#include <fe_nd.hpp>

Inheritance diagram for mfem::ND_FuentesPyramidElement:

Collaboration diagram for mfem::ND_FuentesPyramidElement:

Public Member Functions
	ND_FuentesPyramidElement (const int p, const int cb_type=BasisType::GaussLobatto, const int ob_type=BasisType::GaussLegendre)

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	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	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	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	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	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.

void	CalcRawVShape (const IntegrationPoint &ip, DenseMatrix &shape) const

void	CalcRawCurlShape (const IntegrationPoint &ip, DenseMatrix &dshape) const

real_t	GetZetaMax () const

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::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.

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.

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

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.

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::FuentesPyramid
	FuentesPyramid ()=default

void	phi_E (int p, Vector s, const DenseMatrix &grad_s, Vector &u, DenseMatrix &grad_u) const

void	phi_Q (int p, Vector s, Vector t, DenseMatrix &u) const

void	phi_Q (int p, Vector s, const DenseMatrix &grad_s, Vector t, const DenseMatrix &grad_t, DenseMatrix &u, DenseTensor &grad_u) const

void	phi_T (int p, Vector nu, DenseMatrix &u) const

void	phi_T (int p, Vector nu, const DenseMatrix &grad_nu, DenseMatrix &u, DenseTensor &grad_u) const

void	E_E (int p, Vector s, Vector sds, DenseMatrix &u) const

void	E_E (int p, Vector s, const DenseMatrix &grad_s, DenseMatrix &u, DenseMatrix &curl_u) const

void	E_Q (int p, Vector s, Vector ds, Vector t, DenseTensor &u) const

void	E_Q (int p, Vector s, const DenseMatrix &grad_s, Vector t, const DenseMatrix &grad_t, DenseTensor &u, DenseTensor &curl_u) const

void	E_T (int p, Vector s, Vector sds, DenseTensor &u) const

void	E_T (int p, Vector s, const DenseMatrix &grad_s, DenseTensor &u, DenseTensor &curl_u) const

void	V_Q (int p, Vector s, Vector ds, Vector t, Vector dt, DenseTensor &u) const

void	V_T (int p, Vector s, Vector sdsxds, DenseTensor &u) const

void	V_T (int p, Vector s, Vector sdsxds, real_t dsdsxds, DenseTensor &u, DenseMatrix &du) const

void	VT_T (int p, Vector s, Vector sds, Vector sdsxds, real_t mu, Vector grad_mu, DenseTensor &u) const

void	VT_T (int p, Vector s, Vector sds, Vector sdsxds, Vector grad_s2, real_t mu, Vector grad_mu, DenseTensor &u, DenseMatrix &du) const

void	V_L (int p, Vector sx, const DenseMatrix &grad_sx, Vector sy, const DenseMatrix &grad_sy, real_t t, Vector grad_t, DenseTensor &u) const

void	V_R (int p, Vector s, const DenseMatrix &grad_s, real_t mu, Vector grad_mu, real_t t, Vector grad_t, DenseMatrix &u) 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...

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::FuentesPyramid
static bool	CheckZ (real_t z)

static real_t	lam1 (real_t x, real_t y, real_t z)
	Pyramid "Affine" Coordinates.

static real_t	lam2 (real_t x, real_t y, real_t z)

static real_t	lam3 (real_t x, real_t y, real_t z)

static real_t	lam4 (real_t x, real_t y, real_t z)

static real_t	lam5 (real_t x, real_t y, real_t z)

static Vector	grad_lam1 (real_t x, real_t y, real_t z)
	Gradients of the "Affine" Coordinates.

static Vector	grad_lam2 (real_t x, real_t y, real_t z)

static Vector	grad_lam3 (real_t x, real_t y, real_t z)

static Vector	grad_lam4 (real_t x, real_t y, real_t z)

static Vector	grad_lam5 (real_t x, real_t y, real_t z)

static Vector	lam15 (real_t x, real_t y, real_t z)
	Two component vectors associated with edges touching the apex.

static Vector	lam25 (real_t x, real_t y, real_t z)

static Vector	lam35 (real_t x, real_t y, real_t z)

static Vector	lam45 (real_t x, real_t y, real_t z)

static DenseMatrix	grad_lam15 (real_t x, real_t y, real_t z)
	Gradients of the above two component vectors.

