# Dune Core Modules (2.4.2)

Dune::Richardson< X, Y > Class Template Reference

Richardson preconditioner. More...

#include <dune/istl/preconditioners.hh>

## Public Types

enum  { category =SolverCategory::sequential }

typedef X domain_type
The domain type of the preconditioner.

typedef Y range_type
The range type of the preconditioner.

typedef X::field_type field_type
The field type of the preconditioner.

## Public Member Functions

Richardson (field_type w=1.0)
Constructor. More...

virtual void pre (X &x, Y &b)
Prepare the preconditioner. More...

virtual void apply (X &v, const Y &d)
Apply the precondioner. More...

virtual void post (X &x)
Clean up. More...

## Detailed Description

### template<class X, class Y> class Dune::Richardson< X, Y >

Richardson preconditioner.

Multiply simply by a constant.

Template Parameters
 X Type of the update Y Type of the defect

## ◆ anonymous enum

template<class X , class Y >
 anonymous enum
Enumerator
category

The category the preconditioner is part of.

## ◆ Richardson()

template<class X , class Y >
 Dune::Richardson< X, Y >::Richardson ( field_type w = 1.0 )
inline

Constructor.

Constructor gets all parameters to operate the prec.

Parameters
 w The relaxation factor.

## ◆ apply()

template<class X , class Y >
 virtual void Dune::Richardson< X, Y >::apply ( X & v, const Y & d )
inlinevirtual

Apply the precondioner.

Apply one step of the preconditioner to the system A(v)=d. On entry v=0 and d=b-A(x) (although this might not be computed in that way. On exit v contains the update, i.e one step computes $$v = M^{-1} d$$ where $$M$$ is the approximate inverse of the operator $$A$$ characterizing the preconditioner.

Parameters
 [out] v The update to be computed d The current defect.

Implements Dune::Preconditioner< X, Y >.

## ◆ post()

template<class X , class Y >
 virtual void Dune::Richardson< X, Y >::post ( X & x )
inlinevirtual

Clean up.

Clean up. This method is called after the last apply call for the linear system to be solved. Memory may be deallocated safely here. x is the solution of the linear equation.

Parameters
 x The right hand side of the equation.

Implements Dune::Preconditioner< X, Y >.

References DUNE_UNUSED_PARAMETER.

## ◆ pre()

template<class X , class Y >
 virtual void Dune::Richardson< X, Y >::pre ( X & x, Y & b )
inlinevirtual

Prepare the preconditioner.

Prepare the preconditioner. A solver solves a linear operator equation A(x)=b by applying one or several steps of the preconditioner. The method pre() is called before the first apply operation. b and x are right hand side and solution vector of the linear system respectively. It may. e.g., scale the system, allocate memory or compute a (I)LU decomposition. Note: The ILU decomposition could also be computed in the constructor or with a separate method of the derived method if several linear systems with the same matrix are to be solved.

Parameters
 x The left hand side of the equation. b The right hand side of the equation.

Implements Dune::Preconditioner< X, Y >.

References DUNE_UNUSED_PARAMETER.

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