Base class for solvers with filtering (subspace correction). More...

#include <filteredsolver.hpp>

Inheritance diagram for mfem::FilteredSolver:

Collaboration diagram for mfem::FilteredSolver:

Public Member Functions
	FilteredSolver ()
	Construct an empty filtered solver. Must set operator and solver before use.

virtual void	SetOperator (const Operator &A) override
	Set the system operator A.

virtual void	SetSolver (Solver &B)
	Set the solver B that operates on the full space.

void	SetFilteredSubspaceTransferOperator (const Operator &P)
	Set the transfer operator P from filtered subspace to the full space.

void	SetFilteredSubspaceSolver (Solver &S)
	Set a solver S that operates on the filtered subspace operator \( P^T A P \).

void	Mult (const Vector &x, Vector &y) const override
	Apply the filtered solver.

virtual	~FilteredSolver ()=default

	FilteredSolver (const FilteredSolver &)=delete

FilteredSolver &	operator= (const FilteredSolver &)=delete

	FilteredSolver (FilteredSolver &&)=default

FilteredSolver &	operator= (FilteredSolver &&)=default

Public Member Functions inherited from mfem::Solver
	Solver (int s=0, bool iter_mode=false)
	Initialize a square Solver with size s.

	Solver (int h, int w, bool iter_mode=false)
	Initialize a Solver with height h and width w.

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	AbsMult (const Vector &x, Vector &y) const
	Action of the absolute-value operator: `y=\|A\|(x)`. The default behavior in class Operator is to generate an error. If the Operator is a composition of several operators, the composition unfold into a product of absolute-value operators too.

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.

virtual void	AbsMultTranspose (const Vector &x, Vector &y) const
	Action of the transpose absolute-value operator: `y=\|A\|^t(x)`. The default behavior in class Operator is to generate an error.

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	AddMultTranspose (const Vector &x, Vector &y, const real_t a=1.0) const
	Operator transpose application: `y+=A^t(x)` (default) or `y+=a*A^t(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 Operator &	GetGradient (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 Operator *	GetProlongation () const
	Prolongation operator from linear algebra (linear system) vectors, to input vectors for the operator. `NULL` means identity.

virtual const Operator *	GetRestriction () const
	Restriction operator from input vectors for the operator to linear algebra (linear system) vectors. `NULL` means identity.

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

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

virtual const Operator *	GetOutputRestriction () 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.

Protected Member Functions
void	InitVectors () const
	Initialize work vectors.

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()

Operator *	SetupRAP (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
const Operator *	A = nullptr
	System operator (not owned).

const Operator *	P = nullptr
	Transfer operator (not owned).

Solver *	B = nullptr
	Base solver (not owned).

Solver *	S = nullptr
	Subspace solver (not owned).

std::unique_ptr< const Operator >	PtAP = nullptr
	Projected operator.

bool	solver_set = false

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.

Additional Inherited Members
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...

Public Attributes inherited from mfem::Solver
bool	iterative_mode
	If true, use the second argument of Mult() as an initial guess.

Detailed Description

Base class for solvers with filtering (subspace correction).

FilteredSolver is designed to augment an existing solver with an additional filtering step that targets small subspaces where the solver is less effective. The filtered subspace is defined by a transfer operator P, which maps the subspace into the full space.

Typical usage

Call SetOperator() to define the operator A that acts on the full space.
Call SetSolver() to provide the underlying solver B for the full-space operator.
Call SetFilteredSubspaceTransferOperator() to set transfer operator P.
Call SetFilteredSubspaceSolver() to set the subspace solver S.
Use Mult() to apply the solver.

The preconditioner applied by Mult() is

\[ M = B + P S P^T (I - A B) + B (I - A P S P^T) (I- A B), \]

and the corresponding iteration matrix is

\[ I - M A = (I - B A) (I - P S P^T A) (I - B A). \]

Definition at line 49 of file filteredsolver.hpp.

