Ifpack_BlockRelaxation: a class to define block relaxation preconditioners of Epetra_RowMatrix's. More...

#include <Ifpack_BlockRelaxation.h>

Inheritance diagram for Ifpack_BlockRelaxation< T >:

Collaboration diagram for Ifpack_BlockRelaxation< T >:

Public Member Functions
int	NumLocalBlocks () const
	Returns the number local blocks.

virtual bool	IsInitialized () const
	Returns `true` if the preconditioner has been successfully computed.

virtual bool	IsComputed () const
	Returns `true` if the preconditioner has been successfully computed.

virtual int	SetParameters (Teuchos::ParameterList &List)
	Sets all the parameters for the preconditioner.

virtual int	Initialize ()
	Initializes the preconditioner.

virtual int	Compute ()
	Computes the preconditioner.

virtual const Epetra_RowMatrix &	Matrix () const
	Returns a pointer to the matrix to be preconditioned.

virtual double	Condest (const Ifpack_CondestType=Ifpack_Cheap, const int=1550, const double=1e-9, Epetra_RowMatrix *=0)
	Computes the condition number estimate, returns its value.

virtual double	Condest () const
	Returns the computed condition number estimate, or -1.0 if not computed.

std::ostream &	Print (std::ostream &os) const
	Prints basic information on iostream. This function is used by operator<<.

virtual int	NumInitialize () const
	Returns the number of calls to Initialize().

virtual int	NumCompute () const
	Returns the number of calls to Compute().

virtual int	NumApplyInverse () const
	Returns the number of calls to ApplyInverse().

virtual double	InitializeTime () const
	Returns the time spent in Initialize().

virtual double	ComputeTime () const
	Returns the time spent in Compute().

virtual double	ApplyInverseTime () const
	Returns the time spent in ApplyInverse().

virtual double	InitializeFlops () const
	Returns the number of flops in the initialization phase.

virtual double	ComputeFlops () const
	Returns the number of flops in the computation phase.

virtual double	ApplyInverseFlops () const
	Returns the number of flops in the application of the preconditioner.


	Ifpack_BlockRelaxation (const Epetra_RowMatrix *Matrix)
	Ifpack_BlockRelaxation constructor with given Epetra_RowMatrix. More...


virtual int	Apply (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	Applies the matrix to an Epetra_MultiVector. More...

virtual int	ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const
	Applies the block Jacobi preconditioner to X, returns the result in Y. More...

virtual double	NormInf () const
	Returns the infinity norm of the global matrix (not implemented)


virtual int	SetUseTranspose (bool UseTranspose_in)

virtual const char *	Label () const

virtual bool	UseTranspose () const
	Returns the current UseTranspose setting.

virtual bool	HasNormInf () const
	Returns true if the this object can provide an approximate Inf-norm, false otherwise.

virtual const Epetra_Comm &	Comm () const
	Returns a pointer to the Epetra_Comm communicator associated with this operator.

virtual const Epetra_Map &	OperatorDomainMap () const
	Returns the Epetra_Map object associated with the domain of this operator.

virtual const Epetra_Map &	OperatorRangeMap () const
	Returns the Epetra_Map object associated with the range of this operator.

Detailed Description

template<typename T>
class Ifpack_BlockRelaxation< T >

Ifpack_BlockRelaxation: a class to define block relaxation preconditioners of Epetra_RowMatrix's.

The Ifpack_BlockRelaxation class enables the construction of

block relaxation preconditioners of an Epetra_RowMatrix. Ifpack_PointRelaxation is derived from the Ifpack_Preconditioner class, which is derived from Epetra_Operator. Therefore this object can be used as preconditioner everywhere an ApplyInverse() method is required in the preconditioning step.

The class currently support:

block Jacobi;
block Gauss-Seidel;
symmetric block Gauss-Seidel.

The idea of block relaxation method is to extend their point relaxation counterpart (implemented in Ifpack_PointRelaxation), by working on a group of equation simulteneously. Generally, larger blocks result in better convergence and increased robusteness.

The user can decide:

the number of blocks (say, NumBlocks). If NumBlocks is equal to the number of rows, then the resulting scheme is equivalent to a point relaxation scheme;
how to apply the inverse of each diagonal block, by choosing a dense container or a sparse container. The implementation of block relaxation schemes requires the application of the inverse of each diagonal block. This can be done using LAPACK (dense container), or any Ifpack_Preconditioner derived class (sparse container);
blocks can be defined using a linear decomposition, by a simple greedy algorithm, or by resorting to METIS.

The following is an example of usage of this preconditioner with dense containers. First, we include the header files:

#include "Ifpack_AdditiveSchwarz.h"
#include "Ifpack_BlockPreconditioner.h"
#include "Ifpack_DenseContainer.h"

Then, we declare the preconditioner. Note that this is done through the class Ifpack_AdditiveSchwarz (see note below in this section).

// A is an Epetra_RowMatrix
// List is a Teuchos::ParameterList
Ifpack_AdditiveSchwarz<Ifpack_BlockRelaxation<Ifpack_DenseContainer> > > Prec(A);
IFPACK_CHK_ERR(Prec.SetParameters(List));
IFPACK_CHK_ERR(Prec.Initialize());
IFPACK_CHK_ERR(Prec.Compute());
// action of the preconditioner is given by ApplyInverse()
// Now use it in AztecOO, solver is an AztecOO object
solver.SetPrecOperator(&Prec);

The complete list of supported parameters is reported in page List of Supported Parameters. For a presentation of basic relaxation schemes, please refer to page Ifpack_PointRelaxation.