Multigrid solves a linear system by combining cheap iterative sweeps (smoothers) on a hierarchy of progressively coarser representations of the operator with corrections transferred between adjacent levels. More...

#include <ginkgo/core/solver/multigrid.hpp>

Inheritance diagram for gko::solver::Multigrid:

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Collaboration diagram for gko::solver::Multigrid:

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Classes
class	Factory

struct	parameters_type

Public Member Functions
bool	apply_uses_initial_guess () const override
	Return true as iterative solvers use the data in x as an initial guess or false if multigrid always set the input as zero. More...

std::vector< std::shared_ptr< const gko::multigrid::MultigridLevel > >	get_mg_level_list () const
	Gets the list of MultigridLevel operators. More...

std::vector< std::shared_ptr< const LinOp > >	get_pre_smoother_list () const
	Gets the list of pre-smoother operators. More...

std::vector< std::shared_ptr< const LinOp > >	get_mid_smoother_list () const
	Gets the list of mid-smoother operators. More...

std::vector< std::shared_ptr< const LinOp > >	get_post_smoother_list () const
	Gets the list of post-smoother operators. More...

std::shared_ptr< const LinOp >	get_coarsest_solver () const
	Gets the operator at the coarsest level. More...

multigrid::cycle	get_cycle () const
	Get the cycle of multigrid. More...

void	set_cycle (multigrid::cycle cycle)
	Set the cycle of multigrid. More...

const parameters_type &	get_parameters () const

Public Member Functions inherited from gko::LinOp
void	apply (ptr_param< const LinOp > b, ptr_param< LinOp > x) const
	Applies a linear operator to a vector (or a sequence of vectors). More...

void	apply (ptr_param< const LinOp > alpha, ptr_param< const LinOp > b, ptr_param< const LinOp > beta, ptr_param< LinOp > x) const
	Performs the operation x = alpha * op(b) + beta * x. More...

const dim< 2 > &	get_size () const noexcept
	Returns the size of the operator. More...

LinOp &	operator= (const LinOp &)=default
	Copy-assigns a LinOp. More...

LinOp &	operator= (LinOp &&other)
	Move-assigns a LinOp. More...

	LinOp (const LinOp &)=default
	Copy-constructs a LinOp. More...

	LinOp (LinOp &&other)
	Move-constructs a LinOp. More...

Public Member Functions inherited from gko::PolymorphicObject
virtual void	validate_data () const
	Throws gko::InvalidData exception if we found the data inside the object does not fulfill certain property up to our knowledge.

PolymorphicObject &	operator= (const PolymorphicObject &)

std::shared_ptr< const Executor >	get_executor () const noexcept
	Returns the Executor of the object. More...

Public Member Functions inherited from gko::log::EnableLogging< PolymorphicObject >
void	add_logger (std::shared_ptr< const Logger > logger) override

void	remove_logger (const Logger *logger) override

void	remove_logger (ptr_param< const Logger > logger)

const std::vector< std::shared_ptr< const Logger > > &	get_loggers () const override

void	clear_loggers () override

Public Member Functions inherited from gko::log::Loggable
void	remove_logger (ptr_param< const Logger > logger)

Public Member Functions inherited from gko::solver::EnableSolverBase< Multigrid >
EnableSolverBase &	operator= (const EnableSolverBase &other)
	Creates a shallow copy of the provided system matrix, clones it onto this executor if executors don't match.

EnableSolverBase &	operator= (EnableSolverBase &&other)
	Moves the provided system matrix, clones it onto this executor if executors don't match. More...

	EnableSolverBase (std::shared_ptr< const LinOp > system_matrix)

	EnableSolverBase (const EnableSolverBase &other)
	Creates a shallow copy of the provided system matrix.

	EnableSolverBase (EnableSolverBase &&other)
	Moves the provided system matrix. More...

int	get_num_workspace_ops () const override

std::vector< std::string >	get_workspace_op_names () const override

std::vector< int >	get_workspace_scalars () const override
	Returns the IDs of all scalars (workspace vectors with system dimension-independent size, usually 1 x num_rhs).

std::vector< int >	get_workspace_vectors () const override
	Returns the IDs of all vectors (workspace vectors with system dimension-dependent size, usually system_matrix_size x num_rhs).

Public Member Functions inherited from gko::solver::SolverBase< LinOp >
std::shared_ptr< const LinOp >	get_system_matrix () const
	Returns the system matrix, with its concrete type, used by the solver. More...

Public Member Functions inherited from gko::solver::EnableIterativeBase< Multigrid >
EnableIterativeBase &	operator= (const EnableIterativeBase &other)
	Creates a shallow copy of the provided stopping criterion, clones it onto this executor if executors don't match.

EnableIterativeBase &	operator= (EnableIterativeBase &&other)
	Moves the provided stopping criterion, clones it onto this executor if executors don't match. More...

	EnableIterativeBase (std::shared_ptr< const stop::CriterionFactory > stop_factory)

	EnableIterativeBase (const EnableIterativeBase &other)
	Creates a shallow copy of the provided stopping criterion.

