MFEM  v3.4
Finite element discretization library
Public Types | Public Member Functions | Static Public Member Functions | Protected Attributes | List of all members
mfem::FiniteElement Class Referenceabstract

Abstract class for Finite Elements. More...

#include <fe.hpp>

Inheritance diagram for mfem::FiniteElement:
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Collaboration diagram for mfem::FiniteElement:
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Public Types

enum  { SCALAR, VECTOR }
 Enumeration for RangeType and DerivRangeType. More...
 
enum  { VALUE, INTEGRAL, H_DIV, H_CURL }
 Enumeration for MapType: defines how reference functions are mapped to physical space. More...
 
enum  { NONE, GRAD, DIV, CURL }
 Enumeration for DerivType: defines which derivative method is implemented. More...
 

Public Member Functions

 FiniteElement (int D, int G, int Do, int O, int F=FunctionSpace::Pk)
 
int GetDim () const
 Returns the reference space dimension for the finite element. More...
 
int 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 space on each element. More...
 
int GetRangeType () const
 
int GetDerivRangeType () const
 
int GetMapType () const
 
int GetDerivType () const
 
int GetDerivMapType () const
 
virtual void CalcShape (const IntegrationPoint &ip, Vector &shape) const =0
 Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip. More...
 
void CalcPhysShape (ElementTransformation &Trans, Vector &shape) const
 Evaluate the values of all shape functions of a scalar finite element in physical space at the point described by Trans. More...
 
virtual void CalcDShape (const IntegrationPoint &ip, DenseMatrix &dshape) const =0
 Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip. More...
 
void CalcPhysDShape (ElementTransformation &Trans, DenseMatrix &dshape) const
 Evaluate the gradients of all shape functions of a scalar finite element in physical space at the point described by Trans. More...
 
const IntegrationRuleGetNodes () const
 
virtual void CalcVShape (const IntegrationPoint &ip, DenseMatrix &shape) const
 Evaluate the values of all shape functions of a vector finite element in reference space at the given point ip. More...
 
virtual void CalcVShape (ElementTransformation &Trans, DenseMatrix &shape) const
 Evaluate the values of all shape functions of a vector finite element in physical space at the point described by Trans. More...
 
void CalcPhysVShape (ElementTransformation &Trans, DenseMatrix &shape) const
 Equivalent to the CalcVShape() method with the same arguments. More...
 
virtual void CalcDivShape (const IntegrationPoint &ip, Vector &divshape) const
 Evaluate the divergence of all shape functions of a vector finite element in reference space at the given point ip. More...
 
void CalcPhysDivShape (ElementTransformation &Trans, Vector &divshape) const
 Evaluate the divergence of all shape functions of a vector finite element in physical space at the point described by Trans. More...
 
virtual void CalcCurlShape (const IntegrationPoint &ip, DenseMatrix &curl_shape) const
 Evaluate the curl of all shape functions of a vector finite element in reference space at the given point ip. More...
 
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
 
virtual void CalcHessian (const IntegrationPoint &ip, DenseMatrix &h) const
 
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 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 (Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
 
virtual void Project (VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
 
virtual void ProjectMatrixCoefficient (MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
 
virtual void ProjectDelta (int vertex, Vector &dofs) const
 
virtual void Project (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
 
virtual void ProjectGrad (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &grad) const
 
virtual void ProjectCurl (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const
 
virtual void ProjectDiv (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &div) const
 
virtual ~FiniteElement ()
 

Static Public Member Functions

static bool IsClosedType (int b_type)
 
static bool IsOpenType (int b_type)
 
static int VerifyClosed (int b_type)
 
static int VerifyOpen (int b_type)
 
static int VerifyNodal (int b_type)
 

Protected Attributes

int Dim
 Dimension of reference space. More...
 
int GeomType
 Geometry::Type of the reference element. More...
 
int FuncSpace
 
int RangeType
 
int MapType
 
int DerivType
 
int DerivRangeType
 
int DerivMapType
 
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
 

Detailed Description

Abstract class for Finite Elements.

Definition at line 140 of file fe.hpp.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumeration for RangeType and DerivRangeType.

Enumerator
SCALAR 
VECTOR 

Definition at line 158 of file fe.hpp.

◆ anonymous enum

anonymous enum

Enumeration for MapType: defines how reference functions are mapped to physical space.

