Public Member Functions

PreconditionSOR< MATRIX > Class Template Reference
[Preconditioners and Relaxation Operators]

Inheritance diagram for PreconditionSOR< MATRIX >:
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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

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

 SparseMatrix<double> A;
 Vector<double> x;
 Vector<double> b;
 SolverCG<> solver(...);

 //...initialize and build A

     // Define and initialize preconditioner

 PreconditionSOR<SparseMatrix<double> > precondition;
 precondition.initialize (A, .6);

 solver.solve (A, x, b, precondition);
Author:
Guido Kanschat, 2000

Definition at line 499 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:
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deal.II documentation generated on Fri Feb 3 2012 06:04:10 by doxygen 1.7.2