static DenseMatrix	grad_lam25 (real_t x, real_t y, real_t z)

static DenseMatrix	grad_lam35 (real_t x, real_t y, real_t z)

static DenseMatrix	grad_lam45 (real_t x, real_t y, real_t z)

static Vector	lam15_grad_lam15 (real_t x, real_t y, real_t z)
	Computes $λ_{i} \nabla λ_{5} - λ_{5} \nabla λ_{i}$ .

static Vector	lam25_grad_lam25 (real_t x, real_t y, real_t z)

static Vector	lam35_grad_lam35 (real_t x, real_t y, real_t z)

static Vector	lam45_grad_lam45 (real_t x, real_t y, real_t z)

static Vector	lam125 (real_t x, real_t y, real_t z)
	Three component vectors associated with triangular faces.

static Vector	lam235 (real_t x, real_t y, real_t z)

static Vector	lam345 (real_t x, real_t y, real_t z)

static Vector	lam435 (real_t x, real_t y, real_t z)

static Vector	lam415 (real_t x, real_t y, real_t z)

static Vector	lam145 (real_t x, real_t y, real_t z)

static Vector	lam125_grad_lam125 (real_t x, real_t y, real_t z)

static Vector	lam235_grad_lam235 (real_t x, real_t y, real_t z)

static Vector	lam345_grad_lam345 (real_t x, real_t y, real_t z)

static Vector	lam435_grad_lam435 (real_t x, real_t y, real_t z)

static Vector	lam415_grad_lam415 (real_t x, real_t y, real_t z)

static Vector	lam145_grad_lam145 (real_t x, real_t y, real_t z)

static real_t	div_lam125_grad_lam125 (real_t x, real_t y, real_t z)
	Divergences of the above "normal" vector functions divided by 3.

static real_t	div_lam235_grad_lam235 (real_t x, real_t y, real_t z)

static real_t	div_lam345_grad_lam345 (real_t x, real_t y, real_t z)

static real_t	div_lam435_grad_lam435 (real_t x, real_t y, real_t z)

static real_t	div_lam415_grad_lam415 (real_t x, real_t y, real_t z)

static real_t	div_lam145_grad_lam145 (real_t x, real_t y, real_t z)

static real_t	mu0 (real_t z)

static real_t	mu1 (real_t z)

static Vector	grad_mu0 (real_t z)

static Vector	grad_mu1 (real_t z)

static Vector	mu01 (real_t z)

static DenseMatrix	grad_mu01 (real_t z)

static real_t	mu0 (real_t z, const Vector &xy, unsigned int ab)

static real_t	mu1 (real_t z, const Vector &xy, unsigned int ab)

static Vector	grad_mu0 (real_t z, const Vector xy, unsigned int ab)

static Vector	grad_mu1 (real_t z, const Vector xy, unsigned int ab)

static Vector	mu01 (real_t z, Vector xy, unsigned int ab)

static DenseMatrix	grad_mu01 (real_t z, Vector xy, unsigned int ab)

static Vector	mu01_grad_mu01 (real_t z, Vector xy, unsigned int ab)

static real_t	nu0 (real_t z, Vector xy, unsigned int ab)

static real_t	nu1 (real_t z, Vector xy, unsigned int ab)

static real_t	nu2 (real_t z, Vector xy, unsigned int ab)

static Vector	grad_nu0 (real_t z, const Vector xy, unsigned int ab)

static Vector	grad_nu1 (real_t z, const Vector xy, unsigned int ab)

static Vector	grad_nu2 (real_t z, const Vector xy, unsigned int ab)

static Vector	nu01 (real_t z, Vector xy, unsigned int ab)

static Vector	nu12 (real_t z, Vector xy, unsigned int ab)

static Vector	nu012 (real_t z, Vector xy, unsigned int ab)

static Vector	nu120 (real_t z, Vector xy, unsigned int ab)

static DenseMatrix	grad_nu01 (real_t z, Vector xy, unsigned int ab)

static DenseMatrix	grad_nu012 (real_t z, Vector xy, unsigned int ab)

static DenseMatrix	grad_nu120 (real_t z, Vector xy, unsigned int ab)

static Vector	nu01_grad_nu01 (real_t z, Vector xy, unsigned int ab)

static Vector	nu12_grad_nu12 (real_t z, Vector xy, unsigned int ab)

static Vector	nu012_grad_nu012 (real_t z, Vector xy, unsigned int ab)

static void	CalcScaledLegendre (int p, real_t x, real_t t, real_t *u)
	Shifted and Scaled Legendre Polynomials.

