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Ifpack_PointRelaxation: a class to define point relaxation preconditioners of for Epetra_RowMatrix's. More...
#include <Ifpack_PointRelaxation.h>
Public Member Functions  
virtual int  SetUseTranspose (bool UseTranspose_in) 
Ifpack_PointRelaxation (const Epetra_RowMatrix *Matrix)  
Ifpack_PointRelaxation constructor with given Epetra_RowMatrix.  
virtual  ~Ifpack_PointRelaxation () 
Destructor.  
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)  
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 Infnorm, 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 
Returns true if the preconditioner has been successfully computed.  
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=1e9, 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.  
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. 
Ifpack_PointRelaxation: a class to define point relaxation preconditioners of for Epetra_RowMatrix's.
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 GaussSeidel preconditioner can be defined as
Clearly, the role of E and F can be interchanged. However, Ifpack_GaussSeidel does not consider backward GaussSeidel 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 117 of file Ifpack_PointRelaxation.h.
Ifpack_PointRelaxation::Ifpack_PointRelaxation  (  const Epetra_RowMatrix *  Matrix  ) 
Ifpack_PointRelaxation constructor with given Epetra_RowMatrix.
Creates an instance of Ifpack_PointRelaxation class.
Matrix   (In) Pointer to matrix to precondition. 
Definition at line 48 of file Ifpack_PointRelaxation.cpp.
virtual int Ifpack_PointRelaxation::Apply  (  const Epetra_MultiVector &  X, 
Epetra_MultiVector &  Y  
)  const [inline, virtual] 
Applies the matrix to an Epetra_MultiVector.
X   (In) A Epetra_MultiVector of dimension NumVectors to multiply with matrix. 
Y   (Out) A Epetra_MultiVector of dimension NumVectors containing the result. 
Implements Epetra_Operator.
Definition at line 160 of file Ifpack_PointRelaxation.h.
References IsComputed(), Epetra_MultiVector::NumVectors(), and UseTranspose().
int Ifpack_PointRelaxation::ApplyInverse  (  const Epetra_MultiVector &  X, 
Epetra_MultiVector &  Y  
)  const [virtual] 
Applies the preconditioner to X, returns the result in Y.
X   (In) A Epetra_MultiVector of dimension NumVectors to be preconditioned. 
Y   (InOut) A Epetra_MultiVector of dimension NumVectors containing result. 
Implements Ifpack_Preconditioner.
Definition at line 341 of file Ifpack_PointRelaxation.cpp.
References IsComputed(), Epetra_MultiVector::NumVectors(), Epetra_MultiVector::Pointers(), and Epetra_MultiVector::PutScalar().
virtual int Ifpack_PointRelaxation::SetUseTranspose  (  bool  UseTranspose_in  )  [inline, virtual] 
This flag can be used to apply the preconditioner to the transpose of the input operator.
Implements Epetra_Operator.
Definition at line 141 of file Ifpack_PointRelaxation.h.