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

Richardson preconditioner. More...

#include <dune/istl/preconditioners.hh>

Inheritance diagram for Dune::Richardson< X, Y >:

Public Types
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.
typedef Simd::Scalar< field_type >	scalar_field_type
	scalar type underlying the field_type
typedef FieldTraits< scalar_field_type >::real_type	real_field_type
	real scalar type underlying the field_type

Public Member Functions
	Richardson (real_field_type w=1.0)
	Constructor.
	Richardson (const ParameterTree &configuration)
	Constructor.
void	pre (X &x, Y &b) override
	Prepare the preconditioner.
void	apply (X &v, const Y &d) override
	Apply the precondioner.
void	post (X &x) override
	Clean up.
SolverCategory::Category	category () const override
	Category of the preconditioner (see SolverCategory::Category)

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

Member Typedef Documentation

domain_type

template<class X , class Y >

typedef X Dune::Richardson< X, Y >::domain_type

The domain type of the preconditioner.

field_type

template<class X , class Y >

typedef X::field_type Dune::Richardson< X, Y >::field_type

The field type of the preconditioner.

range_type

template<class X , class Y >

typedef Y Dune::Richardson< X, Y >::range_type

The range type of the preconditioner.

real_field_type

template<class X , class Y >

typedef FieldTraits<scalar_field_type>::real_type Dune::Richardson< X, Y >::real_field_type

real scalar type underlying the field_type

scalar_field_type

template<class X , class Y >

typedef Simd::Scalar<field_type> Dune::Richardson< X, Y >::scalar_field_type

scalar type underlying the field_type

Constructor & Destructor Documentation

Richardson() [1/2]

template<class X , class Y >

Dune::Richardson< X, Y >::Richardson ( real_field_type  w = 1.0 )

inline

Constructor.

Constructor gets all parameters to operate the prec.

Parameters

w	The relaxation factor.

Richardson() [2/2]

template<class X , class Y >

Dune::Richardson< X, Y >::Richardson ( const ParameterTree &  configuration )

inline

Constructor.

Parameters

configuration

ParameterTree containing preconditioner parameters.

ParameterTree Key	Meaning
relaxation	The relaxation factor. default=1.0

See ISTL_Factory for the ParameterTree layout and examples.

Member Function Documentation

apply()

template<class X , class Y >

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

inlineoverridevirtual

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 >.

category()

template<class X , class Y >

SolverCategory::Category Dune::Richardson< X, Y >::category ( ) const

inlineoverridevirtual

Category of the preconditioner (see SolverCategory::Category)

Implements Dune::Preconditioner< X, Y >.

post()

template<class X , class Y >

void Dune::Richardson< X, Y >::post ( X &  x )

inlineoverridevirtual

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 >.

pre()

template<class X , class Y >

void Dune::Richardson< X, Y >::pre ( X &  x, Y &  b  )

inlineoverridevirtual

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.

Note

if a preconditioner is copied (e.g. for a second thread) again the pre() method has to be called to ensure proper memory management.

X x(0.0);
Y b = ...; // rhs
Preconditioner<X,Y> prec(...);
prec.pre(x,b);   // prepare the preconditioner
prec.apply(x,b); // can be called multiple times now...
prec.post(x);    // cleanup internal state

Parameters

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

Implements Dune::Preconditioner< X, Y >.

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

• preconditioners.hh