MFEM  v4.1.0 Finite element discretization library
mfem::NodalFiniteElement Class Reference

#include <fe.hpp>

Inherits mfem::ScalarFiniteElement.

Collaboration diagram for mfem::NodalFiniteElement:
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## Public Member Functions

NodalFiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk)

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 (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 Project (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const

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

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

c_shape (Dof)

void SetMapType (int M)

void NodalLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
Nodal interpolation. More...

void ScalarLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
"Interpolation" defined through local L2-projection. More...

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

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 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 &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 ProjectDelta (int vertex, Vector &dofs) const

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

virtual ~FiniteElement ()

## Protected Member Functions

void ProjectCurl_2D (const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &curl) const

Protected Member Functions inherited from mfem::ScalarFiniteElement

Public Types inherited from mfem::FiniteElement
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...

Static Public Member Functions inherited from mfem::FiniteElement
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)

Public Attributes inherited from mfem::ScalarFiniteElement

G

Do

O

F

Static Protected Member Functions inherited from mfem::ScalarFiniteElement
static const ScalarFiniteElementCheckScalarFE (const FiniteElement &fe)

Protected Attributes inherited from mfem::ScalarFiniteElement
Vector c_shape

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

Geometry::Type 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

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

## Detailed Description

Definition at line 627 of file fe.hpp.

## Constructor & Destructor Documentation

 mfem::NodalFiniteElement::NodalFiniteElement ( int D, Geometry::Type G, int Do, int O, int F = FunctionSpace::Pk )
inline

Definition at line 635 of file fe.hpp.

## Member Function Documentation

 virtual void mfem::NodalFiniteElement::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 639 of file fe.hpp.

 void mfem::NodalFiniteElement::GetLocalRestriction ( ElementTransformation & Trans, DenseMatrix & R ) const
virtual

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 586 of file fe.cpp.

 virtual void mfem::NodalFiniteElement::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 MapType.

Reimplemented from mfem::FiniteElement.

Definition at line 646 of file fe.hpp.

 void mfem::NodalFiniteElement::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 from mfem::FiniteElement.

Definition at line 615 of file fe.cpp.

 void mfem::NodalFiniteElement::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)

Reimplemented from mfem::FiniteElement.

Definition at line 632 of file fe.cpp.

 void mfem::NodalFiniteElement::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.

Reimplemented from mfem::FiniteElement.

Definition at line 676 of file fe.cpp.

 void mfem::NodalFiniteElement::ProjectCurl_2D ( const FiniteElement & fe, ElementTransformation & Trans, DenseMatrix & curl ) const
protected

Definition at line 551 of file fe.cpp.

 void mfem::NodalFiniteElement::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 from mfem::FiniteElement.

Definition at line 746 of file fe.cpp.

 void mfem::NodalFiniteElement::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 from mfem::FiniteElement.

Definition at line 717 of file fe.cpp.

 void mfem::NodalFiniteElement::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 from mfem::FiniteElement.

Definition at line 654 of file fe.cpp.

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