Inheritance diagram for Ifpack_PointRelaxation:
Public Member Functions
|virtual int||SetUseTranspose (bool UseTranspose)|
|Ifpack_PointRelaxation (const Epetra_RowMatrix *Matrix)|
|Ifpack_PointRelaxation constructor with given Epetra_RowMatrix. |
|virtual int||Apply (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const|
|Applies the matrix to an Epetra_MultiVector. |
|virtual int||ApplyInverse (const Epetra_MultiVector &X, Epetra_MultiVector &Y) const|
|Applies the preconditioner to X, returns the result in Y. |
|virtual double||NormInf () const|
|Returns the infinity norm of the global matrix (not implemented). |
Atribute access functions
|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. |
|virtual int||Initialize ()|
|Computes all it is necessary to initialize the preconditioner. |
|virtual bool||IsInitialized () const|
|Returns true if the preconditioner has been successfully initialized, false otherwise. |
|virtual bool||IsComputed () const|
|virtual int||Compute ()|
|Computes the preconditioners. |
|virtual const Epetra_RowMatrix &||Matrix () const|
|Returns a pointer to the matrix to be preconditioned. |
|virtual double||Condest (const Ifpack_CondestType CT=Ifpack_Cheap, const int MaxIters=1550, const double Tol=1e-9, Epetra_RowMatrix *Matrix=0)|
|Computes the condition number estimates and returns the value. |
|virtual double||Condest () const|
|Returns the condition number estimate, or -1.0 if not computed. |
|virtual int||SetParameters (Teuchos::ParameterList &List)|
|Sets all the parameters for the preconditioner. |
|virtual ostream &||Print (ostream &os) const|
|Prints object to an output stream. |
Timing and flop count
|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 for the application of the preconditioner. |
The Ifpack_PointRelaxation class enables the construction of point relaxation preconditioners of an Epetra_RowMatrix. Ifpack_PointRelaxation is derived from the Ifpack_Preconditioner class, which is itself derived from Epetra_Operator. Therefore this object can be used as preconditioner everywhere an ApplyInverse() method is required in the preconditioning step.
This class enables the construction of the following simple preconditioners:
We now briefly describe the main features of the above preconditioners. Consider a linear system of type
where is a square, real matrix, and are two real vectors. We begin with the decomposition
where is the diagonal of A, is the strict lower part, and is the strict upper part. It is assumed that the diagonal entries of are different from zero.
Given an starting solution , an iteration of the (damped) Jacobi method can be written in matrix form as follows:
for , and a damping parameter.
Using Ifpack_Jacobi, the user can apply the specified number of sweeps (), and the damping parameter. If only one sweep is used, then the class simply applies the inverse of the diagonal of A to the input vector.
Given an starting solution , an iteration of the (damped) GaussSeidel method can be written in matrix form as follows:
for , and a damping parameter. Equivalently, the Gauss-Seidel preconditioner can be defined as
Clearly, the role of E and F can be interchanged. However, Ifpack_GaussSeidel does not consider backward Gauss-Seidel methods.
For a list of supported parameters, please refer to page List of Supported Parameters.
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.
Definition at line 85 of file Ifpack_PointRelaxation.h.
Ifpack_PointRelaxation constructor with given Epetra_RowMatrix.
Creates an instance of Ifpack_PointRelaxation class.
Applies the matrix to an Epetra_MultiVector.
Applies the preconditioner to X, returns the result in Y.
This flag can be used to apply the preconditioner to the transpose of the input operator.