Abstract class for all finite elements. More...

#include <fe_base.hpp>

Inheritance diagram for mfem::FiniteElement:

Collaboration diagram for mfem::FiniteElement:

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

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

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

Public Member Functions
	FiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk)
	Construct FiniteElement with given. More...

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

int	GetVDim () const
	Returns the vector dimension for vector-valued finite elements. More...

int	GetCurlDim () const
	Returns the dimension of the curl for vector-valued finite elements. More...

Geometry::Type	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. In the case of anisotropic orders, returns the maximum order. More...

bool	HasAnisotropicOrders () const
	Returns true if the FiniteElement basis may be using different orders/degrees in different spatial directions. More...

const int *	GetAnisotropicOrders () const
	Returns an array containing the anisotropic orders/degrees. More...

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

int	GetRangeType () const
	Returns the FiniteElement::RangeType of the element, one of {SCALAR, VECTOR}. More...

int	GetDerivRangeType () const
	Returns the FiniteElement::RangeType of the element derivative, either SCALAR or VECTOR. More...

int	GetMapType () const
	Returns the FiniteElement::MapType of the element describing how reference functions are mapped to physical space, one of {VALUE, INTEGRAL H_DIV, H_CURL}. More...

int	GetDerivType () const
	Returns the FiniteElement::DerivType of the element describing the spatial derivative method implemented, one of {NONE, GRAD, DIV, CURL}. More...

int	GetDerivMapType () const
	Returns the FiniteElement::DerivType of the element describing how reference function derivatives are mapped to physical space, one of {VALUE, INTEGRAL, H_DIV, H_CURL}. More...

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
	Get a const reference to the nodes of the element. More...

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...

virtual 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
	Get the dofs associated with the given face. dofs is set to an internal array of the local dofc on the face, while ndofs is set to the number of dofs on that face. More...

virtual void	CalcHessian (const IntegrationPoint &ip, DenseMatrix &Hessian) const
	Evaluate the Hessians of all shape functions of a scalar finite element in reference space at the given point ip. More...

virtual void	CalcPhysHessian (ElementTransformation &Trans, DenseMatrix &Hessian) const
	Evaluate the Hessian of all shape functions of a scalar finite element in reference space at the given point ip. More...

virtual void	CalcPhysLaplacian (ElementTransformation &Trans, Vector &Laplacian) const
	Evaluate the Laplacian of all shape functions of a scalar finite element in reference space at the given point ip. More...

virtual void	CalcPhysLinLaplacian (ElementTransformation &Trans, Vector &Laplacian) const

virtual void	GetLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I) const
	Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base geometry under the given transformation. More...

virtual void	GetLocalRestriction (ElementTransformation &Trans, DenseMatrix &R) const
	Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs. More...

virtual void	GetTransferMatrix (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
	Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this finite element. More...

virtual void	Project (Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
	Given a coefficient and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. More...

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

virtual void	ProjectFromNodes (Vector &vc, ElementTransformation &Trans, Vector &dofs) const
	Given a vector of values at the finite element nodes and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. Valid for VectorFiniteElements. More...

virtual void	ProjectMatrixCoefficient (MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
	Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local finite dimensional space in terms of the degrees of freedom. For VectorFiniteElements, the rows of the coefficient are projected in the vector space. More...

virtual void	ProjectDelta (int vertex, Vector &dofs) const
	Project a delta function centered on the given vertex in the local finite dimensional space represented by the dofs. More...

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

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

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

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

virtual const DofToQuad &	GetDofToQuad (const IntegrationRule &ir, DofToQuad::Mode mode) const
	Return a DofToQuad structure corresponding to the given IntegrationRule using the given DofToQuad::Mode. More...

virtual	~FiniteElement ()
	Deconstruct the FiniteElement. More...

Static Public Member Functions
static bool	IsClosedType (int b_type)
	Return true if the BasisType of b_type is closed (has Quadrature1D points on the boundary). More...

static bool	IsOpenType (int b_type)
	Return true if the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary). More...

static int	VerifyClosed (int b_type)
	Ensure that the BasisType of b_type is closed (has Quadrature1D points on the boundary). More...

static int	VerifyOpen (int b_type)
	Ensure that the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary). More...

static int	VerifyNodal (int b_type)
	Ensure that the BasisType of b_type nodal (satisfies the interpolation property). More...

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

int	vdim
	Vector dimension of vector-valued basis functions. More...

int	cdim
	Dimension of curl for vector-valued basis functions. More...

