Generalized Minimal Residual (GMRES) method. Plus de détails...

#include </__w/arcaneframework.github.io/arcaneframework.github.io/framework/arccore/src/alina/arccore/alina/GMRESSolver.h>

Graphe d'héritage de Arcane::Alina::GMRESSolver< Backend, InnerProduct >:

Graphe de collaboration de Arcane::Alina::GMRESSolver< Backend, InnerProduct >:

Types publics
using	backend_type = Backend

using	BackendType = Backend

typedef Backend::vector	vector

typedef Backend::value_type	value_type

typedef Backend::params	backend_params

typedef math::scalar_of< value_type >::type	scalar_type

typedef math::rhs_of< value_type >::type	rhs_type

typedef math::inner_product_impl< rhs_type >::return_type	coef_type

using	params = GMRESSolverParams

Fonctions membres publiques
	GMRESSolver (size_t n, const params &prm=params(), const backend_params &backend_prm=backend_params(), const InnerProduct &inner_product=InnerProduct())
	Preallocates necessary data structures for the system of size `n`.

template<class Matrix, class Precond, class Vec1, class Vec2>
SolverResult	operator() (Matrix const &A, Precond const &P, Vec1 const &rhs, Vec2 &x) const

template<class Precond, class Vec1, class Vec2>
std::tuple< size_t, scalar_type >	operator() (Precond const &P, Vec1 const &rhs, Vec2 &x) const
	Computes the solution for the given right-hand side.

size_t	bytes () const
	Memory used in bytes.

Attributs publics
params	prm

Fonctions membres privées
template<class Vec>
scalar_type	norm (const Vec &x) const

Attributs privés
size_t	n

multi_array< coef_type, 2 >	H

std::vector< coef_type >	s

std::vector< coef_type >	cs

std::vector< coef_type >	sn

std::shared_ptr< vector >	r

std::vector< std::shared_ptr< vector > >	v

InnerProduct	inner_product

Amis
std::ostream &	operator<< (std::ostream &os, const GMRESSolver &s)

Description détaillée

template<class Backend, class InnerProduct = detail::default_inner_product>
class Arcane::Alina::GMRESSolver< Backend, InnerProduct >

Generalized Minimal Residual (GMRES) method.

\rst The Generalized Minimal Residual method is an extension of MINRES (which is only applicable to symmetric systems) to unsymmetric systems [Barr94]_. \endrst

Définition à la ligne 103 du fichier GMRESSolver.h.

Documentation des définitions de type membres

◆ backend_params

template<class Backend, class InnerProduct = detail::default_inner_product>

typedef Backend::params Arcane::Alina::GMRESSolver< Backend, InnerProduct >::backend_params

Définition à la ligne 113 du fichier GMRESSolver.h.

◆ backend_type

template<class Backend, class InnerProduct = detail::default_inner_product>

using Arcane::Alina::GMRESSolver< Backend, InnerProduct >::backend_type = Backend

Définition à la ligne 108 du fichier GMRESSolver.h.

◆ BackendType

template<class Backend, class InnerProduct = detail::default_inner_product>

using Arcane::Alina::GMRESSolver< Backend, InnerProduct >::BackendType = Backend

Définition à la ligne 109 du fichier GMRESSolver.h.

◆ coef_type

template<class Backend, class InnerProduct = detail::default_inner_product>

typedef math::inner_product_impl<rhs_type>::return_type Arcane::Alina::GMRESSolver< Backend, InnerProduct >::coef_type

Définition à la ligne 117 du fichier GMRESSolver.h.

◆ params

template<class Backend, class InnerProduct = detail::default_inner_product>

using Arcane::Alina::GMRESSolver< Backend, InnerProduct >::params = GMRESSolverParams

Définition à la ligne 119 du fichier GMRESSolver.h.

◆ rhs_type

template<class Backend, class InnerProduct = detail::default_inner_product>

typedef math::rhs_of<value_type>::type Arcane::Alina::GMRESSolver< Backend, InnerProduct >::rhs_type

Définition à la ligne 116 du fichier GMRESSolver.h.

◆ scalar_type

template<class Backend, class InnerProduct = detail::default_inner_product>

typedef math::scalar_of<value_type>::type Arcane::Alina::GMRESSolver< Backend, InnerProduct >::scalar_type

Définition à la ligne 115 du fichier GMRESSolver.h.

◆ value_type

template<class Backend, class InnerProduct = detail::default_inner_product>

typedef Backend::value_type Arcane::Alina::GMRESSolver< Backend, InnerProduct >::value_type

Définition à la ligne 112 du fichier GMRESSolver.h.

◆ vector

template<class Backend, class InnerProduct = detail::default_inner_product>

typedef Backend::vector Arcane::Alina::GMRESSolver< Backend, InnerProduct >::vector

Définition à la ligne 111 du fichier GMRESSolver.h.

Documentation des constructeurs et destructeur

◆ GMRESSolver()

template<class Backend, class InnerProduct = detail::default_inner_product>

Arcane::Alina::GMRESSolver< Backend, InnerProduct >::GMRESSolver	(	size_t	n,
		const params &	prm = params(),
		const backend_params &	backend_prm = backend_params(),
		const InnerProduct &	inner_product = InnerProduct() )

inline

Preallocates necessary data structures for the system of size n.

Définition à la ligne 122 du fichier GMRESSolver.h.

Documentation des fonctions membres

◆ bytes()

template<class Backend, class InnerProduct = detail::default_inner_product>

size_t Arcane::Alina::GMRESSolver< Backend, InnerProduct >::bytes ( ) const

inlinevirtual

Memory used in bytes.

Implémente Arcane::Alina::SolverBase.

Définition à la ligne 287 du fichier GMRESSolver.h.

◆ norm()

template<class Backend, class InnerProduct = detail::default_inner_product>

template<class Vec>

scalar_type Arcane::Alina::GMRESSolver< Backend, InnerProduct >::norm ( const Vec & x ) const

inlineprivate

Définition à la ligne 315 du fichier GMRESSolver.h.

◆ operator()() [1/2]

template<class Backend, class InnerProduct = detail::default_inner_product>

template<class Matrix, class Precond, class Vec1, class Vec2>

SolverResult Arcane::Alina::GMRESSolver< Backend, InnerProduct >::operator()	(	Matrix const &	A,
		Precond const &	P,
		Vec1 const &	rhs,
		Vec2 &	x ) const

inline

Computes the solution for the given system matrix.

Computes the solution for the given system matrix A and the right-hand side rhs. Returns the number of iterations made and the achieved residual as a std::tuple. The solution vector x provides initial approximation in input and holds the computed solution on output.

The system matrix may differ from the matrix used during initialization. This may be used for the solution of non-stationary problems with slowly changing coefficients. There is a strong chance that a preconditioner built for a time step will act as a reasonably good preconditioner for several subsequent time steps [DeSh12]_.

Définition à la ligne 156 du fichier GMRESSolver.h.

◆ operator()() [2/2]

template<class Backend, class InnerProduct = detail::default_inner_product>

template<class Precond, class Vec1, class Vec2>

std::tuple< size_t, scalar_type > Arcane::Alina::GMRESSolver< Backend, InnerProduct >::operator()	(	Precond const &	P,
		Vec1 const &	rhs,
		Vec2 &	x ) const

inline

Computes the solution for the given right-hand side.

Computes the solution for the given right-hand side rhs. The system matrix is the same that was used for the setup of the preconditioner P. Returns the number of iterations made and the achieved residual as a std::tuple. The solution vector x provides initial approximation in input and holds the computed solution on output.

Définition à la ligne 270 du fichier GMRESSolver.h.