MFEM  v4.2.0 Finite element discretization library

Arbitrary order Raviart-Thomas elements in 2D on a square. More...

#include <fe.hpp>

[legend]
[legend]

## Public Member Functions

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

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...

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

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

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

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

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

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

virtual void Project (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
Compute the embedding/projection matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the projection depends on it. More...

Compute the discrete gradient matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it. More...

virtual void ProjectCurl (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
Compute the discrete curl matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it. More...

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)

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

~VectorTensorFiniteElement ()

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

FiniteElement (D, G, Do, O, F)

Jinv (D)

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...

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...

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...

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 IntegrationRuleGetNodes () const
Get a const reference to the nodes of the element. More...

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

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

virtual void 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 ProjectDiv (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
Compute the discrete divergence matrix from the given FiniteElement onto 'this' FiniteElement. The ElementTransformation is included to support cases when the matrix depends on it. More...

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

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::BasisGetBasis1D () 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. More...

Public Types inherited from mfem::FiniteElement
enum  RangeType { SCALAR, VECTOR }
Enumeration for range_type and deriv_range_type. More...

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

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

Public 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). 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 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. More...

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 double *nk, const Array< int > &d2n, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const

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

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

void Project_RT (const double *nk, const Array< int > &d2n, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const

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

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

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

void Project_ND (const double *tk, const Array< int > &d2t, VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const

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

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

void Project_ND (const double *tk, const Array< int > &d2t, const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const

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

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

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

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

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

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

Protected Attributes inherited from mfem::VectorTensorFiniteElement
Poly_1D::Basiscbasis1d

Poly_1D::Basisobasis1d

Protected Attributes inherited from mfem::VectorFiniteElement
DenseMatrix J

DenseMatrix Jinv

DenseMatrix curlshape

DenseMatrix curlshape_J

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

Container for all DofToQuad objects created by the FiniteElement. More...

Protected Attributes inherited from mfem::TensorBasisElement
int b_type

Array< int > dof_map

Poly_1D::Basisbasis1d

Array< int > inv_dof_map

## Detailed Description

Arbitrary order Raviart-Thomas elements in 2D on a square.

Definition at line 2671 of file fe.hpp.

## Constructor & Destructor Documentation

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

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

Definition at line 10490 of file fe.cpp.

## Member Function Documentation

 void mfem::RT_QuadrilateralElement::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 10651 of file fe.cpp.

 void mfem::RT_QuadrilateralElement::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 10604 of file fe.cpp.

 virtual void mfem::RT_QuadrilateralElement::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 2690 of file fe.hpp.

 virtual void mfem::RT_QuadrilateralElement::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 2695 of file fe.hpp.

 virtual void mfem::RT_QuadrilateralElement::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 2698 of file fe.hpp.

 virtual void mfem::RT_QuadrilateralElement::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 2701 of file fe.hpp.

 virtual void mfem::RT_QuadrilateralElement::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)

Reimplemented from mfem::FiniteElement.

Definition at line 2706 of file fe.hpp.

 virtual void mfem::RT_QuadrilateralElement::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 2715 of file fe.hpp.

 virtual void mfem::RT_QuadrilateralElement::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 2724 of file fe.hpp.

 virtual void mfem::RT_QuadrilateralElement::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 2709 of file fe.hpp.

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 2719 of file fe.hpp.

 virtual void mfem::RT_QuadrilateralElement::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 2712 of file fe.hpp.

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