Geometry::Type	geom_type
	Geometry::Type of the reference element. More...

int	func_space

int	range_type

int	map_type

int	deriv_type

int	deriv_range_type

int	deriv_map_type

int	dof
	Number of degrees of freedom. More...

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

int	orders [Geometry::MaxDim]
	Anisotropic orders. More...

IntegrationRule	Nodes

DenseMatrix	vshape

Array< DofToQuad * >	dof2quad_array
	Container for all DofToQuad objects created by the FiniteElement. More...

Detailed Description

Abstract class for all finite elements.

Definition at line 235 of file fe_base.hpp.

Member Enumeration Documentation

enum mfem::FiniteElement::DerivType

Enumeration for DerivType: defines which derivative method is implemented.

Each FiniteElement class implements up to 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 292 of file fe_base.hpp.

enum mfem::FiniteElement::MapType

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

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

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

Enumerator
VALUE	For scalar fields; preserves point values \( u(x) = \hat u(\hat x) \)
INTEGRAL	For scalar fields; preserves volume integrals \( u(x) = (1/w) \hat u(\hat x) \)
H_DIV	For vector fields; preserves surface integrals of the normal component \( u(x) = (J/w) \hat u(\hat x) \)
H_CURL	For vector fields; preserves line integrals of the tangential component \( u(x) = J^{-t} \hat u(\hat x) \) (square J), \( u(x) = J(J^t J)^{-1} \hat u(\hat x) \) (general J)

Definition at line 271 of file fe_base.hpp.

enum mfem::FiniteElement::RangeType

Enumeration for range_type and deriv_range_type.

Enumerator
SCALAR
VECTOR

Definition at line 259 of file fe_base.hpp.

Constructor & Destructor Documentation

mfem::FiniteElement::FiniteElement	(	int	D,
		Geometry::Type	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 22 of file fe_base.cpp.

mfem::FiniteElement::~FiniteElement ( )

virtual

Deconstruct the FiniteElement.

Definition at line 373 of file fe_base.cpp.

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::Nedelec1PyrFiniteElement, mfem::Nedelec1WdgFiniteElement, mfem::Nedelec1TetFiniteElement, mfem::Nedelec1HexFiniteElement, mfem::ND_R2D_QuadrilateralElement, mfem::ND_R2D_TriangleElement, mfem::ND_R2D_SegmentElement, mfem::ND_R1D_SegmentElement, mfem::ND_WedgeElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, and mfem::ND_HexahedronElement.

Definition at line 64 of file fe_base.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.

Definition at line 51 of file fe_base.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 &	Hessian
	)		const

virtual

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

Each row of the result DenseMatrix Hessian contains upper triangular part of the Hessian of one shape function. The order in 2D is {u_xx, u_xy, u_yy}. The size (dof x (dim (dim+1)/2) of Hessian must be set in advance.

Reimplemented in mfem::Cubic2DFiniteElement, mfem::BiCubic2DFiniteElement, mfem::Quad2DFiniteElement, mfem::NURBS3DFiniteElement, mfem::H1_TetrahedronElement, mfem::NURBS2DFiniteElement, mfem::H1_TriangleElement, mfem::BiLinear2DFiniteElement, mfem::NURBS1DFiniteElement, mfem::H1_HexahedronElement, mfem::H1_QuadrilateralElement, and mfem::H1_SegmentElement.

Definition at line 100 of file fe_base.cpp.

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

virtual

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.

Reimplemented in mfem::ND_R2D_FiniteElement, and mfem::ND_R1D_SegmentElement.

Definition at line 70 of file fe_base.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 57 of file fe_base.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 191 of file fe_base.cpp.

void mfem::FiniteElement::CalcPhysHessian	(	ElementTransformation &	Trans,
		DenseMatrix &	Hessian
	)		const

virtual

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

The size (dof, dim*(dim+1)/2) of Hessian must be set in advance.

Definition at line 289 of file fe_base.cpp.

void mfem::FiniteElement::CalcPhysLaplacian	(	ElementTransformation &	Trans,
		Vector &	Laplacian
	)		const

virtual

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

The size (dof) of Laplacian must be set in advance.

Definition at line 202 of file fe_base.cpp.

void mfem::FiniteElement::CalcPhysLinLaplacian	(	ElementTransformation &	Trans,
		Vector &	Laplacian
	)		const

virtual

Definition at line 244 of file fe_base.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 181 of file fe_base.cpp.

