestatic

Definition at line 280 of file fe.hpp.

static int mfem::FiniteElement::VerifyOpen ( int pt_type )

inlinestatic

Definition at line 287 of file fe.hpp.

Member Data Documentation

int mfem::FiniteElement::DerivMapType

protected

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::DerivRangeType

protected

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::DerivType

protected

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::Dim

protected

Dimension of reference space.

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::Dof

protected

Number of degrees of freedom.

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::FuncSpace

protected

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::GeomType

protected

Geometry::Type of the reference element.

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::MapType

protected

Definition at line 49 of file fe.hpp.

IntegrationRule mfem::FiniteElement::Nodes

protected

Definition at line 55 of file fe.hpp.

int mfem::FiniteElement::Order

protected

Order/degree of the shape functions.

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::RangeType

protected

Definition at line 49 of file fe.hpp.

DenseMatrix mfem::FiniteElement::vshape

mutableprotected

Definition at line 57 of file fe.hpp.

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation