Ifpack_AdditiveSchwarz: a class to define Additive Schwarz preconditioners of Epetra_RowMatrix's. More...

#include <Ifpack_AdditiveSchwarz.h>

Inheritance diagram for Ifpack_AdditiveSchwarz< T >:

Collaboration diagram for Ifpack_AdditiveSchwarz< T >:

Public Member Functions
virtual bool	IsInitialized () const
	Returns `true` if the preconditioner has been successfully initialized.

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

virtual int	SetParameters (Teuchos::ParameterList &List)
	Sets the parameters. More...


	Ifpack_AdditiveSchwarz (Epetra_RowMatrix *Matrix_in, int OverlapLevel_in=0)
	Ifpack_AdditiveSchwarz constructor with given Epetra_RowMatrix. More...

virtual	~Ifpack_AdditiveSchwarz ()
	Destructor.


virtual int	SetUseTranspose (bool UseTranspose_in)
	If set true, transpose of this operator will be applied (not implemented). More...


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

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

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


virtual const char *	Label () const
	Returns a character string describing the operator.

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.


virtual int	Initialize ()
	Initialized the preconditioner.

virtual int	Compute ()
	Computes the preconditioner.

virtual double	Condest (const Ifpack_CondestType CT=Ifpack_Cheap, const int MaxIters=1550, const double Tol=1e-9, Epetra_RowMatrix *Matrix_in=0)
	Computes the estimated condition number and returns its value.

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

virtual const Epetra_RowMatrix &	Matrix () const
	Returns a refernence to the internally stored matrix.

virtual bool	IsOverlapping () const
	Returns `true` is an overlapping matrix is present.

virtual std::ostream &	Print (std::ostream &) const
	Prints major information about this preconditioner.

virtual const T *	Inverse () const

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.

virtual int	OverlapLevel () const
	Returns the level of overlap.

virtual const Teuchos::ParameterList &	List () const
	Returns a reference to the internally stored list.

Protected Member Functions

	Ifpack_AdditiveSchwarz (const Ifpack_AdditiveSchwarz &RHS)
	Copy constructor (should never be used)

int	Setup ()
	Sets up the localized matrix and the singleton filter.

Protected Attributes

Teuchos::RefCountPtr< const Epetra_RowMatrix >	Matrix_
	Pointers to the matrix to be preconditioned.

Teuchos::RefCountPtr < Ifpack_OverlappingRowMatrix >	OverlappingMatrix_
	Pointers to the overlapping matrix.

Teuchos::RefCountPtr < Ifpack_LocalFilter >	LocalizedMatrix_
	Localized version of Matrix_ or OverlappingMatrix_.

std::string	Label_
	Contains the label of `this` object.

bool	IsInitialized_
	If true, the preconditioner has been successfully initialized.

bool	IsComputed_
	If true, the preconditioner has been successfully computed.

bool	UseTranspose_
	If `true`, solve with the transpose (not supported by all solvers).

bool	IsOverlapping_
	If true, overlapping is used.

int	OverlapLevel_
	Level of overlap among the processors.

Teuchos::ParameterList	List_
	Stores a copy of the list given in SetParameters()

Epetra_CombineMode	CombineMode_
	Combine mode for off-process elements (only if overlap is used)

double	Condest_
	Contains the estimated condition number.

bool	ComputeCondest_
	If `true`, compute the condition number estimate each time Compute() is called.

bool	UseReordering_
	If `true`, reorder the local matrix.

std::string	ReorderingType_
	Type of reordering of the local matrix.

Teuchos::RefCountPtr < Ifpack_Reordering >	Reordering_
	Pointer to a reordering object.

Teuchos::RefCountPtr < Ifpack_ReorderFilter >	ReorderedLocalizedMatrix_
	Pointer to the reorderd matrix.

bool	FilterSingletons_
	Filter for singletons.

Teuchos::RefCountPtr < Ifpack_SingletonFilter >	SingletonFilter_
	filtering object.

int	NumInitialize_
	Contains the number of successful calls to Initialize().

int	NumCompute_
	Contains the number of successful call to Compute().

int	NumApplyInverse_
	Contains the number of successful call to ApplyInverse().

double	InitializeTime_
	Contains the time for all successful calls to Initialize().

double	ComputeTime_
	Contains the time for all successful calls to Compute().

double	ApplyInverseTime_
	Contains the time for all successful calls to ApplyInverse().

double	InitializeFlops_
	Contains the number of flops for Initialize().

double	ComputeFlops_
	Contains the number of flops for Compute().

double	ApplyInverseFlops_
	Contain sthe number of flops for ApplyInverse().

Teuchos::RefCountPtr< Epetra_Time >	Time_
	Object used for timing purposes.

Teuchos::RefCountPtr< T >	Inverse_
	Pointer to the local solver.

Detailed Description

template<typename T>
class Ifpack_AdditiveSchwarz< T >

Ifpack_AdditiveSchwarz: a class to define Additive Schwarz preconditioners of Epetra_RowMatrix's.

Class Ifpack_AdditiveSchwarz enables the construction of Additive Schwarz (one-level overlapping domain decomposition) preconditioners, for a given Epetra_RowMatrix. Ifpack_AdditiveSchwarz is derived from Ifpack_Preconditioner, itself derived from Epetra_Operator. An application of the Additive Schwarz preconditioner can be obtained by calling method ApplyInverse().

One-level overlapping domain decomposition preconditioners use local solvers, of Dirichlet type. This means that the inverse of the local matrix (with minimal or wider overlap) is applied to the residual to be preconditioned.