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

inline

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

Definition at line 412 of file fe_base.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 39 of file fe_base.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_base.cpp.

const int* mfem::FiniteElement::GetAnisotropicOrders ( ) const

inline

Returns an array containing the anisotropic orders/degrees.

Definition at line 334 of file fe_base.hpp.

int mfem::FiniteElement::GetCurlDim ( ) const

inline

Returns the dimension of the curl for vector-valued finite elements.

Definition at line 317 of file fe_base.hpp.

int mfem::FiniteElement::GetDerivMapType ( ) const

inline

Returns the FiniteElement::DerivType of the element describing how reference function derivatives are mapped to physical space, one of {VALUE, INTEGRAL, H_DIV, H_CURL}.

Definition at line 360 of file fe_base.hpp.

int mfem::FiniteElement::GetDerivRangeType ( ) const

inline

Returns the FiniteElement::RangeType of the element derivative, either SCALAR or VECTOR.

Definition at line 344 of file fe_base.hpp.

int mfem::FiniteElement::GetDerivType ( ) const

inline

Returns the FiniteElement::DerivType of the element describing the spatial derivative method implemented, one of {NONE, GRAD, DIV, CURL}.

Definition at line 355 of file fe_base.hpp.

int mfem::FiniteElement::GetDim ( ) const

inline

Returns the reference space dimension for the finite element.

Definition at line 311 of file fe_base.hpp.

int mfem::FiniteElement::GetDof ( ) const

inline

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

Definition at line 323 of file fe_base.hpp.

const DofToQuad & mfem::FiniteElement::GetDofToQuad	(	const IntegrationRule &	ir,
		DofToQuad::Mode	mode
	)		const

virtual

Return a DofToQuad structure corresponding to the given IntegrationRule using the given DofToQuad::Mode.

See the documentation for DofToQuad for more details.

Reimplemented in mfem::VectorTensorFiniteElement, mfem::NodalTensorFiniteElement, mfem::ScalarFiniteElement, and mfem::PositiveTensorFiniteElement.

Definition at line 366 of file fe_base.cpp.

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

virtual

Get the dofs associated with the given face. *dofs is set to an internal array of the local dofc on the face, while *ndofs is set to the number of dofs on that face.

Reimplemented in mfem::Linear3DFiniteElement, mfem::LinearPyramidFiniteElement, and mfem::LinearWedgeFiniteElement.

Definition at line 95 of file fe_base.cpp.

Geometry::Type mfem::FiniteElement::GetGeomType ( ) const

inline

Returns the Geometry::Type of the reference element.

Definition at line 320 of file fe_base.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 106 of file fe_base.cpp.

void mfem::FiniteElement::GetLocalRestriction	(	ElementTransformation &	Trans,
		DenseMatrix &	R
	)		const

virtual

Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.

The fine element is the image of the base geometry under the given transformation, Trans.

The assumption in this method is that a subset of the coarse dofs can be expressed only in terms of the dofs of the given fine element.

Rows in R corresponding to coarse dofs that cannot be expressed in terms of the fine dofs will be marked as invalid by setting the first entry (column 0) in the row to infinity().

This method assumes that the dimensions of R are set before it is called.

Reimplemented in mfem::NodalFiniteElement, mfem::ND_R2D_FiniteElement, mfem::ND_R2D_SegmentElement, mfem::ND_R1D_SegmentElement, mfem::RT_R2D_FiniteElement, mfem::RT_R2D_SegmentElement, mfem::ND_WedgeElement, mfem::RT_WedgeElement, mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::RT_TetrahedronElement, mfem::ND_TetrahedronElement, mfem::RT_TriangleElement, mfem::ND_QuadrilateralElement, mfem::RT_HexahedronElement, mfem::ND_HexahedronElement, mfem::RT_QuadrilateralElement, and mfem::PositiveFiniteElement.

Definition at line 112 of file fe_base.cpp.

int mfem::FiniteElement::GetMapType ( ) const

inline

Returns the FiniteElement::MapType of the element describing how reference functions are mapped to physical space, one of {VALUE, INTEGRAL H_DIV, H_CURL}.

Definition at line 349 of file fe_base.hpp.

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

inline

Get a const reference to the nodes of the element.

Definition at line 390 of file fe_base.hpp.

int mfem::FiniteElement::GetOrder ( ) const

inline

Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order.

Definition at line 327 of file fe_base.hpp.

int mfem::FiniteElement::GetRangeType ( ) const

inline

Returns the FiniteElement::RangeType of the element, one of {SCALAR, VECTOR}.

