terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT > Class Template Reference

Multigrid solver for linear systems. More...

#include <multigrid.hpp>

Public Types
using	OperatorType = OperatorT
	Operator type to be solved.
using	ProlongationType = ProlongationT
	Prolongation operator type.
using	RestrictionType = RestrictionT
	Restriction operator type.
using	SmootherType = SmootherT
	Smoother type.
using	CoarseGridSolverType = CoarseGridSolverT
	Coarse grid solver type.
using	SolutionVectorType = SrcOf< OperatorType >
	Solution vector type.
using	RHSVectorType = DstOf< OperatorType >
	Right-hand side vector type.
using	ScalarType = SolutionVectorType::ScalarType
	Scalar type for computations.

Public Member Functions
	Multigrid (const std::vector< ProlongationType > &P_additive, const std::vector< RestrictionType > &R, const std::vector< OperatorT > &A_c, const std::vector< SolutionVectorType > &tmp_r, const std::vector< SolutionVectorType > &tmp_e, const std::vector< SolutionVectorType > &tmp, const std::vector< SmootherType > &smoothers_pre, const std::vector< SmootherType > &smoothers_post, const CoarseGridSolverType &coarse_grid_solver, int num_cycles, ScalarType relative_residual_threshold)
	Construct a multigrid solver.
	Multigrid (const std::vector< ProlongationType > &P_additive, const std::vector< RestrictionType > &R, const std::vector< OperatorT > &A_c, const std::vector< SolutionVectorType > &tmp_r, const std::vector< SolutionVectorType > &tmp_e, const std::vector< SolutionVectorType > &tmp, const std::vector< SmootherType > &smoothers_pre, const std::vector< SmootherType > &smoothers_post, const CoarseGridSolverType &coarse_grid_solver, int num_cycles, ScalarType relative_residual_threshold, std::vector< RedistributeT > redistribute_down, std::vector< SolutionVectorType > tmp_r_fine, std::vector< SolutionVectorType > tmp_e_fine)
	Construct an agglomerated multigrid solver.
void	set_tag (const std::string &tag)
	Set a tag string for statistics output.
void	collect_statistics (const std::shared_ptr< util::Table > &statistics)
	Collect statistics in a shared table.
void	solve_impl (OperatorType &A, SolutionVectorType &x, const RHSVectorType &b)
	Solve the linear system using multigrid cycles. Calls the recursive V-cycle and updates statistics.

Detailed Description

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>
class terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >

Multigrid solver for linear systems.

Satisfies the SolverLike concept (see solver.hpp). Supports arbitrary operators, prolongation/restriction, smoothers, and coarse grid solvers. Implements recursive V-cycle multigrid.

Optionally supports hierarchical agglomeration: per level, a Redistribute operator moves the restricted residual from the fine level's communicator to a (smaller) coarse level communicator, and the coarse correction back up. Inactive coarse ranks skip the recursive descent but still participate in the collectives inside Redistribute::apply / apply_transpose.

Template Parameters

OperatorT	Operator type (must satisfy OperatorLike).
ProlongationT	Prolongation operator type (must satisfy OperatorLike).
RestrictionT	Restriction operator type (must satisfy OperatorLike).
SmootherT	Smoother type (must satisfy SolverLike).
CoarseGridSolverT	Coarse grid solver type (must satisfy SolverLike).
RedistributeT	Optional; defaults to NoRedistribute. Pass the concrete Redistribute<GridDataType> type when using agglomeration.

Member Typedef Documentation

CoarseGridSolverType

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

using terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::CoarseGridSolverType = CoarseGridSolverT

Coarse grid solver type.

OperatorType

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

using terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::OperatorType = OperatorT

Operator type to be solved.

ProlongationType

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

using terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::ProlongationType = ProlongationT

Prolongation operator type.

RestrictionType

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

using terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::RestrictionType = RestrictionT

Restriction operator type.

RHSVectorType

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

using terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::RHSVectorType = DstOf< OperatorType >

Right-hand side vector type.

ScalarType

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

using terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::ScalarType = SolutionVectorType::ScalarType

Scalar type for computations.

SmootherType

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

using terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::SmootherType = SmootherT

Smoother type.

SolutionVectorType

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

using terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::SolutionVectorType = SrcOf< OperatorType >

Solution vector type.

Constructor & Destructor Documentation

Multigrid() [1/2]

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::Multigrid ( const std::vector< ProlongationType > &  P_additive, const std::vector< RestrictionType > &  R, const std::vector< OperatorT > &  A_c, const std::vector< SolutionVectorType > &  tmp_r, const std::vector< SolutionVectorType > &  tmp_e, const std::vector< SolutionVectorType > &  tmp, const std::vector< SmootherType > &  smoothers_pre, const std::vector< SmootherType > &  smoothers_post, const CoarseGridSolverType &  coarse_grid_solver, int  num_cycles, ScalarType  relative_residual_threshold  )

inline

Construct a multigrid solver.

Vector ordering of arguments always goes from the coarsest level (index 0) to the finest.

Parameters

P_additive	Prolongation operators for each coarse level. Size must match the number of levels - 1. Must be additive prolongation operators, i.e., apply( P, x, y ) computes \( y = y + P x \).
R	Restriction operators for each coarse level.
A_c	Coarse grid operators for each coarse level.
tmp_r	Temporary residual vectors for each coarse level.
tmp_e	Temporary error vectors for each coarse level.
tmp	Temporary workspace vectors for each level (including the finest level).
smoothers_pre	Pre-smoothers for each level (including the finest level).
smoothers_post	Post-smoothers for each level (including the finest level).
coarse_grid_solver	Coarse grid solver.
num_cycles	Number of multigrid cycles to perform.
relative_residual_threshold	Relative residual threshold for stopping.

Multigrid() [2/2]

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::Multigrid ( const std::vector< ProlongationType > &  P_additive, const std::vector< RestrictionType > &  R, const std::vector< OperatorT > &  A_c, const std::vector< SolutionVectorType > &  tmp_r, const std::vector< SolutionVectorType > &  tmp_e, const std::vector< SolutionVectorType > &  tmp, const std::vector< SmootherType > &  smoothers_pre, const std::vector< SmootherType > &  smoothers_post, const CoarseGridSolverType &  coarse_grid_solver, int  num_cycles, ScalarType  relative_residual_threshold, std::vector< RedistributeT >  redistribute_down, std::vector< SolutionVectorType >  tmp_r_fine, std::vector< SolutionVectorType >  tmp_e_fine  )

inline

Construct an agglomerated multigrid solver.

Same as the non-agglomerated constructor, plus:

• redistribute_down: Redistribute operators, one per coarse descent step. redistribute_down[L-1] moves a vector from level L's comm to level L-1's comm. apply_transpose is used on the way back up.
• tmp_r_fine, tmp_e_fine: per-coarse-level scratch vectors allocated on the fine level's communicator. Restriction output goes into tmp_r_fine; prolongation input is read from tmp_e_fine. tmp_r, tmp_e must carry the coarse level's sub-comm; on ranks not part of the sub-comm they are empty (zero-subdomain) vectors.

Member Function Documentation

collect_statistics()

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

void terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::collect_statistics ( const std::shared_ptr< util::Table > &  statistics )

inline

Collect statistics in a shared table.

Parameters

statistics

Shared pointer to statistics table.

set_tag()

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

void terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::set_tag ( const std::string &  tag )

inline

Set a tag string for statistics output.

Parameters

tag	Tag string.

solve_impl()

template<OperatorLike OperatorT, OperatorLike ProlongationT, OperatorLike RestrictionT, SolverLike SmootherT, SolverLike CoarseGridSolverT, class RedistributeT = NoRedistribute>

void terra::linalg::solvers::Multigrid< OperatorT, ProlongationT, RestrictionT, SmootherT, CoarseGridSolverT, RedistributeT >::solve_impl ( OperatorType &  A, SolutionVectorType &  x, const RHSVectorType &  b  )

inline

Solve the linear system using multigrid cycles. Calls the recursive V-cycle and updates statistics.

Parameters

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

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

• multigrid.hpp