A reference function, uh(xh), can be mapped to a function, u(x), on a general physical element in following ways:

VALUE       u(x) = uh(xh)
INTEGRAL    u(x) = (1/w) * uh(xh)
H_DIV       u(x) = (J/w) * uh(xh)
H_CURL      u(x) = J^{-t} * uh(xh)           (square J)
H_CURL      u(x) = J*(J^t*J)^{-1} * uh(xh)   (general J)

where

x = T(xh) is the image of the reference point xh ("x hat"),
J = J(xh) is the Jacobian matrix of the transformation T, and
w = w(xh) = / det(J),           for square J,
            \ det(J^t*J)^{1/2}, for general J,
          is the transformation weight factor.
Enumerator
VALUE 

For scalar fields; preserves point values.

INTEGRAL 

For scalar fields; preserves volume integrals.

H_DIV 

For vector fields; preserves surface integrals of the normal component

H_CURL 

For vector fields; preserves line integrals of the tangential component

Definition at line 180 of file fe.hpp.

◆ anonymous enum

anonymous enum

Enumeration for DerivType: defines which derivative method is implemented.

Each FiniteElement class implements only one type of derivative. The value returned by GetDerivType() indicates which derivative method is implemented.

Enumerator
NONE 

No derivatives implemented.

GRAD 

Implements CalcDShape methods.

DIV 

Implements CalcDivShape methods.

CURL 

Implements CalcCurlShape methods.

Definition at line 195 of file fe.hpp.

Constructor & Destructor Documentation

◆ FiniteElement()

mfem::FiniteElement::FiniteElement ( int  D,
int  G,
int  Do,
int  O,
int  F = FunctionSpace::Pk 
)

Construct FiniteElement with given

Parameters
DReference space dimension
GGeometry type (of type Geometry::Type)
DoNumber of degrees of freedom in the FiniteElement
OOrder/degree of the FiniteElement
FFunctionSpace type of the FiniteElement

Definition at line 25 of file fe.cpp.

◆ ~FiniteElement()

virtual mfem::FiniteElement::~FiniteElement ( )
inlinevirtual

Definition at line 401 of file fe.hpp.

Member Function Documentation

◆ CalcCurlShape()

void mfem::FiniteElement::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 in mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::Nedelec1TetFiniteElement, and mfem::Nedelec1HexFiniteElement.

Definition at line 68 of file fe.cpp.

◆ CalcDivShape()

void mfem::FiniteElement::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 in mfem::RT_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, mfem::RT0TetFiniteElement, mfem::RT1HexFiniteElement, mfem::RT0HexFiniteElement, mfem::RT2QuadFiniteElement, mfem::RT2TriangleFiniteElement, mfem::RT1QuadFiniteElement, mfem::RT1TriangleFiniteElement, mfem::RT0QuadFiniteElement, and mfem::RT0TriangleFiniteElement.

Definition at line 54 of file fe.cpp.

◆ CalcDShape()

virtual void mfem::FiniteElement::CalcDShape ( const IntegrationPoint ip,
DenseMatrix dshape 
) const
pure virtual

Evaluate the gradients of all shape functions of a scalar finite element in reference space at the given point ip.

Each row of the result DenseMatrix dshape contains the derivatives of one shape function. The size (Dof x Dim) of dshape must be set in advance.

Implemented in mfem::NURBS3DFiniteElement, mfem::NURBS2DFiniteElement, mfem::NURBS1DFiniteElement, mfem::L2Pos_TetrahedronElement, mfem::L2_TetrahedronElement, mfem::L2Pos_TriangleElement, mfem::L2_TriangleElement, mfem::L2Pos_HexahedronElement, mfem::L2_HexahedronElement, mfem::L2Pos_QuadrilateralElement, mfem::L2_QuadrilateralElement, mfem::L2Pos_SegmentElement, mfem::L2_SegmentElement, mfem::H1Pos_TetrahedronElement, mfem::H1Pos_TriangleElement, mfem::H1_TetrahedronElement, mfem::H1_TriangleElement, mfem::H1Pos_HexahedronElement, mfem::H1Pos_QuadrilateralElement, mfem::H1Pos_SegmentElement, mfem::H1_HexahedronElement, mfem::H1_QuadrilateralElement, mfem::H1_SegmentElement, mfem::RotTriLinearHexFiniteElement, mfem::RefinedTriLinear3DFiniteElement, mfem::RefinedBiLinear2DFiniteElement, mfem::RefinedLinear3DFiniteElement, mfem::RefinedLinear2DFiniteElement, mfem::RefinedLinear1DFiniteElement, mfem::LagrangeHexFiniteElement, mfem::P0HexFiniteElement, mfem::P0TetFiniteElement, mfem::P1TetNonConfFiniteElement, mfem::Lagrange1DFiniteElement, mfem::P2SegmentFiniteElement, mfem::P1SegmentFiniteElement, mfem::P0SegmentFiniteElement, mfem::CrouzeixRaviartQuadFiniteElement, mfem::CrouzeixRaviartFiniteElement, mfem::TriLinear3DFiniteElement, mfem::Quadratic3DFiniteElement, mfem::Linear3DFiniteElement, mfem::P0QuadFiniteElement, mfem::P0TriangleFiniteElement, mfem::Cubic3DFiniteElement, mfem::Cubic2DFiniteElement, mfem::Cubic1DFiniteElement, mfem::BiCubic2DFiniteElement, mfem::GaussBiQuad2DFiniteElement, mfem::BiQuadPos2DFiniteElement, mfem::BiQuad2DFiniteElement, mfem::GaussQuad2DFiniteElement, mfem::Quad2DFiniteElement, mfem::QuadPos1DFiniteElement, mfem::Quad1DFiniteElement, mfem::P1OnQuadFiniteElement, mfem::GaussBiLinear2DFiniteElement, mfem::GaussLinear2DFiniteElement, mfem::BiLinear2DFiniteElement, mfem::Linear2DFiniteElement, mfem::Linear1DFiniteElement, and mfem::PointFiniteElement.