The preconditioner can be written as:

\[ P_{AS}^{-1} = \sum_{i=1}^M P_i A_i^{-1} R_i , \]

where \(M\) is the number of subdomains (that is, the number of processors in the computation), \(R_i\) is an operator that restricts the global vector to the vector lying on subdomain \(i\), \(P_i\) is the prolongator operator, and

\[ A_i = R_i A P_i. \]

The construction of Schwarz preconditioners is mainly composed by two steps:

definition of the restriction and prolongation operator \(R_i\) and \(R_i^T\). If minimal overlap is chosen, their implementation is trivial, \(R_i\) will return all the local components. For wider overlaps, instead, Epetra_Import and Epetra_Export will be used to import/export data. The user must provide both the matrix to be preconditioned (which is suppose to have minimal-overlap) and the matrix with wider overlap.
definition of a technique to apply the inverse of \(A_i\). To solve on each subdomain, the user can adopt any class, derived from Ifpack_Preconditioner. This can be easily accomplished, as Ifpack_AdditiveSchwarz is templated with the solver for each subdomain.

The local matrix \(A_i\) can be filtered, to eliminate singletons, and reordered. At the present time, RCM and METIS can be used to reorder the local matrix.

The complete list of supported parameters is reported in page List of Supported Parameters.

Author: Marzio Sala, SNL 9214.

Date: Last modified on 22-Jan-05.

Definition at line 142 of file Ifpack_AdditiveSchwarz.h.

Constructor & Destructor Documentation

template<typename T >

Ifpack_AdditiveSchwarz< T >::Ifpack_AdditiveSchwarz	(	Epetra_RowMatrix *	Matrix_in,
		int	OverlapLevel_in = `0`
	)

Ifpack_AdditiveSchwarz constructor with given Epetra_RowMatrix.

Creates an Ifpack_AdditiveSchwarz preconditioner with overlap. To use minimal-overlap, OverlappingMatrix is omitted (as defaulted to 0).

Parameters

Matrix	- (In) Pointer to matrix to be preconditioned
OverlappingMatrix	- (In) Pointer to the matrix extended with the desired level of overlap.

Definition at line 509 of file Ifpack_AdditiveSchwarz.h.

References Ifpack_AdditiveSchwarz< T >::IsOverlapping_, Ifpack_AdditiveSchwarz< T >::Matrix_, Ifpack_AdditiveSchwarz< T >::OverlapLevel_, Ifpack_AdditiveSchwarz< T >::SetParameters(), and Zero.

Member Function Documentation

template<typename T >

int Ifpack_AdditiveSchwarz< T >::Apply	(	const Epetra_MultiVector &	X,
		Epetra_MultiVector &	Y
	)		const

virtual

Applies the matrix to X, returns the result in Y.

Parameters

X	- (In) A Epetra_MultiVector of dimension NumVectors to multiply with matrix.
Y	-(Out) A Epetra_MultiVector of dimension NumVectors containing the result.

Returns: Integer error code, set to 0 if successful.

Implements Epetra_Operator.

Definition at line 946 of file Ifpack_AdditiveSchwarz.h.

template<typename T >

int Ifpack_AdditiveSchwarz< T >::ApplyInverse	(	const Epetra_MultiVector &	X,
		Epetra_MultiVector &	Y
	)		const

virtual

Applies the preconditioner to X, returns the result in Y.

Parameters

X	- (In) A Epetra_MultiVector of dimension NumVectors to be preconditioned.
Y	-(Out) A Epetra_MultiVector of dimension NumVectors containing result.

Returns: Integer error code, set to 0 if successful.

Warning: In order to work with AztecOO, any implementation of this method must support the case where X and Y are the same object.

Implements Ifpack_Preconditioner.

Definition at line 1004 of file Ifpack_AdditiveSchwarz.h.

References Insert.

template<typename T >

int Ifpack_AdditiveSchwarz< T >::SetParameters ( Teuchos::ParameterList & List )

virtual

Sets the parameters.

Sets the parameter for the additive Schwarz preconditioner, as well as for all the preconditioners that may need to be defined on each subblock. Parameters accepted by List are:

"schwarz: combine mode" : It must be an Epetra_CombineMode. Default: Zero. It Can be assume of the following values:
- Add: Components on the receiving processor will be added together;
- Zero: Off-processor components will be ignored;
- Insert: Off-processor components will be inserted into locations on receiving processor replacing existing values.
- Average: Off-processor components will be averaged with existing;
- AbsMax: Magnitudes of Off-processor components will be maxed with magnitudes of existing components on the receiving processor.
"schwarz: compute condest" : if true, Compute() will estimate the condition number of the preconditioner. Default: true.

Implements Ifpack_Preconditioner.

Definition at line 719 of file Ifpack_AdditiveSchwarz.h.

References AbsMax, Add, Average, Insert, InsertAdd, and Zero.

Referenced by Ifpack_AdditiveSchwarz< T >::Ifpack_AdditiveSchwarz().

template<typename T >

int Ifpack_AdditiveSchwarz< T >::SetUseTranspose ( bool UseTranspose_in )

virtual

If set true, transpose of this operator will be applied (not implemented).

This flag allows the transpose of the given operator to be used

implicitly.

Parameters

UseTranspose_in - (In) If true, multiply by the transpose of operator, otherwise just use operator.

Returns: Integer error code, set to 0 if successful. Set to -1 if this implementation does not support transpose.

Implements Epetra_Operator.

Definition at line 931 of file Ifpack_AdditiveSchwarz.h.

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

Ifpack_AdditiveSchwarz.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<typename T> class Ifpack_AdditiveSchwarz< T >

Constructor & Destructor Documentation

Member Function Documentation

template<typename T>
class Ifpack_AdditiveSchwarz< T >