Generalized Minimal Residual (GMRES) method. More...

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

Inheritance diagram for Arcane::Alina::GMRESSolver< Backend, InnerProduct >:

Collaboration diagram for Arcane::Alina::GMRESSolver< Backend, InnerProduct >:

Public Types
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

Public Member Functions
	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.

Public Attributes
params	prm

Private Member Functions
template<class Vec>
scalar_type	norm (const Vec &x) const

Private Attributes
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

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

Detailed Description

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

Definition at line 103 of file GMRESSolver.h.

Member Typedef Documentation

◆ backend_params

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

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

Definition at line 113 of file GMRESSolver.h.

◆ backend_type

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

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

Definition at line 108 of file GMRESSolver.h.

◆ BackendType

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

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

Definition at line 109 of file 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

Definition at line 117 of file GMRESSolver.h.

◆ params

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

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

Definition at line 119 of file 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

Definition at line 116 of file 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

Definition at line 115 of file GMRESSolver.h.

◆ value_type

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

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

Definition at line 112 of file GMRESSolver.h.

◆ vector

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

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

Definition at line 111 of file GMRESSolver.h.

Constructor & Destructor Documentation

◆ 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.

Definition at line 122 of file GMRESSolver.h.

Member Function Documentation

◆ bytes()

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

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

inlinevirtual

Memory used in bytes.

Implements Arcane::Alina::SolverBase.

Definition at line 287 of file 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

Definition at line 315 of file 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]_.

Definition at line 156 of file 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.

Definition at line 270 of file GMRESSolver.h.

◆ operator<<

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

std::ostream & operator<<	(	std::ostream &	os,
		const GMRESSolver< Backend, InnerProduct > &	s )

friend

Definition at line 275 of file GMRESSolver.h.

Member Data Documentation

◆ cs

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

std::vector<coef_type> Arcane::Alina::GMRESSolver< Backend, InnerProduct >::cs

private

Definition at line 308 of file GMRESSolver.h.

◆ H

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

multi_array<coef_type, 2> Arcane::Alina::GMRESSolver< Backend, InnerProduct >::H

mutableprivate

Definition at line 307 of file GMRESSolver.h.

◆ inner_product

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

InnerProduct Arcane::Alina::GMRESSolver< Backend, InnerProduct >::inner_product

private

Definition at line 312 of file GMRESSolver.h.

◆ n

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

size_t Arcane::Alina::GMRESSolver< Backend, InnerProduct >::n

private

Definition at line 305 of file GMRESSolver.h.

◆ prm

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

params Arcane::Alina::GMRESSolver< Backend, InnerProduct >::prm

Definition at line 285 of file GMRESSolver.h.

◆ r

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

std::shared_ptr<vector> Arcane::Alina::GMRESSolver< Backend, InnerProduct >::r

private

Definition at line 309 of file GMRESSolver.h.

◆ s

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

std::vector<coef_type> Arcane::Alina::GMRESSolver< Backend, InnerProduct >::s

mutableprivate

Definition at line 308 of file GMRESSolver.h.

◆ sn

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

std::vector<coef_type> Arcane::Alina::GMRESSolver< Backend, InnerProduct >::sn

private

Definition at line 308 of file GMRESSolver.h.

◆ v

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

std::vector<std::shared_ptr<vector> > Arcane::Alina::GMRESSolver< Backend, InnerProduct >::v

private

Definition at line 310 of file GMRESSolver.h.

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

GMRESSolver.h

Public Types

Public Member Functions

Public Attributes

Private Member Functions

Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ backend_params

◆ backend_type

◆ BackendType

◆ coef_type

◆ params

◆ rhs_type

◆ scalar_type

◆ value_type

◆ vector

Constructor & Destructor Documentation

◆ GMRESSolver()

Member Function Documentation

◆ bytes()

◆ norm()

◆ operator()() [1/2]

◆ operator()() [2/2]

Friends And Related Symbol Documentation

◆ operator<<

Member Data Documentation

◆ cs

◆ H

◆ inner_product

◆ n

◆ prm

◆ r

◆ s

◆ sn

◆ v