MFEM  v4.4.0 Finite element discretization library
mfem::Operator Class Referenceabstract

Abstract operator. More...

#include <operator.hpp>

Inherited by GradT, GradT, LinearScaleOperator, LinearScaleOperator, mfem::BilinearFormExtension, mfem::BlockNonlinearForm, mfem::BlockOperator, mfem::common::IrrotationalProjector, mfem::ComplexOperator, mfem::ConformingProlongationOperator, mfem::ConstrainedOperator, mfem::ElementRestriction, mfem::EliminationProjection, mfem::FaceRestriction, mfem::FiniteElementSpace::DerefinementOperator, mfem::FiniteElementSpace::RefinementOperator, mfem::HypreParMatrix, mfem::IdentityOperator, mfem::L2ElementRestriction, mfem::L2ProjectionGridTransfer::L2Projection, mfem::L2ProjectionGridTransfer::L2Prolongation, mfem::Matrix, mfem::MixedBilinearFormExtension, mfem::NonlinearForm, mfem::NonlinearFormExtension, mfem::PANonlinearFormExtension::Gradient, mfem::ParametricBNLForm, mfem::PetscParMatrix, mfem::PRefinementTransferOperator, mfem::ProductOperator, mfem::RAPOperator, mfem::RectangularConstrainedOperator, mfem::ScaledOperator, mfem::Solver, mfem::STRUMPACKRowLocMatrix, mfem::SuperLURowLocMatrix, mfem::TBilinearForm< meshType, solFESpace, IR, IntegratorType, solVecLayout_t, complex_t, real_t, impl_traits_t >, mfem::TensorProductPRefinementTransferOperator, mfem::TimeDependentOperator, mfem::TransferOperator, mfem::TransposeOperator, mfem::TripleProductOperator, mfem::TrueTransferOperator, ReducedSystemOperator, ReducedSystemOperator, ReducedSystemOperator, ReducedSystemOperator, ReducedSystemOperator, RubberOperator, RubberOperator, TanhSumOperator, and TanhSumOperator.

## Public Types

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
}
Enumeration defining IDs for some classes derived from Operator. More...

## Public Member Functions

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. More...

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

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

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

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

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

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

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

virtual void Mult (const Vector &x, Vector &y) const =0
Operator application: y=A(x). More...

virtual void MultTranspose (const Vector &x, Vector &y) const
Action of the transpose operator: y=A^t(x). The default behavior in class Operator is to generate an error. More...

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. More...

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. More...

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

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

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

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

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

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. More...

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. More...

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(). More...

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

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). More...

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

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

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

virtual ~Operator ()
Virtual destructor. More...

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

## Protected Member Functions

void FormConstrainedSystemOperator (const Array< int > &ess_tdof_list, ConstrainedOperator *&Aout)
see FormSystemOperator() More...

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

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". More...

## Protected Attributes

int height
Dimension of the output / number of rows in the matrix. More...

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

## Detailed Description

Abstract operator.

Definition at line 24 of file operator.hpp.

## Member Enumeration Documentation

Defines operator diagonal policy upon elimination of rows and/or columns.

Enumerator
DIAG_ZERO

Set the diagonal value to zero.

DIAG_ONE

Set the diagonal value to one.

DIAG_KEEP

Keep the diagonal value.

Definition at line 46 of file operator.hpp.

 enum mfem::Operator::Type

Enumeration defining IDs for some classes derived from Operator.

This enumeration is primarily used with class OperatorHandle.

Enumerator
ANY_TYPE

ID for the base class Operator, i.e. any type.

MFEM_SPARSEMAT

ID for class SparseMatrix.

Hypre_ParCSR

ID for class HypreParMatrix.

PETSC_MATAIJ

ID for class PetscParMatrix, MATAIJ format.

PETSC_MATIS

ID for class PetscParMatrix, MATIS format.

PETSC_MATSHELL

ID for class PetscParMatrix, MATSHELL format.

PETSC_MATNEST

ID for class PetscParMatrix, MATNEST format.

PETSC_MATHYPRE

ID for class PetscParMatrix, MATHYPRE format.

PETSC_MATGENERIC

ID for class PetscParMatrix, unspecified format.

Complex_Operator

ID for class ComplexOperator.

MFEM_ComplexSparseMat

ID for class ComplexSparseMatrix.

Complex_Hypre_ParCSR

ID for class ComplexHypreParMatrix.

Definition at line 255 of file operator.hpp.

