Auxiliary space solvers for MatrixFreeAMS preconditioner. More...

#include <auxiliary.hpp>

Inheritance diagram for mfem::MatrixFreeAuxiliarySpace:

Collaboration diagram for mfem::MatrixFreeAuxiliarySpace:

Public Member Functions
	MatrixFreeAuxiliarySpace (ParMesh &mesh_lor, Coefficient alpha_coeff, Coefficient beta_coeff, MatrixCoefficient *beta_mcoeff, Array< int > &ess_bdr, Operator &curlcurl_oper, Operator &pi, #ifdef MFEM_USE_AMGX bool useAmgX_, #endif int cg_iterations=0)
	Pi space constructor.

	MatrixFreeAuxiliarySpace (ParMesh &mesh_lor, Coefficient beta_coeff, MatrixCoefficient beta_mcoeff, Array< int > &ess_bdr, Operator &curlcurl_oper, Operator &g, #ifdef MFEM_USE_AMGX bool useAmgX_, #endif int cg_iterations=1)
	G space constructor.

	~MatrixFreeAuxiliarySpace ()

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

void	SetOperator (const Operator &op)
	Set/update the solver for the given operator.

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	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	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.

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.

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 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

Auxiliary space solvers for MatrixFreeAMS preconditioner.

Given an operator A and a transfer G, create a solver that approximates (G^T A G)^{-1}. Used for two different auxiliary spaces in the AMS cycle.

The produced solver is based on a low-order refined discretization for the high-order H1 problem.

Definition at line 38 of file auxiliary.hpp.

Constructor & Destructor Documentation

◆ MatrixFreeAuxiliarySpace() [1/2]

mfem::MatrixFreeAuxiliarySpace::MatrixFreeAuxiliarySpace	(	ParMesh &	mesh_lor,
		Coefficient *	alpha_coeff,
		Coefficient *	beta_coeff,
		MatrixCoefficient *	beta_mcoeff,
		Array< int > &	ess_bdr,
		Operator &	curlcurl_oper,
		Operator &	pi,
		#ifdef MFEM_USE_AMGX bool	useAmgX_,
		#endif int	cg_iterations = 0 )

Pi space constructor.

In the AMS framework this auxiliary space has two coefficients.

Parameters

mesh_lor	Low-order refined auxiliary mesh
alpha_coeff	Coefficient on curl-curl term (1 if null)
beta_coeff	Coefficient on mass term (1 if null)
beta_mcoeff	Matrix coefficient on mass term
ess_bdr	Attributes for essential boundaries
curlcurl_oper	High-order operator for the system
pi	Identity interpolation operator
useAmgX_	Use AmgX instead of hypre for auxiliary solves
cg_iterations	Number of CG iterations used to invert auxiliary system, choosing 0 means to use a single V-cycle

Definition at line 120 of file auxiliary.cpp.

◆ MatrixFreeAuxiliarySpace() [2/2]

mfem::MatrixFreeAuxiliarySpace::MatrixFreeAuxiliarySpace	(	ParMesh &	mesh_lor,
		Coefficient *	beta_coeff,
		MatrixCoefficient *	beta_mcoeff,
		Array< int > &	ess_bdr,
		Operator &	curlcurl_oper,
		Operator &	g,
		#ifdef MFEM_USE_AMGX bool	useAmgX_,
		#endif int	cg_iterations = 1 )

G space constructor.

This has one coefficient in the AMS framework.

Parameters

mesh_lor	Low-order refined auxiliary mesh
beta_coeff	Coefficient on mass term (1 if null)
beta_mcoeff	Matrix coefficient on mass term
ess_bdr	Attributes for essential boundaries
curlcurl_oper	High-order operator for the system
g	Gradient interpolation operator
useAmgX_	Use AmgX instead of hypre for auxiliary solves
cg_iterations	Number of CG iterations used to invert auxiliary system, choosing 0 means to use a single V-cycle

Definition at line 203 of file auxiliary.cpp.

◆ ~MatrixFreeAuxiliarySpace()

mfem::MatrixFreeAuxiliarySpace::~MatrixFreeAuxiliarySpace ( )

Definition at line 413 of file auxiliary.cpp.

Member Function Documentation

◆ Mult()

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

virtual

Operator application: y=A(x).

Implements mfem::Operator.

Definition at line 399 of file auxiliary.cpp.

◆ SetOperator()

void mfem::MatrixFreeAuxiliarySpace::SetOperator ( const Operator & op )

inlinevirtual

Set/update the solver for the given operator.

Implements mfem::Solver.

Definition at line 92 of file auxiliary.hpp.

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

linalg/auxiliary.hpp
linalg/auxiliary.cpp

Public Member Functions

Additional Inherited Members