Constructor & Destructor Documentation

◆ FilteredSolver() [1/3]

mfem::FilteredSolver::FilteredSolver ( )

inline

Construct an empty filtered solver. Must set operator and solver before use.

Definition at line 53 of file filteredsolver.hpp.

◆ ~FilteredSolver()

virtual mfem::FilteredSolver::~FilteredSolver ( )

virtualdefault

◆ FilteredSolver() [2/3]

mfem::FilteredSolver::FilteredSolver ( const FilteredSolver & )

delete

◆ FilteredSolver() [3/3]

mfem::FilteredSolver::FilteredSolver ( FilteredSolver && )

default

Member Function Documentation

◆ InitVectors()

void mfem::FilteredSolver::InitVectors ( ) const

protected

Initialize work vectors.

Definition at line 43 of file filteredsolver.cpp.

◆ Mult()

void mfem::FilteredSolver::Mult	(	const Vector &	x,
		Vector &	y ) const

overridevirtual

Apply the filtered solver.

Implements mfem::Operator.

Definition at line 104 of file filteredsolver.cpp.

◆ operator=() [1/2]

FilteredSolver & mfem::FilteredSolver::operator= ( const FilteredSolver & )

delete

◆ operator=() [2/2]

FilteredSolver & mfem::FilteredSolver::operator= ( FilteredSolver && )

default

◆ SetFilteredSubspaceSolver()

void mfem::FilteredSolver::SetFilteredSubspaceSolver ( Solver & S )

Set a solver S that operates on the filtered subspace operator \( P^T A P \).

Definition at line 98 of file filteredsolver.cpp.

◆ SetFilteredSubspaceTransferOperator()

void mfem::FilteredSolver::SetFilteredSubspaceTransferOperator ( const Operator & P )

Set the transfer operator P from filtered subspace to the full space.

Definition at line 92 of file filteredsolver.cpp.

◆ SetOperator()

void mfem::FilteredSolver::SetOperator ( const Operator & A )

overridevirtual

Set the system operator A.

Implements mfem::Solver.

Reimplemented in mfem::AMGFSolver.

Definition at line 78 of file filteredsolver.cpp.

◆ SetSolver()

void mfem::FilteredSolver::SetSolver ( Solver & B )

virtual

Set the solver B that operates on the full space.

Reimplemented in mfem::AMGFSolver.

Definition at line 86 of file filteredsolver.cpp.

Member Data Documentation

◆ A

const Operator* mfem::FilteredSolver::A = nullptr

protected

System operator (not owned).

Definition at line 79 of file filteredsolver.hpp.

◆ B

Solver* mfem::FilteredSolver::B = nullptr

protected

Base solver (not owned).

Definition at line 83 of file filteredsolver.hpp.

◆ P

const Operator* mfem::FilteredSolver::P = nullptr

protected

Transfer operator (not owned).

Definition at line 81 of file filteredsolver.hpp.

◆ PtAP

std::unique_ptr<const Operator> mfem::FilteredSolver::PtAP = nullptr

mutableprotected

Projected operator.

Definition at line 87 of file filteredsolver.hpp.

◆ S

Solver* mfem::FilteredSolver::S = nullptr

protected

Subspace solver (not owned).

Definition at line 85 of file filteredsolver.hpp.

◆ solver_set

bool mfem::FilteredSolver::solver_set = false

mutableprotected

Definition at line 90 of file filteredsolver.hpp.

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

linalg/filteredsolver.hpp
linalg/filteredsolver.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Typical usage

Constructor & Destructor Documentation

◆ FilteredSolver() [1/3]

◆ ~FilteredSolver()

◆ FilteredSolver() [2/3]

◆ FilteredSolver() [3/3]

Member Function Documentation

◆ InitVectors()

◆ Mult()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ SetFilteredSubspaceSolver()

◆ SetFilteredSubspaceTransferOperator()

◆ SetOperator()

◆ SetSolver()

Member Data Documentation

◆ A

◆ B

◆ P

◆ PtAP

◆ S

◆ solver_set