Reference documentation for deal.II version Git f53b282 2016-05-27 00:38:34 -0500
Public Member Functions | List of all members

#include <deal.II/lac/precondition.h>

Inheritance diagram for PreconditionSOR< MatrixType >:
[legend]

Public Member Functions

template<class VectorType >
void vmult (VectorType &, const VectorType &) const
 
template<class VectorType >
void Tvmult (VectorType &, const VectorType &) const
 
template<class VectorType >
void step (VectorType &x, const VectorType &rhs) const
 
template<class VectorType >
void Tstep (VectorType &x, const VectorType &rhs) const
 
- Public Member Functions inherited from PreconditionRelaxation< MatrixType >
void initialize (const MatrixType &A, const AdditionalData &parameters=AdditionalData())
 
void clear ()
 
size_type m () const
 
size_type n () const
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Additional Inherited Members

- Public Types inherited from PreconditionRelaxation< MatrixType >
typedef MatrixType::size_type size_type
 
- Static Public Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, char *arg2, std::string &arg3)
 
static::ExceptionBase & ExcNoSubscriber (char *arg1, char *arg2)
 
- Protected Attributes inherited from PreconditionRelaxation< MatrixType >
SmartPointer< const MatrixType, PreconditionRelaxation< MatrixType > > A
 
double relaxation
 

Detailed Description

template<typename MatrixType = SparseMatrix<double>>
class PreconditionSOR< MatrixType >

SOR preconditioner using matrix built-in function.

Assuming the matrix A = D + L + U is split into its diagonal D as well as the strict lower and upper triangles L and U, then the SOR preconditioner with relaxation parameter r is

\[ P^{-1} = r (D+rL)^{-1}. \]

It is this operator P-1, which is implemented by vmult() through forward substitution. Analogously, Tvmult() implements the operation of r(D+rU)-1.

The SOR iteration itself can be directly written as

\[ x^{k+1} = x^k - r D^{-1} \bigl(L x^{k+1} + U x^k - b\bigr). \]

Using the right hand side b and the previous iterate x, this is the operation implemented by step().

The MatrixType class used is required to have functions precondition_SOR(VectorType&, const VectorType&, double) and precondition_TSOR(VectorType&, const VectorType&, double). This class satisfies the relaxation concept.

// Declare related objects
SolverCG<> solver(...);
//...initialize and build A
// Define and initialize preconditioner
precondition.initialize (A, .6);
solver.solve (A, x, b, precondition);
Author
Guido Kanschat, 2000

Definition at line 552 of file precondition.h.

Member Function Documentation

template<typename MatrixType = SparseMatrix<double>>
template<class VectorType >
void PreconditionSOR< MatrixType >::vmult ( VectorType &  ,
const VectorType &   
) const

Apply preconditioner.

template<typename MatrixType = SparseMatrix<double>>
template<class VectorType >
void PreconditionSOR< MatrixType >::Tvmult ( VectorType &  ,
const VectorType &   
) const

Apply transpose preconditioner.

template<typename MatrixType = SparseMatrix<double>>
template<class VectorType >
void PreconditionSOR< MatrixType >::step ( VectorType &  x,
const VectorType &  rhs 
) const

Perform one step of the preconditioned Richardson iteration.

template<typename MatrixType = SparseMatrix<double>>
template<class VectorType >
void PreconditionSOR< MatrixType >::Tstep ( VectorType &  x,
const VectorType &  rhs 
) const

Perform one transposed step of the preconditioned Richardson iteration.


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