static void	CalcScaledLegendre (int p, real_t x, real_t t, real_t u, real_t dudx, real_t *dudt)

static void	CalcScaledLegendre (int p, real_t x, real_t t, Vector &u)

static void	CalcScaledLegendre (int p, real_t x, real_t t, Vector &u, Vector &dudx, Vector &dudt)

static void	CalcIntegratedLegendre (int p, real_t x, real_t t, real_t *u)
	Integrated Legendre Polynomials.

static void	CalcIntegratedLegendre (int p, real_t x, real_t t, real_t u, real_t dudx, real_t *dudt)

static void	CalcIntegratedLegendre (int p, real_t x, real_t t, Vector &u)

static void	CalcIntegratedLegendre (int p, real_t x, real_t t, Vector &u, Vector &dudx, Vector &dudt)

static void	CalcHomogenizedScaLegendre (int p, real_t s0, real_t s1, real_t *u)

static void	CalcHomogenizedScaLegendre (int p, real_t s0, real_t s1, real_t u, real_t duds0, real_t *duds1)

static void	CalcHomogenizedScaLegendre (int p, real_t s0, real_t s1, Vector &u)

static void	CalcHomogenizedScaLegendre (int p, real_t s0, real_t s1, Vector &u, Vector &duds0, Vector &duds1)

static void	CalcHomogenizedIntLegendre (int p, real_t t0, real_t t1, real_t *u)

static void	CalcHomogenizedIntLegendre (int p, real_t t0, real_t t1, real_t u, real_t dudt0, real_t *dudt1)

static void	CalcHomogenizedIntLegendre (int p, real_t t0, real_t t1, Vector &u)

static void	CalcHomogenizedIntLegendre (int p, real_t t0, real_t t1, Vector &u, Vector &dudt0, Vector &dudt1)

static void	CalcScaledJacobi (int p, real_t alpha, real_t x, real_t t, real_t *u)
	Shifted and Scaled Jacobi Polynomials.

static void	CalcScaledJacobi (int p, real_t alpha, real_t x, real_t t, real_t u, real_t dudx, real_t *dudt)

static void	CalcScaledJacobi (int p, real_t alpha, real_t x, real_t t, Vector &u)

static void	CalcScaledJacobi (int p, real_t alpha, real_t x, real_t t, Vector &u, Vector &dudx, Vector &dudt)

static void	CalcIntegratedJacobi (int p, real_t alpha, real_t x, real_t t, real_t *u)
	Integrated Jacobi Polynomials.

static void	CalcIntegratedJacobi (int p, real_t alpha, real_t x, real_t t, real_t u, real_t dudx, real_t *dudt)

static void	CalcIntegratedJacobi (int p, real_t alpha, real_t x, real_t t, Vector &u)

static void	CalcIntegratedJacobi (int p, real_t alpha, real_t x, real_t t, Vector &u, Vector &dudx, Vector &dudt)

static void	CalcHomogenizedScaJacobi (int p, real_t alpha, real_t t0, real_t t1, real_t *u)

static void	CalcHomogenizedScaJacobi (int p, real_t alpha, real_t t0, real_t t1, real_t u, real_t dudt0, real_t *dudt1)

static void	CalcHomogenizedScaJacobi (int p, real_t alpha, real_t t0, real_t t1, Vector &u)

static void	CalcHomogenizedScaJacobi (int p, real_t alpha, real_t t0, real_t t1, Vector &u, Vector &dudt0, Vector &dudt1)

static void	CalcHomogenizedIntJacobi (int p, real_t alpha, real_t t0, real_t t1, real_t *u)

static void	CalcHomogenizedIntJacobi (int p, real_t alpha, real_t t0, real_t t1, real_t u, real_t dudt0, real_t *dudt1)

static void	CalcHomogenizedIntJacobi (int p, real_t alpha, real_t t0, real_t t1, Vector &u)

static void	CalcHomogenizedIntJacobi (int p, real_t alpha, real_t t0, real_t t1, Vector &u, Vector &dudt0, Vector &dudt1)

static void	phi_E (int p, real_t s0, real_t s1, real_t *u)

static void	phi_E (int p, real_t s0, real_t s1, real_t u, real_t duds0, real_t *duds1)

static void	phi_E (int p, Vector s, Vector &u)

static void	phi_E (int p, Vector s, Vector &u, DenseMatrix &duds)

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

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

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.