Definition at line 340 of file fe_base.hpp.

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

virtual

Return interpolation matrix, I, which maps dofs from a coarse element, fe, to the fine dofs on this finite element.

Trans represents the mapping from the reference element of this element into a subset of the reference space of the element fe, thus allowing the "coarse" FiniteElement to be different from the "fine" FiniteElement as when h-refinement is combined with p-refinement or p-derefinement. It is assumed that both finite elements use the same FiniteElement::MapType.

Reimplemented in mfem::NodalTensorFiniteElement, mfem::NodalFiniteElement, mfem::ND_R2D_FiniteElement, mfem::ND_R2D_SegmentElement, mfem::ND_R1D_SegmentElement, mfem::RT_R2D_FiniteElement, mfem::RT_R2D_SegmentElement, mfem::ND_WedgeElement, mfem::RT_WedgeElement, mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::RT_TetrahedronElement, mfem::ND_TetrahedronElement, mfem::RT_TriangleElement, mfem::ND_QuadrilateralElement, mfem::RT_HexahedronElement, mfem::ND_HexahedronElement, mfem::RT_QuadrilateralElement, and mfem::PositiveFiniteElement.

Definition at line 118 of file fe_base.cpp.

int mfem::FiniteElement::GetVDim ( ) const

inline

Returns the vector dimension for vector-valued finite elements.

Definition at line 314 of file fe_base.hpp.

bool mfem::FiniteElement::HasAnisotropicOrders ( ) const

inline

Returns true if the FiniteElement basis may be using different orders/degrees in different spatial directions.

Definition at line 331 of file fe_base.hpp.

static bool mfem::FiniteElement::IsClosedType ( int b_type )

inlinestatic

Return true if the BasisType of b_type is closed (has Quadrature1D points on the boundary).

Definition at line 585 of file fe_base.hpp.

static bool mfem::FiniteElement::IsOpenType ( int b_type )

inlinestatic

Return true if the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).

Definition at line 594 of file fe_base.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.

The approximation used to project is usually local interpolation of degrees of freedom. The derived class could use other methods not implemented yet, e.g. local L2 projection.

Reimplemented in mfem::NodalFiniteElement, mfem::BiQuadPos2DFiniteElement, mfem::L2_HexahedronElement, mfem::L2_QuadrilateralElement, and mfem::PositiveFiniteElement.

Definition at line 125 of file fe_base.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)

The approximation used to project is usually local interpolation of degrees of freedom. The derived class could use other methods not implemented yet, e.g. local L2 projection.

Definition at line 131 of file fe_base.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::NodalFiniteElement, mfem::ND_R2D_FiniteElement, mfem::ND_R1D_SegmentElement, mfem::RT_R2D_FiniteElement, mfem::ND_WedgeElement, mfem::RT_R1D_SegmentElement, mfem::RT_WedgeElement, mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::RT_TetrahedronElement, mfem::ND_TetrahedronElement, mfem::RT_TriangleElement, mfem::ND_QuadrilateralElement, mfem::RT_HexahedronElement, mfem::ND_HexahedronElement, mfem::RT_QuadrilateralElement, and mfem::PositiveFiniteElement.

Definition at line 154 of file fe_base.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::RT0PyrFiniteElement, mfem::RT0WdgFiniteElement, mfem::ND_R1D_SegmentElement, mfem::RT_R2D_FiniteElement, mfem::ND_WedgeElement, mfem::RT_R1D_SegmentElement, mfem::RT_WedgeElement, mfem::RT_TetrahedronElement, mfem::ND_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::L2_TriangleElement, mfem::ND_HexahedronElement, mfem::RT_QuadrilateralElement, and mfem::L2_QuadrilateralElement.

Definition at line 167 of file fe_base.cpp.

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

virtual

Project a delta function centered on the given vertex in the local finite dimensional space represented by the dofs.

Definition at line 149 of file fe_base.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, mfem::L2_HexahedronElement, and mfem::L2_QuadrilateralElement.

Definition at line 174 of file fe_base.cpp.

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

virtual

Given a vector of values at the finite element nodes and a transformation, compute its projection (approximation) in the local finite dimensional space in terms of the degrees of freedom. Valid for VectorFiniteElements.

Reimplemented in mfem::ND_R1D_SegmentElement, mfem::ND_TriangleElement, mfem::RT_TetrahedronElement, mfem::ND_TetrahedronElement, mfem::RT_TriangleElement, mfem::ND_QuadrilateralElement, mfem::RT_HexahedronElement, mfem::ND_HexahedronElement, and mfem::RT_QuadrilateralElement.

