MFEM v4.7.0 Finite element discretization library
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mfem::FaceRestriction Class Referenceabstract

Base class for operators that extracts Face degrees of freedom. More...

#include <restriction.hpp>

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

FaceRestriction ()

FaceRestriction (int h, int w)

virtual ~FaceRestriction ()

void Mult (const Vector &x, Vector &y) const override=0
Extract the face degrees of freedom from x into y.

virtual void AddMultTranspose (const Vector &x, Vector &y, const real_t a=1.0) const override=0
Add the face degrees of freedom x to the element degrees of freedom y.

virtual void AddMultTransposeUnsigned (const Vector &x, Vector &y, const real_t a=1.0) const
Add the face degrees of freedom x to the element degrees of freedom y ignoring the signs from DOF orientation.

virtual void AddMultTransposeInPlace (Vector &x, Vector &y) const
Add the face degrees of freedom x to the element degrees of freedom y. Perform the same computation as AddMultTranspose, but x is invalid after calling this method.

void MultTranspose (const Vector &x, Vector &y) const override
Set the face degrees of freedom in the element degrees of freedom y to the values given in x.

virtual void NormalDerivativeMult (const Vector &x, Vector &y) const
For each face, sets y to the partial derivative of x with respect to the reference coordinate whose direction is perpendicular to the face on the reference element.

virtual void NormalDerivativeAddMultTranspose (const Vector &x, Vector &y) const
Add the face reference-normal derivative degrees of freedom in x to the element degrees of freedom in y.

Public Member Functions inherited from mfem::Operator
void InitTVectors (const Operator *Po, const Operator *Ri, const Operator *Pi, Vector &x, Vector &b, Vector &X, Vector &B) const
Initializes memory for true vectors of linear system.

Operator (int s=0)
Construct a square Operator with given size s (default 0).

Operator (int h, int w)
Construct an Operator with the given height (output size) and width (input size).

int Height () const
Get the height (size of output) of the Operator. Synonym with NumRows().

int NumRows () const
Get the number of rows (size of output) of the Operator. Synonym with Height().

int Width () const
Get the width (size of input) of the Operator. Synonym with NumCols().

int NumCols () const
Get the number of columns (size of input) of the Operator. Synonym with Width().

virtual MemoryClass GetMemoryClass () const
Return the MemoryClass preferred by the Operator.

virtual void AddMult (const Vector &x, Vector &y, const real_t a=1.0) const
Operator application: y+=A(x) (default) or y+=a*A(x).

virtual void ArrayMult (const Array< const Vector * > &X, Array< Vector * > &Y) const
Operator application on a matrix: Y=A(X).

virtual void ArrayMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y) const
Action of the transpose operator on a matrix: Y=A^t(X).

virtual void ArrayAddMult (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
Operator application on a matrix: Y+=A(X) (default) or Y+=a*A(X).

virtual void ArrayAddMultTranspose (const Array< const Vector * > &X, Array< Vector * > &Y, const real_t a=1.0) const
Operator transpose application on a matrix: Y+=A^t(X) (default) or Y+=a*A^t(X).

virtual OperatorGetGradient (const Vector &x) const
Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error.

virtual void AssembleDiagonal (Vector &diag) const
Computes the diagonal entries into diag. Typically, this operation only makes sense for linear Operators. In some cases, only an approximation of the diagonal is computed.

virtual const OperatorGetProlongation () const
Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. NULL means identity.

virtual const OperatorGetRestriction () const
Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. NULL means identity.

virtual const OperatorGetOutputProlongation () const
Prolongation operator from linear algebra (linear system) vectors, to output vectors for the operator. NULL means identity.

virtual const OperatorGetOutputRestrictionTranspose () const
Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.

virtual const OperatorGetOutputRestriction () const
Restriction operator from output vectors for the operator to linear algebra (linear system) vectors. NULL means identity.

void FormLinearSystem (const Array< int > &ess_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B, int copy_interior=0)
Form a constrained linear system using a matrix-free approach.