Static Protected Attributes inherited from mfem::FuentesPyramid
static constexpr real_t	one = 1.0

static constexpr real_t	zero = 0.0

static constexpr real_t	apex_tol = 1e-8

Detailed Description

Arbitrary order H(Curl) basis functions defined on pyramid-shaped elements

This implementation is closely based on the finite elements described in section 9.2 of the paper "Orientation embedded high order shape functions for the exact sequence elements of all shapes" by Federico Fuentes, Brendan Keith, Leszek Demkowicz, and Sriram Nagaraj, see https://doi.org/10.1016/j.camwa.2015.04.027.

Definition at line 427 of file fe_nd.hpp.

Constructor & Destructor Documentation

◆ ND_FuentesPyramidElement()

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

Definition at line 1591 of file fe_nd.cpp.

Member Function Documentation

◆ CalcCurlShape()

void mfem::ND_FuentesPyramidElement::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 from mfem::FiniteElement.

Definition at line 1811 of file fe_nd.cpp.

◆ CalcRawCurlShape()

void mfem::ND_FuentesPyramidElement::CalcRawCurlShape	(	const IntegrationPoint &	ip,
		DenseMatrix &	dshape ) const

Definition at line 1862 of file fe_nd.cpp.

◆ CalcRawVShape()

void mfem::ND_FuentesPyramidElement::CalcRawVShape	(	const IntegrationPoint &	ip,
		DenseMatrix &	shape ) const

Definition at line 1840 of file fe_nd.cpp.

◆ CalcVShape() [1/2]

void mfem::ND_FuentesPyramidElement::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 1786 of file fe_nd.cpp.

◆ CalcVShape() [2/2]

virtual void mfem::ND_FuentesPyramidElement::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 491 of file fe_nd.hpp.

◆ GetLocalInterpolation()

virtual void mfem::ND_FuentesPyramidElement::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 496 of file fe_nd.hpp.

◆ GetLocalRestriction()

virtual void mfem::ND_FuentesPyramidElement::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 499 of file fe_nd.hpp.

◆ GetTransferMatrix()

virtual void mfem::ND_FuentesPyramidElement::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 502 of file fe_nd.hpp.

◆ GetZetaMax()

real_t mfem::ND_FuentesPyramidElement::GetZetaMax ( ) const

inline

Definition at line 535 of file fe_nd.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 529 of file fe_base.cpp.

◆ Project() [2/3]

virtual void mfem::ND_FuentesPyramidElement::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 515 of file fe_nd.hpp.

◆ Project() [3/3]

virtual void mfem::ND_FuentesPyramidElement::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 509 of file fe_nd.hpp.

◆ ProjectCurl()

virtual void mfem::ND_FuentesPyramidElement::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 524 of file fe_nd.hpp.

◆ ProjectGrad()

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

inlinevirtual

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 519 of file fe_nd.hpp.

◆ ProjectMatrixCoefficient()

virtual void mfem::ND_FuentesPyramidElement::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 512 of file fe_nd.hpp.

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

fem/fe/fe_nd.hpp
fem/fe/fe_nd.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ND_FuentesPyramidElement()

Member Function Documentation

◆ CalcCurlShape()

◆ CalcRawCurlShape()

◆ CalcRawVShape()

◆ CalcVShape() [1/2]

◆ CalcVShape() [2/2]

◆ GetLocalInterpolation()

◆ GetLocalRestriction()

◆ GetTransferMatrix()

◆ GetZetaMax()

◆ Project() [1/3]

◆ Project() [2/3]

◆ Project() [3/3]

◆ ProjectCurl()

◆ ProjectGrad()

◆ ProjectMatrixCoefficient()