MFEM  v3.3
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:
[legend]
Collaboration diagram for mfem::FiniteElement:
[legend]

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. 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
 
virtual void Project (Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
 
virtual void Project (VectorCoefficient &vc, ElementTransformation &Trans, 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 int VerifyClosed (int pt_type)
 
static int VerifyOpen (int pt_type)
 

Protected Attributes

int Dim
 Dimension of reference space. More...
 
int GeomType
 Geometry::Type of the reference element. More...
 
int Dof
 Number of degrees of freedom. More...
 
int Order
 Order/degree of the shape functions. More...
 
int FuncSpace
 
int RangeType
 
int MapType
 
int DerivType
 
int DerivRangeType
 
int DerivMapType
 
IntegrationRule Nodes
 
DenseMatrix vshape
 

Detailed Description

Abstract class for Finite Elements.

Definition at line 46 of file fe.hpp.

Member Enumeration Documentation

anonymous enum

Enumeration for RangeType and DerivRangeType.

Enumerator
SCALAR 
VECTOR 

Definition at line 62 of file fe.hpp.

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 84 of file fe.hpp.

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 99 of file fe.hpp.

Constructor & Destructor Documentation

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 24 of file fe.cpp.

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

Definition at line 278 of file fe.hpp.

Member Function Documentation

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 66 of file fe.cpp.

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 52 of file fe.cpp.

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.

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 103 of file fe.cpp.

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 73 of file fe.cpp.

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 59 of file fe.cpp.

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 174 of file fe.cpp.

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 164 of file fe.cpp.

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

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

Definition at line 188 of file fe.hpp.

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.

void mfem::FiniteElement::CalcVShape ( const IntegrationPoint ip,
DenseMatrix shape 
) const
virtual
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 45 of file fe.cpp.

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

Definition at line 137 of file fe.hpp.

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

Definition at line 131 of file fe.hpp.

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

Definition at line 135 of file fe.hpp.

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

Returns the reference space dimension for the finite element.

Definition at line 115 of file fe.hpp.

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

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

Definition at line 121 of file fe.hpp.

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

Reimplemented in mfem::Linear3DFiniteElement.

Definition at line 98 of file fe.cpp.

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

Returns the Geometry::Type of the reference element.

Definition at line 118 of file fe.hpp.

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

Definition at line 133 of file fe.hpp.

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

Definition at line 166 of file fe.hpp.

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

Returns the order of the finite element.

Definition at line 124 of file fe.hpp.

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

Definition at line 129 of file fe.hpp.

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 115 of file fe.cpp.

void mfem::FiniteElement::Project ( VectorCoefficient vc,
ElementTransformation Trans,
Vector dofs 
) const
virtual
void mfem::FiniteElement::Project ( const FiniteElement fe,
ElementTransformation Trans,
DenseMatrix I 
) const
virtual
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 148 of file fe.cpp.

void mfem::FiniteElement::ProjectDelta ( int  vertex,
Vector dofs 
) const
virtual
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 156 of file fe.cpp.

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 140 of file fe.cpp.

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

Returns the type of space on each element.

Definition at line 127 of file fe.hpp.

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

Definition at line 280 of file fe.hpp.

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

Definition at line 287 of file fe.hpp.

Member Data Documentation

int mfem::FiniteElement::DerivMapType
protected

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::DerivRangeType
protected

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::DerivType
protected

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::Dim
protected

Dimension of reference space.

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::Dof
protected

Number of degrees of freedom.

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::FuncSpace
protected

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::GeomType
protected

Geometry::Type of the reference element.

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::MapType
protected

Definition at line 49 of file fe.hpp.

IntegrationRule mfem::FiniteElement::Nodes
protected

Definition at line 55 of file fe.hpp.

int mfem::FiniteElement::Order
protected

Order/degree of the shape functions.

Definition at line 49 of file fe.hpp.

int mfem::FiniteElement::RangeType
protected

Definition at line 49 of file fe.hpp.

DenseMatrix mfem::FiniteElement::vshape
mutableprotected

Definition at line 57 of file fe.hpp.


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