◆ CalcHessian()

void mfem::FiniteElement::CalcHessian ( const IntegrationPoint ip,
DenseMatrix h 
) const
virtual

each row of h contains the upper triangular part of the hessian of one shape function; the order in 2D is {u_xx, u_xy, u_yy}

Reimplemented in mfem::Cubic2DFiniteElement, mfem::BiCubic2DFiniteElement, mfem::Quad2DFiniteElement, and mfem::BiLinear2DFiniteElement.

Definition at line 105 of file fe.cpp.

◆ CalcPhysCurlShape()

void mfem::FiniteElement::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.

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.

Definition at line 75 of file fe.cpp.

◆ CalcPhysDivShape()

void mfem::FiniteElement::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.

The size (Dof) of the result Vector divshape must be set in advance.

Definition at line 61 of file fe.cpp.

◆ CalcPhysDShape()

void mfem::FiniteElement::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.

Each row of the result DenseMatrix dshape contains the derivatives of one shape function. The size (Dof x SDim) of dshape must be set in advance, where SDim >= Dim is the physical space dimension as described by Trans.

Definition at line 189 of file fe.cpp.

◆ CalcPhysShape()

void mfem::FiniteElement::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.

The size (Dof) of the result Vector shape must be set in advance.

Definition at line 179 of file fe.cpp.

◆ CalcPhysVShape()

void mfem::FiniteElement::CalcPhysVShape ( ElementTransformation Trans,
DenseMatrix shape 
) const
inline

Equivalent to the CalcVShape() method with the same arguments.

Definition at line 292 of file fe.hpp.

◆ CalcShape()

virtual void mfem::FiniteElement::CalcShape ( const IntegrationPoint ip,
Vector shape 
) const
pure virtual

Evaluate the values of all shape functions of a scalar finite element in reference space at the given point ip.

The size (Dof) of the result Vector shape must be set in advance.