## Constructor & Destructor Documentation

 mfem::Operator::Operator ( int s = 0 )
inlineexplicit

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

Definition at line 59 of file operator.hpp.

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

Construct an Operator with the given height (output size) and width (input size).

Definition at line 63 of file operator.hpp.

 virtual mfem::Operator::~Operator ( )
inlinevirtual

Virtual destructor.

Definition at line 251 of file operator.hpp.

## Member Function Documentation

 virtual void mfem::Operator::AssembleDiagonal ( Vector & diag ) const
inlinevirtual

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.

Definition at line 107 of file operator.hpp.

 void mfem::Operator::FormConstrainedSystemOperator ( const Array< int > & ess_tdof_list, ConstrainedOperator *& Aout )
protected

Definition at line 134 of file operator.cpp.

 void mfem::Operator::FormDiscreteOperator ( Operator *& A )

Return in A a parallel (on truedofs) version of this rectangular operator.

This is similar to FormSystemOperator(), but for dof-to-dof mappings (discrete linear operators), which can also correspond to rectangular matrices. The user should provide specializations of GetProlongation() for the input dofs and GetOutputRestriction() for the output dofs in their Operator implementation that are appropriate for the two spaces the Operator maps between. These are e.g. available through the (parallel) finite element space of any (parallel) bilinear form operator. We have: A(X)=[Rout (*this) Pin](X).

Definition at line 181 of file operator.cpp.

 void mfem::Operator::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.

Assuming square operator, form the operator linear system A(X)=B, corresponding to it and the right-hand side b, by applying any necessary transformations such as: parallel assembly, conforming constraints for non-conforming AMR and eliminating boundary conditions.

Note
Static condensation and hybridization are not supported for general operators (cf. the analogous methods BilinearForm::FormLinearSystem() and ParBilinearForm::FormLinearSystem()).

The constraints are specified through the prolongation P from GetProlongation(), and restriction R from GetRestriction() methods, which are e.g. available through the (parallel) finite element space of any (parallel) bilinear form operator. We assume that the operator is square, using the same input and output space, so we have: A(X)=[P^t (*this) P](X), B=P^t(b), and X=R(x).

The vector x must contain the essential boundary condition values. These are eliminated through the ConstrainedOperator class and the vector X is initialized by setting its essential entries to the boundary conditions and all other entries to zero (copy_interior == 0) or copied from x (copy_interior != 0).

After solving the system A(X)=B, the (finite element) solution x can be recovered by calling Operator::RecoverFEMSolution() with the same vectors X, b, and x.

Note
The caller is responsible for destroying the output operator A!
If there are no transformations, X simply reuses the data of x.

Definition at line 51 of file operator.cpp.

 void mfem::Operator::FormRectangularConstrainedSystemOperator ( const Array< int > & trial_tdof_list, const Array< int > & test_tdof_list, RectangularConstrainedOperator *& Aout )
protected

Definition at line 147 of file operator.cpp.

 void mfem::Operator::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.

Form the operator linear system A(X)=B corresponding to the operator and the right-hand side b, by applying any necessary transformations such as: parallel assembly, conforming constraints for non-conforming AMR and eliminating boundary conditions.

Note
Static condensation and hybridization are not supported for general operators (cf. the method MixedBilinearForm::FormRectangularLinearSystem())

The constraints are specified through the input prolongation Pi from GetProlongation(), and output restriction Ro from GetOutputRestriction() methods, which are e.g. available through the (parallel) finite element spaces of any (parallel) mixed bilinear form operator. So we have: A(X)=[Ro (*this) Pi](X), B=Ro(b), and X=Pi^T(x).

The vector x must contain the essential boundary condition values. The "columns" in this operator corresponding to these values are eliminated through the RectangularConstrainedOperator class.

After solving the system A(X)=B, the (finite element) solution x can be recovered by calling Operator::RecoverFEMSolution() with the same vectors X, b, and x.

Note
The caller is responsible for destroying the output operator A!
If there are no transformations, X simply reuses the data of x.

Definition at line 68 of file operator.cpp.

 void mfem::Operator::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).

This returns the same operator as FormRectangularLinearSystem(), but does without the transformations of the right-hand side.

Definition at line 172 of file operator.cpp.

 void mfem::Operator::FormSystemOperator ( const Array< int > & ess_tdof_list, Operator *& A )

Return in A a parallel (on truedofs) version of this square operator.

