Arbitrary order Raviart-Thomas elements in 3D on a cube. More...

#include <fe_rt.hpp>

Inheritance diagram for mfem::RT_HexahedronElement:

Collaboration diagram for mfem::RT_HexahedronElement:

Public Member Functions
	RT_HexahedronElement (const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)
	Construct the RT_HexahedronElement of order p and closed and open BasisType cb_type and ob_type.

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.

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.

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.

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

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.

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)

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	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.

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.

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 void	GetFaceMap (const int face_id, Array< int > &face_map) const
	Return the mapping from lexicographically ordered face DOFs to lexicographically ordered element DOFs corresponding to local face face_id.

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.

Public Member Functions inherited from mfem::VectorTensorFiniteElement
	VectorTensorFiniteElement (const int dims, const int d, const int p, const int cbtype, const int obtype, const int M, const DofMapType dmtype)

	VectorTensorFiniteElement (const int dims, const int d, const int p, const int obtype, const int M, 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.

const DofToQuad &	GetDofToQuadOpen (const IntegrationRule &ir, DofToQuad::Mode mode) const

virtual	~VectorTensorFiniteElement ()

Public Member Functions inherited from mfem::VectorFiniteElement
	VectorFiniteElement (int D, Geometry::Type G, int Do, int O, int M, int F=FunctionSpace::Pk)

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}.

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.

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.

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

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	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.

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.

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.

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

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	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.

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.

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.

Protected Member Functions
void	ProjectIntegrated (VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const

Protected Member Functions inherited from mfem::VectorFiniteElement
void	SetDerivMembers ()

void	CalcVShape_RT (ElementTransformation &Trans, DenseMatrix &shape) const

void	CalcVShape_ND (ElementTransformation &Trans, DenseMatrix &shape) const

void	Project_RT (const real_t *nk, const Array< int > &d2n, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
	Project a vector coefficient onto the RT basis functions.

void	Project_RT (const real_t *nk, const Array< int > &d2n, Vector &vc, ElementTransformation &Trans, Vector &dofs) const
	Projects the vector of values given at FE nodes to RT space.

void	ProjectMatrixCoefficient_RT (const real_t *nk, const Array< int > &d2n, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
	Project the rows of the matrix coefficient in an RT space.

void	Project_RT (const real_t *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
	Project vector-valued basis functions onto the RT basis functions.

void	ProjectGrad_RT (const real_t *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const

void	ProjectCurl_ND (const real_t *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const

void	ProjectCurl_RT (const real_t *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const

void	Project_ND (const real_t *tk, const Array< int > &d2t, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
	Project a vector coefficient onto the ND basis functions.

void	Project_ND (const real_t *tk, const Array< int > &d2t, Vector &vc, ElementTransformation &Trans, Vector &dofs) const
	Projects the vector of values given at FE nodes to ND space.

void	ProjectMatrixCoefficient_ND (const real_t *tk, const Array< int > &d2t, MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
	Project the rows of the matrix coefficient in an ND space.

void	Project_ND (const real_t *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
	Project vector-valued basis functions onto the ND basis functions.

void	ProjectGrad_ND (const real_t *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const

void	LocalL2Projection_RT (const VectorFiniteElement &cfe, ElementTransformation &Trans, DenseMatrix &I) const

void	LocalInterpolation_RT (const VectorFiniteElement &cfe, const real_t *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &I) const

void	LocalL2Projection_ND (const VectorFiniteElement &cfe, ElementTransformation &Trans, DenseMatrix &I) const

void	LocalInterpolation_ND (const VectorFiniteElement &cfe, const real_t *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &I) const

void	LocalRestriction_RT (const real_t *nk, const Array< int > &d2n, ElementTransformation &Trans, DenseMatrix &R) const

void	LocalRestriction_ND (const real_t *tk, const Array< int > &d2t, ElementTransformation &Trans, DenseMatrix &R) const

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)

Static Protected Member Functions inherited from mfem::VectorFiniteElement
static const VectorFiniteElement &	CheckVectorFE (const FiniteElement &fe)

Protected Attributes inherited from mfem::VectorTensorFiniteElement
Poly_1D::Basis &	obasis1d

Protected Attributes inherited from mfem::VectorFiniteElement
bool	is_nodal

DenseMatrix	JtJ

DenseMatrix	curlshape

DenseMatrix	curlshape_J

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

Arbitrary order Raviart-Thomas elements in 3D on a cube.

Definition at line 94 of file fe_rt.hpp.

Constructor & Destructor Documentation

◆ RT_HexahedronElement()

mfem::RT_HexahedronElement::RT_HexahedronElement	(	const int	p,
		const int	cb_type = BasisType::GaussLobatto,
		const int	ob_type = BasisType::GaussLegendre )

Construct the RT_HexahedronElement of order p and closed and open BasisType cb_type and ob_type.

Definition at line 326 of file fe_rt.cpp.

Member Function Documentation

◆ CalcDivShape()

void mfem::RT_HexahedronElement::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 from mfem::FiniteElement.

Definition at line 582 of file fe_rt.cpp.

◆ CalcVShape() [1/2]

void mfem::RT_HexahedronElement::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.

Reimplemented from mfem::FiniteElement.

Definition at line 492 of file fe_rt.cpp.

◆ CalcVShape() [2/2]

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

inlinevirtual

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.

Reimplemented from mfem::FiniteElement.

Definition at line 114 of file fe_rt.hpp.

◆ GetFaceMap()

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

virtual

Return the mapping from lexicographically ordered face DOFs to lexicographically ordered element DOFs corresponding to local face face_id.

Reimplemented from mfem::FiniteElement.

Definition at line 711 of file fe_rt.cpp.

◆ GetLocalInterpolation()

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

inlinevirtual

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 119 of file fe_rt.hpp.

◆ GetLocalRestriction()

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

inlinevirtual

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.

Definition at line 122 of file fe_rt.hpp.

◆ GetTransferMatrix()

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

inlinevirtual

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.

Definition at line 125 of file fe_rt.hpp.

◆ Project() [1/3]

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 from mfem::FiniteElement.

Definition at line 523 of file fe_base.cpp.

◆ Project() [2/3]

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

inlinevirtual

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 142 of file fe_rt.hpp.

◆ Project() [3/3]

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

inlinevirtual

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 130 of file fe_rt.hpp.

◆ ProjectCurl()

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

inlinevirtual

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 from mfem::FiniteElement.

Definition at line 145 of file fe_rt.hpp.

◆ ProjectFromNodes()

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

inlinevirtual

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 from mfem::FiniteElement.

Definition at line 136 of file fe_rt.hpp.

◆ ProjectIntegrated()

void mfem::RT_HexahedronElement::ProjectIntegrated	(	VectorCoefficient &	vc,
		ElementTransformation &	Trans,
		Vector &	dofs ) const

protected

Definition at line 661 of file fe_rt.cpp.

◆ ProjectMatrixCoefficient()

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

inlinevirtual

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 139 of file fe_rt.hpp.

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

fem/fe/fe_rt.hpp
fem/fe/fe_rt.cpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RT_HexahedronElement()

Member Function Documentation

◆ CalcDivShape()

◆ CalcVShape() [1/2]

◆ CalcVShape() [2/2]

◆ GetFaceMap()

◆ GetLocalInterpolation()

◆ GetLocalRestriction()

◆ GetTransferMatrix()

◆ Project() [1/3]

◆ Project() [2/3]

◆ Project() [3/3]

◆ ProjectCurl()

◆ ProjectFromNodes()

◆ ProjectIntegrated()

◆ ProjectMatrixCoefficient()