Implemented in mfem::NURBS3DFiniteElement, mfem::NURBS2DFiniteElement, mfem::NURBS1DFiniteElement, mfem::ND_SegmentElement, mfem::L2Pos_TetrahedronElement, mfem::L2_TetrahedronElement, mfem::L2Pos_TriangleElement, mfem::L2_TriangleElement, mfem::L2Pos_HexahedronElement, mfem::L2_HexahedronElement, mfem::L2Pos_QuadrilateralElement, mfem::L2_QuadrilateralElement, mfem::L2Pos_SegmentElement, mfem::L2_SegmentElement, mfem::H1Pos_TetrahedronElement, mfem::H1Pos_TriangleElement, mfem::H1_TetrahedronElement, mfem::H1_TriangleElement, mfem::H1Pos_HexahedronElement, mfem::H1Pos_QuadrilateralElement, mfem::H1Pos_SegmentElement, mfem::H1_HexahedronElement, mfem::H1_QuadrilateralElement, mfem::H1_SegmentElement, mfem::RotTriLinearHexFiniteElement, mfem::RefinedTriLinear3DFiniteElement, mfem::RefinedBiLinear2DFiniteElement, mfem::RefinedLinear3DFiniteElement, mfem::RefinedLinear2DFiniteElement, mfem::RefinedLinear1DFiniteElement, mfem::LagrangeHexFiniteElement, mfem::P0HexFiniteElement, mfem::P0TetFiniteElement, mfem::P1TetNonConfFiniteElement, mfem::Lagrange1DFiniteElement, mfem::P2SegmentFiniteElement, mfem::P1SegmentFiniteElement, mfem::P0SegmentFiniteElement, mfem::CrouzeixRaviartQuadFiniteElement, mfem::CrouzeixRaviartFiniteElement, mfem::TriLinear3DFiniteElement, mfem::Quadratic3DFiniteElement, mfem::Linear3DFiniteElement, mfem::P0QuadFiniteElement, mfem::P0TriangleFiniteElement, mfem::Cubic3DFiniteElement, mfem::Cubic2DFiniteElement, mfem::Cubic1DFiniteElement, mfem::BiCubic2DFiniteElement, mfem::GaussBiQuad2DFiniteElement, mfem::BiQuadPos2DFiniteElement, mfem::BiQuad2DFiniteElement, mfem::GaussQuad2DFiniteElement, mfem::Quad2DFiniteElement, mfem::QuadPos1DFiniteElement, mfem::Quad1DFiniteElement, mfem::P1OnQuadFiniteElement, mfem::GaussBiLinear2DFiniteElement, mfem::GaussLinear2DFiniteElement, mfem::BiLinear2DFiniteElement, mfem::Linear2DFiniteElement, mfem::Linear1DFiniteElement, and mfem::PointFiniteElement.

◆ CalcVShape() [1/2]

void mfem::FiniteElement::CalcVShape ( const IntegrationPoint ip,
DenseMatrix shape 
) const
virtual

◆ CalcVShape() [2/2]

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

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 in mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::RT_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, mfem::RT0TetFiniteElement, mfem::RT1HexFiniteElement, mfem::RT0HexFiniteElement, mfem::Nedelec1TetFiniteElement, mfem::Nedelec1HexFiniteElement, mfem::RT2QuadFiniteElement, mfem::RT2TriangleFiniteElement, mfem::RT1QuadFiniteElement, mfem::RT1TriangleFiniteElement, mfem::RT0QuadFiniteElement, and mfem::RT0TriangleFiniteElement.

Definition at line 47 of file fe.cpp.

◆ GetAnisotropicOrders()

const int* mfem::FiniteElement::GetAnisotropicOrders ( ) const
inline

Returns an array containing the anisotropic orders/degrees.

Definition at line 228 of file fe.hpp.

◆ GetDerivMapType()

int mfem::FiniteElement::GetDerivMapType ( ) const
inline

Definition at line 241 of file fe.hpp.

◆ GetDerivRangeType()

int mfem::FiniteElement::GetDerivRangeType ( ) const
inline

Definition at line 235 of file fe.hpp.

◆ GetDerivType()

int mfem::FiniteElement::GetDerivType ( ) const
inline

Definition at line 239 of file fe.hpp.

◆ GetDim()

int mfem::FiniteElement::GetDim ( ) const
inline

Returns the reference space dimension for the finite element.

Definition at line 211 of file fe.hpp.

◆ GetDof()

int mfem::FiniteElement::GetDof ( ) const
inline

Returns the number of degrees of freedom in the finite element.

Definition at line 217 of file fe.hpp.

◆ GetFaceDofs()

void mfem::FiniteElement::GetFaceDofs ( int  face,
int **  dofs,
int *  ndofs 
) const
virtual

Reimplemented in mfem::Linear3DFiniteElement.

Definition at line 100 of file fe.cpp.

◆ GetGeomType()

int mfem::FiniteElement::GetGeomType ( ) const
inline

Returns the Geometry::Type of the reference element.

Definition at line 214 of file fe.hpp.

◆ GetLocalInterpolation()

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

◆ GetMapType()

int mfem::FiniteElement::GetMapType ( ) const
inline

Definition at line 237 of file fe.hpp.

◆ GetNodes()

const IntegrationRule& mfem::FiniteElement::GetNodes ( ) const
inline

Definition at line 270 of file fe.hpp.

◆ GetOrder()

int mfem::FiniteElement::GetOrder ( ) const
inline

Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order.

Definition at line 221 of file fe.hpp.

◆ GetRangeType()

int mfem::FiniteElement::GetRangeType ( ) const
inline

Definition at line 233 of file fe.hpp.

◆ GetTransferMatrix()

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

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 MapType.

Reimplemented in mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::RT_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, mfem::PositiveFiniteElement, and mfem::NodalFiniteElement.