void FormRectangularLinearSystem (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Vector &x, Vector &b, Operator *&A, Vector &X, Vector &B)
Form a column-constrained linear system using a matrix-free approach.

virtual void RecoverFEMSolution (const Vector &X, const Vector &b, Vector &x)
Reconstruct a solution vector x (e.g. a GridFunction) from the solution X of a constrained linear system obtained from Operator::FormLinearSystem() or Operator::FormRectangularLinearSystem().

void FormSystemOperator (const Array< int > &ess_tdof_list, Operator *&A)
Return in A a parallel (on truedofs) version of this square operator.

void FormRectangularSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, Operator *&A)
Return in A a parallel (on truedofs) version of this rectangular operator (including constraints).

void FormDiscreteOperator (Operator *&A)
Return in A a parallel (on truedofs) version of this rectangular operator.

void PrintMatlab (std::ostream &out, int n, int m=0) const
Prints operator with input size n and output size m in Matlab format.

virtual void PrintMatlab (std::ostream &out) const
Prints operator in Matlab format.

virtual ~Operator ()
Virtual destructor.

Type GetType () const
Return the type ID of the Operator class.

Public Types inherited from mfem::Operator
enum  DiagonalPolicy { DIAG_ZERO , DIAG_ONE , DIAG_KEEP }
Defines operator diagonal policy upon elimination of rows and/or columns. More...

enum  Type {
ANY_TYPE , MFEM_SPARSEMAT , Hypre_ParCSR , PETSC_MATAIJ ,
PETSC_MATIS , PETSC_MATSHELL , PETSC_MATNEST , PETSC_MATHYPRE ,
PETSC_MATGENERIC , Complex_Operator , MFEM_ComplexSparseMat , Complex_Hypre_ParCSR ,
Complex_DenseMat , MFEM_Block_Matrix , MFEM_Block_Operator
}
Enumeration defining IDs for some classes derived from Operator. More...

Protected Member Functions inherited from mfem::Operator
void FormConstrainedSystemOperator (const Array< int > &ess_tdof_list, ConstrainedOperator *&Aout)
see FormSystemOperator()

void FormRectangularConstrainedSystemOperator (const Array< int > &trial_tdof_list, const Array< int > &test_tdof_list, RectangularConstrainedOperator *&Aout)
see FormRectangularSystemOperator()

OperatorSetupRAP (const Operator *Pi, const Operator *Po)
Returns RAP Operator of this, using input/output Prolongation matrices Pi corresponds to "P", Po corresponds to "Rt".

Protected Attributes inherited from mfem::Operator
int height
Dimension of the output / number of rows in the matrix.

int width
Dimension of the input / number of columns in the matrix.

## Detailed Description

Base class for operators that extracts Face degrees of freedom.

In order to compute quantities on the faces of a mesh, it is often useful to extract the degrees of freedom on the faces of the elements. This class provides an interface for such operations.

If the FiniteElementSpace is ordered by Ordering::byVDIM, then the expected format for the L-vector is (vdim x ndofs), otherwise if Ordering::byNODES the expected format is (ndofs x vdim), where ndofs is the total number of degrees of freedom. Since FiniteElementSpace can either be continuous or discontinuous, the degrees of freedom on a face can either be single valued or double valued, this is what we refer to as the multiplicity and is represented by the L2FaceValues enum type. The format of the output face E-vector of degrees of freedom is (face_dofs x vdim x multiplicity x nfaces), where face_dofs is the number of degrees of freedom on each face, and nfaces the number of faces of the requested FaceType (see FiniteElementSpace::GetNFbyType).

Note
Objects of this type are typically created and owned by FiniteElementSpace objects, see FiniteElementSpace::GetFaceRestriction().

Definition at line 162 of file restriction.hpp.

## ◆ FaceRestriction() [1/2]

 mfem::FaceRestriction::FaceRestriction ( )
inline

Definition at line 165 of file restriction.hpp.

## ◆ FaceRestriction() [2/2]

 mfem::FaceRestriction::FaceRestriction ( int h, int w )
inline

Definition at line 167 of file restriction.hpp.

