Class for standard nodal finite elements. More...

#include <fe_base.hpp>

Inheritance diagram for mfem::NodalFiniteElement:

Collaboration diagram for mfem::NodalFiniteElement:

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

void	GetLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I) const override
	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...

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

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

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

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

void	ProjectMatrixCoefficient (MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const override
	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...

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

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

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

const Array< int > &	GetLexicographicOrdering () const
	Get an Array<int> that maps lexicographically ordered indices to the indices of the respective nodes/dofs/basis functions. More...

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

virtual void	SetMapType (int M)
	Set the FiniteElement::MapType of the element to either VALUE or INTEGRAL. Also sets the FiniteElement::DerivType to GRAD if the FiniteElement::MapType is VALUE. More...

void	NodalLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
	Get the matrix I that defines nodal interpolation between this element and the refined element fine_fe. More...

void	ScalarLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
	Get matrix I "Interpolation" defined through local L2-projection in the space defined by the fine_fe. More...

void	ScalarLocalL2Restriction (ElementTransformation &Trans, DenseMatrix &R, const ScalarFiniteElement &coarse_fe) const
	Get restriction matrix R defined through local L2-projection in the space defined by the coarse_fe. More...

Public Member Functions inherited from mfem::FiniteElement
	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	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	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	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 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 void	GetFaceMap (const int face_id, Array< int > &face_map) const
	Return the mapping from lexicographic face DOFs to lexicographic element DOFs for the given local face face_id. More...

virtual StatelessDofTransformation *	GetDofTransformation () const
	Return a DoF transformation object for this particular type of basis. More...

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

Protected Member Functions
void	ProjectCurl_2D (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const

Protected Attributes
Array< int >	lex_ordering

Protected Attributes inherited from mfem::FiniteElement
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...

Additional Inherited Members
Public Types inherited from mfem::FiniteElement
enum	RangeType { UNKNOWN_RANGE_TYPE = -1, SCALAR, VECTOR }
	Enumeration for range_type and deriv_range_type. More...

enum	MapType { UNKNOWN_MAP_TYPE = -1, 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...

Static Public Member Functions inherited from mfem::FiniteElement
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...

Static Protected Member Functions inherited from mfem::ScalarFiniteElement
static const ScalarFiniteElement &	CheckScalarFE (const FiniteElement &fe)

Detailed Description

Class for standard nodal finite elements.

Definition at line 708 of file fe_base.hpp.

Constructor & Destructor Documentation

◆ NodalFiniteElement()

mfem::NodalFiniteElement::NodalFiniteElement	(	int	D,
		Geometry::Type	G,
		int	Do,
		int	O,
		int	F = `FunctionSpace::Pk`
	)

inline

Construct NodalFiniteElement 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 724 of file fe_base.hpp.

Member Function Documentation

◆ GetLexicographicOrdering()

const Array<int>& mfem::NodalFiniteElement::GetLexicographicOrdering ( ) const

inline

Get an Array<int> that maps lexicographically ordered indices to the indices of the respective nodes/dofs/basis functions.

Lexicographic ordering of nodes is defined in terms of reference-space coordinates (x,y,z). Lexicographically ordered nodes are listed first in order of increasing x-coordinate, and then in order of increasing y-coordinate, and finally in order of increasing z-coordinate.

For example, the six nodes of a quadratic triangle are lexicographically ordered as follows:

5 |\ 3 4 | \ 0-1-2

The resulting array may be empty if the DOFs are already ordered lexicographically, or if the finite element does not support creating this permutation. The array returned is the same as the array given by TensorBasisElement::GetDofMap, but it is also available for non-tensor elements.

Definition at line 783 of file fe_base.hpp.

◆ GetLocalInterpolation()

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

inlineoverridevirtual

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 from mfem::FiniteElement.

Definition at line 728 of file fe_base.hpp.

◆ GetLocalRestriction()

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

overridevirtual

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 from mfem::FiniteElement.

Reimplemented in mfem::L2_TetrahedronElement, mfem::L2_TriangleElement, mfem::L2_HexahedronElement, mfem::L2_QuadrilateralElement, and mfem::L2_SegmentElement.

Definition at line 678 of file fe_base.cpp.

◆ GetTransferMatrix()

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

inlineoverridevirtual

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 from mfem::FiniteElement.

Reimplemented in mfem::NodalTensorFiniteElement.

Definition at line 735 of file fe_base.hpp.

◆ Project() [1/3]

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

overridevirtual

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 from mfem::FiniteElement.

Reimplemented in mfem::L2_HexahedronElement, and mfem::L2_QuadrilateralElement.

Definition at line 710 of file fe_base.cpp.

◆ Project() [2/3]

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

overridevirtual

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.

Reimplemented from mfem::FiniteElement.

Definition at line 727 of file fe_base.cpp.

◆ Project() [3/3]

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

overridevirtual

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 from mfem::FiniteElement.

Definition at line 771 of file fe_base.cpp.

◆ ProjectCurl_2D()

void mfem::NodalFiniteElement::ProjectCurl_2D	(	const FiniteElement &	fe,
		ElementTransformation &	Trans,
		DenseMatrix &	curl
	)		const

protected

Definition at line 638 of file fe_base.cpp.

◆ ProjectDiv()

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

overridevirtual

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 from mfem::FiniteElement.

Reimplemented in mfem::L2_HexahedronElement, and mfem::L2_QuadrilateralElement.

Definition at line 859 of file fe_base.cpp.

◆ ProjectGrad()

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

overridevirtual

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 from mfem::FiniteElement.

Definition at line 830 of file fe_base.cpp.

◆ ProjectMatrixCoefficient()

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

overridevirtual

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 from mfem::FiniteElement.

Definition at line 749 of file fe_base.cpp.

Member Data Documentation

◆ lex_ordering

Array<int> mfem::NodalFiniteElement::lex_ordering

protected

Definition at line 711 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 Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ NodalFiniteElement()

Member Function Documentation

◆ GetLexicographicOrdering()

◆ GetLocalInterpolation()

◆ GetLocalRestriction()

◆ GetTransferMatrix()

◆ Project() [1/3]

◆ Project() [2/3]

◆ Project() [3/3]

◆ ProjectCurl_2D()

◆ ProjectDiv()

◆ ProjectGrad()

◆ ProjectMatrixCoefficient()

Member Data Documentation

◆ lex_ordering