Definition at line 117 of file fe.cpp.

◆ HasAnisotropicOrders()

bool mfem::FiniteElement::HasAnisotropicOrders ( ) const
inline

Returns true if the FiniteElement basis may be using different orders/degrees in different spatial directions.

Definition at line 225 of file fe.hpp.

◆ IsClosedType()

static bool mfem::FiniteElement::IsClosedType ( int  b_type)
inlinestatic

Definition at line 403 of file fe.hpp.

◆ IsOpenType()

static bool mfem::FiniteElement::IsOpenType ( int  b_type)
inlinestatic

Definition at line 410 of file fe.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.

Reimplemented in mfem::BiQuadPos2DFiniteElement, mfem::PositiveFiniteElement, and mfem::NodalFiniteElement.

Definition at line 124 of file fe.cpp.

◆ Project() [2/3]

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

◆ Project() [3/3]

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

◆ ProjectCurl()

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

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 in mfem::ND_TetrahedronElement, mfem::ND_HexahedronElement, mfem::RT_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, mfem::L2_TriangleElement, and mfem::L2_QuadrilateralElement.

Definition at line 163 of file fe.cpp.

◆ ProjectDelta()

void mfem::FiniteElement::ProjectDelta ( int  vertex,
Vector dofs 
) const
virtual

◆ ProjectDiv()

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

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

Reimplemented in mfem::NodalFiniteElement.

Definition at line 171 of file fe.cpp.

◆ ProjectGrad()

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

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 in mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::RT_TriangleElement, mfem::RT_QuadrilateralElement, and mfem::NodalFiniteElement.

Definition at line 155 of file fe.cpp.

◆ ProjectMatrixCoefficient()

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

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 in mfem::ND_SegmentElement, mfem::ND_TriangleElement, mfem::ND_TetrahedronElement, mfem::ND_QuadrilateralElement, mfem::ND_HexahedronElement, mfem::RT_TetrahedronElement, mfem::RT_TriangleElement, mfem::RT_HexahedronElement, mfem::RT_QuadrilateralElement, and mfem::NodalFiniteElement.

Definition at line 136 of file fe.cpp.

◆ Space()

int mfem::FiniteElement::Space ( ) const
inline

Returns the type of space on each element.

Definition at line 231 of file fe.hpp.

◆ VerifyClosed()

static int mfem::FiniteElement::VerifyClosed ( int  b_type)
inlinestatic

Definition at line 417 of file fe.hpp.

◆ VerifyNodal()

static int mfem::FiniteElement::VerifyNodal ( int  b_type)
inlinestatic

Definition at line 428 of file fe.hpp.

◆ VerifyOpen()

static int mfem::FiniteElement::VerifyOpen ( int  b_type)
inlinestatic

Definition at line 423 of file fe.hpp.

Member Data Documentation

◆ DerivMapType

int mfem::FiniteElement::DerivMapType
protected

Definition at line 143 of file fe.hpp.

◆ DerivRangeType

int mfem::FiniteElement::DerivRangeType
protected

Definition at line 143 of file fe.hpp.

◆ DerivType

int mfem::FiniteElement::DerivType
protected

Definition at line 143 of file fe.hpp.

◆ Dim

int mfem::FiniteElement::Dim
protected

Dimension of reference space.

Definition at line 143 of file fe.hpp.

◆ Dof

int mfem::FiniteElement::Dof
mutableprotected

Number of degrees of freedom.

Definition at line 148 of file fe.hpp.

◆ FuncSpace

int mfem::FiniteElement::FuncSpace
protected

Definition at line 143 of file fe.hpp.

◆ GeomType

int mfem::FiniteElement::GeomType
protected

Geometry::Type of the reference element.

Definition at line 143 of file fe.hpp.

◆ MapType

int mfem::FiniteElement::MapType
protected

Definition at line 143 of file fe.hpp.

◆ Nodes

IntegrationRule mfem::FiniteElement::Nodes
protected

Definition at line 151 of file fe.hpp.

◆ Order

int mfem::FiniteElement::Order
mutableprotected

Order/degree of the shape functions.

Definition at line 148 of file fe.hpp.

◆ Orders

int mfem::FiniteElement::Orders[Geometry::MaxDim]
mutableprotected

Anisotropic orders.

Definition at line 150 of file fe.hpp.

◆ RangeType

int mfem::FiniteElement::RangeType
protected

Definition at line 143 of file fe.hpp.

◆ vshape

DenseMatrix mfem::FiniteElement::vshape
mutableprotected

Definition at line 153 of file fe.hpp.


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