terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT > Class Template Reference

Preconditioned MINRES (PMINRES) iterative solver for symmetric indefinite linear systems. More...

#include <pminres.hpp>

Public Types
using	OperatorType = OperatorT
	Operator type to be solved.
using	SolutionVectorType = SrcOf< OperatorType >
	Solution vector type.
using	RHSVectorType = DstOf< OperatorType >
	Right-hand side vector type.
using	ScalarType = typename SolutionVectorType::ScalarType
	Scalar type for computations.

Public Member Functions
	PMINRES (const IterativeSolverParameters &params, const std::shared_ptr< util::Table > &statistics, const std::vector< SolutionVectorType > &tmp)
	Construct a PMINRES solver with default identity preconditioner.
	PMINRES (const IterativeSolverParameters &params, const std::shared_ptr< util::Table > &statistics, const std::vector< SolutionVectorType > &tmp, const PreconditionerT preconditioner)
	Construct a PMINRES solver with a custom preconditioner.
void	set_tag (const std::string &tag)
	Set a tag string for statistics output.
void	solve_impl (OperatorType &A, SolutionVectorType &x, const RHSVectorType &b)
	Solve the linear system \( Ax = b \) using PMINRES. Calls the iterative solver and updates statistics.

Detailed Description

template<OperatorLike OperatorT, SolverLike PreconditionerT = IdentitySolver< OperatorT >>
class terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT >

Preconditioned MINRES (PMINRES) iterative solver for symmetric indefinite linear systems.

See, e.g.,

Elman, H. C., Silvester, D. J., & Wathen, A. J. (2014). 
Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. 
Oxford university press. 

Satisfies the SolverLike concept (see solver.hpp). Supports optional preconditioning.

Template Parameters

OperatorT	Operator type (must satisfy OperatorLike).
PreconditionerT	Preconditioner type (must satisfy SolverLike, defaults to IdentitySolver).

Member Typedef Documentation

OperatorType

template<OperatorLike OperatorT, SolverLike PreconditionerT = IdentitySolver< OperatorT >>

using terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT >::OperatorType = OperatorT

Operator type to be solved.

RHSVectorType

template<OperatorLike OperatorT, SolverLike PreconditionerT = IdentitySolver< OperatorT >>

using terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT >::RHSVectorType = DstOf< OperatorType >

Right-hand side vector type.

ScalarType

template<OperatorLike OperatorT, SolverLike PreconditionerT = IdentitySolver< OperatorT >>

using terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT >::ScalarType = typename SolutionVectorType::ScalarType

Scalar type for computations.

SolutionVectorType

template<OperatorLike OperatorT, SolverLike PreconditionerT = IdentitySolver< OperatorT >>

using terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT >::SolutionVectorType = SrcOf< OperatorType >

Solution vector type.

Constructor & Destructor Documentation

PMINRES() [1/2]

template<OperatorLike OperatorT, SolverLike PreconditionerT = IdentitySolver< OperatorT >>

terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT >::PMINRES ( const IterativeSolverParameters &  params, const std::shared_ptr< util::Table > &  statistics, const std::vector< SolutionVectorType > &  tmp  )

inline

Construct a PMINRES solver with default identity preconditioner.

Parameters

params	Iterative solver parameters.
statistics	Shared pointer to statistics table.
tmp	Temporary vectors for workspace.

PMINRES() [2/2]

template<OperatorLike OperatorT, SolverLike PreconditionerT = IdentitySolver< OperatorT >>

terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT >::PMINRES ( const IterativeSolverParameters &  params, const std::shared_ptr< util::Table > &  statistics, const std::vector< SolutionVectorType > &  tmp, const PreconditionerT  preconditioner  )

inline

Construct a PMINRES solver with a custom preconditioner.

Parameters

params	Iterative solver parameters.
statistics	Shared pointer to statistics table.
tmp	Temporary vectors for workspace.
preconditioner	Preconditioner solver.

Member Function Documentation

set_tag()

template<OperatorLike OperatorT, SolverLike PreconditionerT = IdentitySolver< OperatorT >>

void terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT >::set_tag ( const std::string &  tag )

inline

Set a tag string for statistics output.

Parameters

tag	Tag string.

solve_impl()

template<OperatorLike OperatorT, SolverLike PreconditionerT = IdentitySolver< OperatorT >>

void terra::linalg::solvers::PMINRES< OperatorT, PreconditionerT >::solve_impl ( OperatorType &  A, SolutionVectorType &  x, const RHSVectorType &  b  )

inline

Solve the linear system \( Ax = b \) using PMINRES. Calls the iterative solver and updates statistics.

Parameters

A	Operator (matrix).
x	Solution vector (output).
b	Right-hand side vector (input).

< Temporary vector for A*z.

< Temporary vector for v_{j-1}.

< Temporary vector for v_j.

< Temporary vector for w_{j-1}.

< Temporary vector for w_j.

< Temporary vector for z_{j+1}.

< Temporary vector for z.

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

• pminres.hpp