#include <fe_base.hpp>

Inheritance diagram for mfem::NodalTensorFiniteElement:

Collaboration diagram for mfem::NodalTensorFiniteElement:

Public Member Functions
	NodalTensorFiniteElement (const int dims, const int p, const int btype, const DofMapType dmtype)

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

void	SetMapType (const int map_type_) override
	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.

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.

void	GetFaceMap (const int face_id, Array< int > &face_map) const override
	Return the mapping from lexicographic face DOFs to lexicographic element DOFs for the given local face face_id.

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

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.

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

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.

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)

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.

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.

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.

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.

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

void	ReorderLexToNative (int ncomp, Vector &dofs) const

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.

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.

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.

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.

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.

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

int	GetRangeDim () const
	Returns the vector dimension for vector-valued finite elements, which is also the dimension of the interpolation operation.

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

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

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

int	GetOrder () const
	Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order.

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

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

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

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

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

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}.

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

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}.

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.

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.

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.

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.

const IntegrationRule &	GetNodes () const
	Get a const reference to the nodes of the element.

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.

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

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

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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

virtual	~FiniteElement ()
	Deconstruct the FiniteElement.

Public Member Functions inherited from mfem::TensorBasisElement
	TensorBasisElement (const int dims, const int p, const int btype, const DofMapType dmtype)

int	GetBasisType () const

const Poly_1D::Basis &	GetBasis1D () const

const Array< int > &	GetDofMap () const
	Get an Array<int> that maps lexicographically ordered indices to the indices of the respective nodes/dofs/basis functions. If the dofs are ordered lexicographically, i.e. the mapping is identity, the returned Array will be empty.

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...

Public Types inherited from mfem::TensorBasisElement
enum	DofMapType { L2_DOF_MAP = 0 , H1_DOF_MAP = 1 , Sr_DOF_MAP = 2 }

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).

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

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

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

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

Static Public Member Functions inherited from mfem::TensorBasisElement
static Geometry::Type	GetTensorProductGeometry (int dim)

static int	Pow (int base, int dim)
	Return base raised to the power dim.

static const DofToQuad &	GetTensorDofToQuad (const FiniteElement &fe, const IntegrationRule &ir, DofToQuad::Mode mode, const Poly_1D::Basis &basis, bool closed, Array< DofToQuad * > &dof2quad_array)

Protected Member Functions inherited from mfem::NodalFiniteElement
void	ProjectCurl_2D (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const

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

Protected Attributes inherited from mfem::NodalFiniteElement
Array< int >	lex_ordering

Protected Attributes inherited from mfem::FiniteElement
int	dim
	Dimension of reference space.

int	vdim
	Vector dimension of vector-valued basis functions.

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

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

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.

int	order
	Order/degree of the shape functions.

int	orders [Geometry::MaxDim]
	Anisotropic orders.

IntegrationRule	Nodes

DenseMatrix	vshape

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

Protected Attributes inherited from mfem::TensorBasisElement
int	b_type

Array< int >	dof_map

Poly_1D::Basis &	basis1d

Array< int >	inv_dof_map

Detailed Description

Definition at line 1306 of file fe_base.hpp.

Constructor & Destructor Documentation

◆ NodalTensorFiniteElement()

mfem::NodalTensorFiniteElement::NodalTensorFiniteElement	(	const int	dims,
		const int	p,
		const int	btype,
		const DofMapType	dmtype )

Definition at line 2648 of file fe_base.cpp.

Member Function Documentation

◆ GetDofToQuad()

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

overridevirtual

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

See the documentation for DofToQuad for more details.

Reimplemented from mfem::NodalFiniteElement.

Definition at line 2672 of file fe_base.cpp.

◆ GetFaceMap()

void mfem::NodalTensorFiniteElement::GetFaceMap	(	const int	face_id,
		Array< int > &	face_map ) const

overridevirtual

Return the mapping from lexicographic face DOFs to lexicographic element DOFs for the given local face face_id.

Given the ith DOF (lexicographically ordered) on the face referenced by face_id, face_map[i] gives the corresponding index of the DOF in the element (also lexicographically ordered).

Note: For L2 spaces, this is only well-defined for "closed" bases such as the Gauss-Lobatto or Bernstein (positive) bases.

Warning: GetFaceMap() is currently only implemented for tensor-product (quadrilateral and hexahedral) elements. Its functionality may change when simplex elements are supported in the future.

Reimplemented from mfem::FiniteElement.

Definition at line 2686 of file fe_base.cpp.

◆ GetTransferMatrix()

void mfem::NodalTensorFiniteElement::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::NodalFiniteElement.

Definition at line 1318 of file fe_base.hpp.