MFEM  v4.5.1 Finite element discretization library
mfem::NodalFiniteElement Class Reference

Class for standard nodal finite elements. More...

#include <fe_base.hpp>

Inheritance diagram for mfem::NodalFiniteElement:
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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)
Construct NodalFiniteElement with given. 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 (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 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 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 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...

const Array< int > & GetLexicographicOrdering () const
Get an Array<int> that maps lexicographically ordered indices to the indices of the respective nodes/dofs/basis functions. More...

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

c_shape (dof)

virtual void SetMapType (int M)
Set the FiniteElement::MapType of the element to either VALUE or INTEGRAL. Also sets the FiniteElement::DerivType to GRAD if the FiniteElement::MapType is VALUE. More...

void NodalLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
Get the matrix I that defines nodal interpolation between this element and the refined element fine_fe. More...

void ScalarLocalInterpolation (ElementTransformation &Trans, DenseMatrix &I, const ScalarFiniteElement &fine_fe) const
Get matrix I "Interpolation" defined through local L2-projection in the space defined by the fine_fe. More...

void ScalarLocalRestriction (ElementTransformation &Trans, DenseMatrix &R, const ScalarFiniteElement &coarse_fe) const
Get restriction matrix R defined through local L2-projection in the space defined by the coarse_fe. More...

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

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...

int GetVDim () const
Returns the vector dimension for vector-valued finite elements. More...

int GetCurlDim () const
Returns the dimension of the curl for vector-valued finite elements. 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...

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
Get a const reference to the nodes of the element. 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...

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...

virtual 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 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 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 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...

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

## Protected Member Functions

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

Protected Member Functions inherited from mfem::ScalarFiniteElement

## Protected Attributes

Array< int > lex_ordering

Protected Attributes inherited from mfem::ScalarFiniteElement
Vector c_shape

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

int vdim
Vector dimension of vector-valued basis functions. More...

int cdim
Dimension of curl for vector-valued basis functions. 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...

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...

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...

Public Attributes inherited from mfem::ScalarFiniteElement

G

Do

O

F

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

## Detailed Description

Class for standard nodal finite elements.

Definition at line 706 of file fe_base.hpp.

## Constructor & Destructor Documentation

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

Construct NodalFiniteElement 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 722 of file fe_base.hpp.

## Member Function Documentation

 const Array& mfem::NodalFiniteElement::GetLexicographicOrdering ( ) const
inline

Get an Array<int> that maps lexicographically ordered indices to the indices of the respective nodes/dofs/basis functions.

Lexicographic ordering of nodes is defined in terms of reference-space coordinates (x,y,z). Lexicographically ordered nodes are listed first in order of increasing x-coordinate, and then in order of increasing y-coordinate, and finally in order of increasing z-coordinate.

For example, the six nodes of a quadratic triangle are lexicographically ordered as follows:

5 |\ 3 4 | \ 0-1-2

The resulting array may be empty if the DOFs are already ordered lexicographically, or if the finite element does not support creating this permutation. The array returned is the same as the array given by TensorBasisElement::GetDofMap, but it is also available for non-tensor elements.

Definition at line 781 of file fe_base.hpp.

 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 726 of file fe_base.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 627 of file fe_base.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 FiniteElement::MapType.

Reimplemented from mfem::FiniteElement.

Reimplemented in mfem::NodalTensorFiniteElement.

Definition at line 733 of file fe_base.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.

The approximation used to project is usually local interpolation of degrees of freedom. The derived class could use other methods not implemented yet, e.g. local L2 projection.

Reimplemented from mfem::FiniteElement.

Definition at line 656 of file fe_base.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)

The approximation used to project is usually local interpolation of degrees of freedom. The derived class could use other methods not implemented yet, e.g. local L2 projection.

Reimplemented from mfem::FiniteElement.

Definition at line 673 of file fe_base.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 717 of file fe_base.cpp.

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

Definition at line 587 of file fe_base.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 805 of file fe_base.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 776 of file fe_base.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 695 of file fe_base.cpp.

## Member Data Documentation

 Array mfem::NodalFiniteElement::lex_ordering
protected

Definition at line 709 of file fe_base.hpp.

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