This returns the same operator as FormLinearSystem(), but does without the transformations of the right-hand side and initial guess.

Definition at line 164 of file operator.cpp.

 virtual Operator& mfem::Operator::GetGradient ( const Vector & x ) const
inlinevirtual

Evaluate the gradient operator at the point x. The default behavior in class Operator is to generate an error.

Definition at line 98 of file operator.hpp.

 virtual MemoryClass mfem::Operator::GetMemoryClass ( ) const
inlinevirtual

Return the MemoryClass preferred by the Operator.

This is the MemoryClass that will be used to access the input and output vectors in the Mult() and MultTranspose() methods.

For example, classes using the MFEM_FORALL macro for implementation can return the value returned by Device::GetMemoryClass().

The default implementation of this method in class Operator returns MemoryClass::HOST.

Definition at line 86 of file operator.hpp.

 virtual const Operator* mfem::Operator::GetOutputProlongation ( ) const
inlinevirtual

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

Reimplemented in mfem::MixedBilinearForm, mfem::BilinearForm, and mfem::MixedBilinearFormExtension.

Definition at line 121 of file operator.hpp.

 virtual const Operator* mfem::Operator::GetOutputRestriction ( ) const
inlinevirtual

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

Reimplemented in mfem::MixedBilinearForm, mfem::BilinearForm, and mfem::MixedBilinearFormExtension.

Definition at line 132 of file operator.hpp.

 virtual const Operator* mfem::Operator::GetOutputRestrictionTranspose ( ) const
inlinevirtual

Transpose of GetOutputRestriction, directly available in this form to facilitate matrix-free RAP-type operators.

NULL means identity.

Reimplemented in mfem::DiscreteLinearOperator, mfem::BilinearForm, and mfem::PADiscreteLinearOperatorExtension.

Definition at line 129 of file operator.hpp.

 virtual const Operator* mfem::Operator::GetProlongation ( ) const
inlinevirtual

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

Definition at line 115 of file operator.hpp.

 virtual const Operator* mfem::Operator::GetRestriction ( ) const
inlinevirtual

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

Definition at line 118 of file operator.hpp.

 Type mfem::Operator::GetType ( ) const
inline

Return the type ID of the Operator class.

This method is intentionally non-virtual, so that it returns the ID of the specific pointer or reference type used when calling this method. If not overridden by derived classes, they will automatically use the type ID of the base Operator class, ANY_TYPE.

Definition at line 276 of file operator.hpp.

 int mfem::Operator::Height ( ) const
inline

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

Definition at line 66 of file operator.hpp.

 void mfem::Operator::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.

Definition at line 22 of file operator.cpp.

 virtual void mfem::Operator::MultTranspose ( const Vector & x, Vector & y ) const
inlinevirtual
 int mfem::Operator::NumCols ( ) const
inline

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

Definition at line 75 of file operator.hpp.

 int mfem::Operator::NumRows ( ) const
inline

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

Definition at line 69 of file operator.hpp.

 void mfem::Operator::PrintMatlab ( std::ostream & out, int n, int m = 0 ) const

Prints operator with input size n and output size m in Matlab format.

Definition at line 188 of file operator.cpp.

 void mfem::Operator::PrintMatlab ( std::ostream & out ) const
virtual

Prints operator in Matlab format.

Reimplemented in mfem::SparseMatrix, mfem::DenseMatrix, and mfem::BlockMatrix.

Definition at line 213 of file operator.cpp.

 void mfem::Operator::RecoverFEMSolution ( const Vector & X, const Vector & b, Vector & x )
virtual

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().

Call this method after solving a linear system constructed using Operator::FormLinearSystem() to recover the solution as an input vector, x, for this Operator (presumably a finite element grid function). This method has identical signature to the analogous method for bilinear forms, though currently b is not used in the implementation.

Reimplemented in mfem::BilinearForm, and mfem::ParBilinearForm.

Definition at line 85 of file operator.cpp.

 Operator * mfem::Operator::SetupRAP ( const Operator * Pi, const Operator * Po )
protected

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

Definition at line 105 of file operator.cpp.

 int mfem::Operator::Width ( ) const
inline

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

Definition at line 72 of file operator.hpp.

## Member Data Documentation

 int mfem::Operator::height
protected

Dimension of the output / number of rows in the matrix.

Definition at line 27 of file operator.hpp.

 int mfem::Operator::width
protected

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

Definition at line 28 of file operator.hpp.

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