MFEM  v3.4 Finite element discretization library
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 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.

## ◆ 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.

Implements CalcDShape methods.

DIV

Implements CalcDivShape methods.

CURL

Implements CalcCurlShape methods.

Definition at line 195 of file fe.hpp.

## ◆ FiniteElement()

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

Construct FiniteElement with given

Parameters
 D Reference space dimension G Geometry type (of type Geometry::Type) Do Number of degrees of freedom in the FiniteElement O Order/degree of the FiniteElement F FunctionSpace 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.

## ◆ 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.

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.

Definition at line 54 of file fe.cpp.

## ◆ CalcDShape()

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

## ◆ 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}

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

## ◆ CalcVShape() [1/2]

 void mfem::FiniteElement::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.

Definition at line 40 of file fe.cpp.

## ◆ 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.

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

Return the local interpolation matrix I (Dof x Dof) where the fine element is the image of the base geometry under the given transformation.

Definition at line 111 of file fe.cpp.

## ◆ 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.

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

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)

Definition at line 130 of file fe.cpp.

## ◆ Project() [3/3]

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

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.

Definition at line 148 of file fe.cpp.

## ◆ 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.

Definition at line 163 of file fe.cpp.

## ◆ ProjectDelta()

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

Compute a representation (up to multiplicative constant) for the delta function at the vertex with the given index.

Definition at line 142 of file fe.cpp.

## ◆ 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.

 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.

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.

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.

## ◆ 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: