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

Preconditioned Conjugate Gradient (PCG) iterative solver for symmetric positive definite linear systems. More...

#include <pcg.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
	PCG (const IterativeSolverParameters &params, const std::shared_ptr< util::Table > &statistics, const std::vector< SolutionVectorType > &tmps)
	Construct a PCG solver with default identity preconditioner.
	PCG (const IterativeSolverParameters &params, const std::shared_ptr< util::Table > &statistics, const std::vector< SolutionVectorType > &tmps, const PreconditionerT preconditioner)
	Construct a PCG 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 PCG. Calls the iterative solver and updates statistics.

Detailed Description

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

Preconditioned Conjugate Gradient (PCG) iterative solver for symmetric positive definite 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::PCG< OperatorT, PreconditionerT >::OperatorType = OperatorT

Operator type to be solved.

RHSVectorType

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

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

Right-hand side vector type.

ScalarType

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

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

Scalar type for computations.

SolutionVectorType

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

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

Solution vector type.

Constructor & Destructor Documentation

PCG() [1/2]

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

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

inline

Construct a PCG solver with default identity preconditioner.

Parameters

params	Iterative solver parameters.
statistics	Shared pointer to statistics table.
tmps	Temporary vectors for workspace. (At least 4 vectors are required.)

PCG() [2/2]

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

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

inline

Construct a PCG solver with a custom preconditioner.

Parameters

params	Iterative solver parameters.
statistics	Shared pointer to statistics table.
tmps	Temporary vectors for workspace. (At least 4 vectors are required.)
preconditioner	Preconditioner solver.

Member Function Documentation

set_tag()

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

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

inline

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

Parameters

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

< Residual vector.

< Search direction vector.

< Temporary vector for A*p.

< Preconditioned residual vector.

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

• pcg.hpp