Definition at line 137 of file fe_base.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::Nedelec1PyrFiniteElement, mfem::Nedelec1WdgFiniteElement, mfem::Nedelec1TetFiniteElement, mfem::Nedelec1HexFiniteElement, mfem::NodalFiniteElement, mfem::ND_R2D_FiniteElement, mfem::ND_R1D_SegmentElement, mfem::ND_WedgeElement, mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::RT_TriangleElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, and mfem::RT_QuadrilateralElement.

Definition at line 160 of file fe_base.cpp.

void mfem::FiniteElement::ProjectMatrixCoefficient	(	MatrixCoefficient &	mc,
		ElementTransformation &	T,
		Vector &	dofs
	)		const

virtual

Given a matrix coefficient and a transformation, compute an approximation ("projection") in the local finite dimensional space in terms of the degrees of freedom. For VectorFiniteElements, the rows of the coefficient are projected in the vector space.

Reimplemented in mfem::NodalFiniteElement, mfem::ND_R1D_SegmentElement, mfem::ND_WedgeElement, mfem::RT_WedgeElement, mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::RT_TetrahedronElement, mfem::ND_TetrahedronElement, mfem::RT_TriangleElement, mfem::ND_QuadrilateralElement, mfem::RT_HexahedronElement, mfem::ND_HexahedronElement, and mfem::RT_QuadrilateralElement.

Definition at line 143 of file fe_base.cpp.

int mfem::FiniteElement::Space ( ) const

inline

Returns the type of FunctionSpace on the element.

Definition at line 337 of file fe_base.hpp.

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

inlinestatic

Ensure that the BasisType of b_type is closed (has Quadrature1D points on the boundary).

Definition at line 603 of file fe_base.hpp.

static int mfem::FiniteElement::VerifyNodal ( int b_type )

inlinestatic

Ensure that the BasisType of b_type nodal (satisfies the interpolation property).

Definition at line 620 of file fe_base.hpp.

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

inlinestatic

Ensure that the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).

Definition at line 612 of file fe_base.hpp.

Member Data Documentation

int mfem::FiniteElement::cdim

protected

Dimension of curl for vector-valued basis functions.

Definition at line 240 of file fe_base.hpp.

int mfem::FiniteElement::deriv_map_type

protected

Definition at line 242 of file fe_base.hpp.

int mfem::FiniteElement::deriv_range_type

protected

Definition at line 242 of file fe_base.hpp.

int mfem::FiniteElement::deriv_type

protected

Definition at line 242 of file fe_base.hpp.

int mfem::FiniteElement::dim

protected

Dimension of reference space.

Definition at line 238 of file fe_base.hpp.

int mfem::FiniteElement::dof

mutableprotected

Number of degrees of freedom.

Definition at line 245 of file fe_base.hpp.

Array<DofToQuad*> mfem::FiniteElement::dof2quad_array

mutableprotected

Container for all DofToQuad objects created by the FiniteElement.

Multiple DofToQuad objects may be needed when different quadrature rules or different DofToQuad::Mode are used.

Definition at line 255 of file fe_base.hpp.

int mfem::FiniteElement::func_space

protected

Definition at line 242 of file fe_base.hpp.

Geometry::Type mfem::FiniteElement::geom_type

protected

Geometry::Type of the reference element.

Definition at line 241 of file fe_base.hpp.

int mfem::FiniteElement::map_type

protected

Definition at line 242 of file fe_base.hpp.

IntegrationRule mfem::FiniteElement::Nodes

protected

Definition at line 248 of file fe_base.hpp.

int mfem::FiniteElement::order

mutableprotected

Order/degree of the shape functions.

Definition at line 245 of file fe_base.hpp.

int mfem::FiniteElement::orders[Geometry::MaxDim]

mutableprotected

Anisotropic orders.

Definition at line 247 of file fe_base.hpp.

int mfem::FiniteElement::range_type

protected

Definition at line 242 of file fe_base.hpp.

int mfem::FiniteElement::vdim

protected

Vector dimension of vector-valued basis functions.

Definition at line 239 of file fe_base.hpp.

DenseMatrix mfem::FiniteElement::vshape

mutableprotected

Definition at line 250 of file fe_base.hpp.

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

fem/fe/fe_base.hpp
fem/fe/fe_base.cpp

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