Reference documentation for deal.II version Git 063e7ff 2014-09-30 18:32:14 -0500
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PreconditionSOR< MATRIX > Class Template Reference

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

Inheritance diagram for PreconditionSOR< MATRIX >:
[legend]

Public Member Functions

template<class VECTOR >
void vmult (VECTOR &, const VECTOR &) const
 
template<class VECTOR >
void Tvmult (VECTOR &, const VECTOR &) const
 
template<class VECTOR >
void step (VECTOR &x, const VECTOR &rhs) const
 
template<class VECTOR >
void Tstep (VECTOR &x, const VECTOR &rhs) const
 
- Public Member Functions inherited from PreconditionRelaxation< MATRIX >
void initialize (const MATRIX &A, const AdditionalData &parameters=AdditionalData())
 
void clear ()
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
 DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.")
 
 DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1)
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Additional Inherited Members

- Protected Attributes inherited from PreconditionRelaxation< MATRIX >
SmartPointer< const MATRIX,
PreconditionRelaxation< MATRIX > > 
A
 
double relaxation
 

Detailed Description

template<class MATRIX = SparseMatrix<double>>
class PreconditionSOR< MATRIX >

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 MATRIX class used is required to have functions precondition_SOR(VECTOR&, const VECTOR&, double) and precondition_TSOR(VECTOR&, const VECTOR&, double).

// 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 515 of file precondition.h.

Member Function Documentation

template<class MATRIX = SparseMatrix<double>>
template<class VECTOR >
void PreconditionSOR< MATRIX >::vmult ( VECTOR &  ,
const VECTOR &   
) const

Apply preconditioner.

template<class MATRIX = SparseMatrix<double>>
template<class VECTOR >
void PreconditionSOR< MATRIX >::Tvmult ( VECTOR &  ,
const VECTOR &   
) const

Apply transpose preconditioner.

template<class MATRIX = SparseMatrix<double>>
template<class VECTOR >
void PreconditionSOR< MATRIX >::step ( VECTOR &  x,
const VECTOR &  rhs 
) const

Perform one step of the preconditioned Richardson iteration.

template<class MATRIX = SparseMatrix<double>>
template<class VECTOR >
void PreconditionSOR< MATRIX >::Tstep ( VECTOR &  x,
const VECTOR &  rhs 
) const

Perform one transposed step of the preconditioned Richardson iteration.


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