MFEM v4.7.0 Finite element discretization library
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mfem::ScalarFiniteElement Class Reference

Class for finite elements with basis functions that return scalar values. More...

#include <fe_base.hpp>

Inheritance diagram for mfem::ScalarFiniteElement:
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Collaboration diagram for mfem::ScalarFiniteElement:
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## Public Member Functions

ScalarFiniteElement (int D, Geometry::Type G, int Do, int O, int F=FunctionSpace::Pk)
Construct ScalarFiniteElement with given.

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.

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.

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.

void ScalarLocalL2Restriction (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.

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.

int GetDim () const
Returns the reference space dimension for the finite element.

int GetRangeDim () const
Returns the vector dimension for vector-valued finite elements, which is also the dimension of the interpolation operation.

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

Geometry::Type GetGeomType () const
Returns the Geometry::Type of the reference element.

int GetDof () const
Returns the number of degrees of freedom in the finite element.

int GetOrder () const
Returns the order of the finite element. In the case of anisotropic orders, returns the maximum order.

bool HasAnisotropicOrders () const
Returns true if the FiniteElement basis may be using different orders/degrees in different spatial directions.

const int * GetAnisotropicOrders () const
Returns an array containing the anisotropic orders/degrees.

int Space () const
Returns the type of FunctionSpace on the element.

int GetRangeType () const
Returns the FiniteElement::RangeType of the element, one of {SCALAR, VECTOR}.

int GetDerivRangeType () const
Returns the FiniteElement::RangeType of the element derivative, either SCALAR or VECTOR.

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}.

int GetDerivType () const
Returns the FiniteElement::DerivType of the element describing the spatial derivative method implemented, one of {NONE, GRAD, DIV, CURL}.

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}.

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.

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.

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.

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.

const IntegrationRuleGetNodes () const
Get a const reference to the nodes of the element.

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.

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.

void CalcPhysVShape (ElementTransformation &Trans, DenseMatrix &shape) const
Equivalent to the CalcVShape() method with the same arguments.

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.

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.

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.

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.

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.

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.

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.

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.

virtual void CalcPhysLinLaplacian (ElementTransformation &Trans, Vector &Laplacian) 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.

virtual void GetLocalRestriction (ElementTransformation &Trans, DenseMatrix &R) const
Return a local restriction matrix R (Dof x Dof) mapping fine dofs to coarse dofs.

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.

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.

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)

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.

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.

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.

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.

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.

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.

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.

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

virtual void GetFaceMap (const int face_id, Array< int > &face_map) const
Return the mapping from lexicographic face DOFs to lexicographic element DOFs for the given local face face_id.

virtual const StatelessDofTransformationGetDofTransformation () const
Return a DoF transformation object for this particular type of basis.

virtual ~FiniteElement ()
Deconstruct the FiniteElement.

## Static Protected Member Functions

static const ScalarFiniteElementCheckScalarFE (const FiniteElement &fe)

Public Types inherited from mfem::FiniteElement
enum  RangeType { UNKNOWN_RANGE_TYPE = -1 , SCALAR , VECTOR }
Enumeration for range_type and deriv_range_type. More...

enum  MapType {
UNKNOWN_MAP_TYPE = -1 , 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).

static bool IsOpenType (int b_type)
Return true if the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).

static int VerifyClosed (int b_type)
Ensure that the BasisType of b_type is closed (has Quadrature1D points on the boundary).

static int VerifyOpen (int b_type)
Ensure that the BasisType of b_type is open (doesn't have Quadrature1D points on the boundary).

static int VerifyNodal (int b_type)
Ensure that the BasisType of b_type nodal (satisfies the interpolation property).

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

int vdim
Vector dimension of vector-valued basis functions.

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

Geometry::Type geom_type
Geometry::Type of the reference element.

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.

int order
Order/degree of the shape functions.

int orders [Geometry::MaxDim]
Anisotropic orders.

IntegrationRule Nodes

DenseMatrix vshape

Container for all DofToQuad objects created by the FiniteElement.

## Detailed Description

Class for finite elements with basis functions that return scalar values.

Definition at line 655 of file fe_base.hpp.

## ◆ ScalarFiniteElement()

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

Construct ScalarFiniteElement 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 673 of file fe_base.hpp.

## ◆ CheckScalarFE()

 static const ScalarFiniteElement & mfem::ScalarFiniteElement::CheckScalarFE ( const FiniteElement & fe )
inlinestaticprotected

Definition at line 658 of file fe_base.hpp.

## ◆ NodalLocalInterpolation()

 void mfem::ScalarFiniteElement::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.

Definition at line 522 of file fe_base.cpp.

## ◆ ScalarLocalInterpolation()

 void mfem::ScalarFiniteElement::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.

If the "fine" elements cannot represent all basis functions of the "coarse" element, then boundary values from different sub-elements are generally different.

Definition at line 561 of file fe_base.cpp.

## ◆ ScalarLocalL2Restriction()

 void mfem::ScalarFiniteElement::ScalarLocalL2Restriction ( 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.

If the "fine" elements cannot represent all basis functions of the "coarse" element, then boundary values from different sub-elements are generally different.

Definition at line 602 of file fe_base.cpp.

## ◆ SetMapType()

 virtual void mfem::ScalarFiniteElement::SetMapType ( int M )
inlinevirtual

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.

Reimplemented in mfem::NodalTensorFiniteElement.

Definition at line 681 of file fe_base.hpp.

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