## ◆ ~FaceRestriction()

 virtual mfem::FaceRestriction::~FaceRestriction ( )
inlinevirtual

Definition at line 169 of file restriction.hpp.

## Member Function Documentation

 virtual void mfem::FaceRestriction::AddMultTranspose ( const Vector & x, Vector & y, const real_t a = 1.0 ) const
overridepure virtual

Add the face degrees of freedom x to the element degrees of freedom y.

Parameters
 [in] x The face degrees of freedom on the face. [in,out] y The L-vector of degrees of freedom to which we add the face degrees of freedom. [in] a Scalar coefficient for addition.

Reimplemented from mfem::Operator.

 virtual void mfem::FaceRestriction::AddMultTransposeInPlace ( Vector & x, Vector & y ) const
inlinevirtual

Add the face degrees of freedom x to the element degrees of freedom y. Perform the same computation as AddMultTranspose, but x is invalid after calling this method.

Parameters
 [in,out] x The face degrees of freedom on the face. [in,out] y The L-vector of degrees of freedom to which we add the face degrees of freedom.
Note
This method is an optimization of AddMultTranspose where the x Vector is used and modified to avoid memory allocation and memcpy.

Definition at line 209 of file restriction.hpp.

 virtual void mfem::FaceRestriction::AddMultTransposeUnsigned ( const Vector & x, Vector & y, const real_t a = 1.0 ) const
inlinevirtual

Add the face degrees of freedom x to the element degrees of freedom y ignoring the signs from DOF orientation.

Reimplemented in mfem::ConformingFaceRestriction.

Definition at line 192 of file restriction.hpp.

## ◆ Mult()

 void mfem::FaceRestriction::Mult ( const Vector & x, Vector & y ) const
overridepure virtual

Extract the face degrees of freedom from x into y.

Parameters
 [in] x The L-vector of degrees of freedom. [out] y The degrees of freedom on the face, corresponding to a face E-vector.

Implements mfem::Operator.

## ◆ MultTranspose()

 void mfem::FaceRestriction::MultTranspose ( const Vector & x, Vector & y ) const
inlineoverridevirtual

Set the face degrees of freedom in the element degrees of freedom y to the values given in x.

Parameters
 [in] x The face degrees of freedom on the face. [in,out] y The L-vector of degrees of freedom to which we add the face degrees of freedom.

Reimplemented from mfem::Operator.

Definition at line 221 of file restriction.hpp.

 virtual void mfem::FaceRestriction::NormalDerivativeAddMultTranspose ( const Vector & x, Vector & y ) const
inlinevirtual

Add the face reference-normal derivative degrees of freedom in x to the element degrees of freedom in y.

see NormalDerivativeMult.

Parameters
 [in] x The degrees of freedom of the face reference-normal derivative. Is E-vector like. [in,out] y The L-vector degrees of freedom.

Reimplemented in mfem::L2FaceRestriction.

Definition at line 261 of file restriction.hpp.

## ◆ NormalDerivativeMult()

 virtual void mfem::FaceRestriction::NormalDerivativeMult ( const Vector & x, Vector & y ) const
inlinevirtual

For each face, sets y to the partial derivative of x with respect to the reference coordinate whose direction is perpendicular to the face on the reference element.

This is not the normal derivative in physical coordinates, but can be mapped to the physical normal derivative using the element Jacobian and the tangential derivatives (in reference coordinates) which can be computed from the face values (provided by Mult).

Note that due to the polynomial degree of the element mapping, the physical normal derivative may be a higher degree polynomial than the restriction of the values to the face. However, the normal derivative in reference coordinates has degree-1, and therefore can be exactly represented with the degrees of freedom of a face E-vector.

Parameters
 [in] x The L-vector degrees of freedom. [in,out] y The reference normal derivative degrees of freedom. Is E-vector like.

Reimplemented in mfem::L2FaceRestriction.

Definition at line 247 of file restriction.hpp.

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