	EnableIterativeBase (EnableIterativeBase &&other)
	Moves the provided stopping criterion. More...

void	set_stop_criterion_factory (std::shared_ptr< const stop::CriterionFactory > new_stop_factory) override
	Sets the stopping criterion of the solver. More...

Public Member Functions inherited from gko::solver::IterativeBase
std::shared_ptr< const stop::CriterionFactory >	get_stop_criterion_factory () const
	Gets the stopping criterion factory of the solver. More...

Static Public Member Functions
static auto	build () -> decltype(Factory ::create())

static parameters_type	parse (const config::pnode &config, const config::registry &context, const config::type_descriptor &td_for_child=config::make_type_descriptor<>())
	Create the parameters from the property_tree. More...

Friends
class	EnableApplyWithInitialGuess< Multigrid >

Detailed Description

Multigrid solves a linear system by combining cheap iterative sweeps (smoothers) on a hierarchy of progressively coarser representations of the operator with corrections transferred between adjacent levels.

A smoother on the fine level removes the high-frequency components of the error quickly; the remaining low-frequency error is well-resolved on a coarser space, where it is computed by a cheaper solve — or, recursively, by another multigrid call. The correction is prolongated back to the fine level and a second smoothing sweep removes any high-frequency error introduced by the transfer. Because each coarser level holds only a fraction of the unknowns of the next, the total work per cycle stays close to that of a single fine-level matrix-vector apply.

Each level \( \ell \) holds a system matrix \( A_\ell \), a smoother \( S_\ell \), a restriction operator \( R_\ell : \mathbb{R}^{n_\ell} \to \mathbb{R}^{n_{\ell+1}} \) and a prolongation operator \( P_\ell : \mathbb{R}^{n_{\ell+1}} \to \mathbb{R}^{n_\ell} \). The Galerkin coarse operator is \( A_{\ell+1} = R_\ell A_\ell P_\ell \). One V-cycle step at level \( \ell \) on a fine-level system \( A_\ell x = b \) is:

\[ \begin{aligned} x &\leftarrow x + S_\ell^{\mathrm{pre}}(b - A_\ell x) && \text{(pre-smooth)}, \\ r_{\ell+1} &= R_\ell (b - A_\ell x) && \text{(restrict)}, \\ e_{\ell+1} &\approx A_{\ell+1}^{-1} r_{\ell+1} && \text{(recursive coarse solve)}, \\ x &\leftarrow x + P_\ell e_{\ell+1} && \text{(prolongate and correct)}, \\ x &\leftarrow x + S_\ell^{\mathrm{post}}(b - A_\ell x) && \text{(post-smooth)}. \end{aligned} \]

At the coarsest level the recursive call is replaced by a direct or iterative coarse solver. W- and F-cycles differ from V only in how many recursive coarse-solves are performed per level (see the cycle enum above).

Ginkgo uses the index from 0 for finest level (original problem size) ~ N for the coarsest level (the coarsest solver), and its level counts is N (N multigrid level generation).

References

Briggs, W. L., Henson, V. E., McCormick, S. F. A Multigrid Tutorial. 2nd ed. SIAM, 2000. https://doi.org/10.1137/1.9780898719505
Trottenberg, U., Oosterlee, C. W., Schüller, A. Multigrid. 1st ed. Academic Press, 2001. ISBN 978-0-12-701070-0.

Member Function Documentation

◆ apply_uses_initial_guess()

bool gko::solver::Multigrid::apply_uses_initial_guess ( ) const

inlineoverridevirtual

Return true as iterative solvers use the data in x as an initial guess or false if multigrid always set the input as zero.

Returns: bool it is related to parameters variable zero_guess

Reimplemented from gko::LinOp.

References gko::solver::provided.

◆ get_coarsest_solver()

std::shared_ptr<const LinOp> gko::solver::Multigrid::get_coarsest_solver ( ) const

inline

Gets the operator at the coarsest level.

Returns: the coarsest operator

◆ get_cycle()

multigrid::cycle gko::solver::Multigrid::get_cycle ( ) const

inline

Get the cycle of multigrid.

Returns: the multigrid::cycle

References gko::solver::Multigrid::parameters_type::cycle.

◆ get_mg_level_list()

std::vector<std::shared_ptr<const gko::multigrid::MultigridLevel> > gko::solver::Multigrid::get_mg_level_list ( ) const

inline

Gets the list of MultigridLevel operators.

Returns: the list of MultigridLevel operators

◆ get_mid_smoother_list()

std::vector<std::shared_ptr<const LinOp> > gko::solver::Multigrid::get_mid_smoother_list ( ) const

inline

Gets the list of mid-smoother operators.

Returns: the list of mid-smoother operators

◆ get_post_smoother_list()

std::vector<std::shared_ptr<const LinOp> > gko::solver::Multigrid::get_post_smoother_list ( ) const

inline

Gets the list of post-smoother operators.

Returns: the list of post-smoother operators

◆ get_pre_smoother_list()

std::vector<std::shared_ptr<const LinOp> > gko::solver::Multigrid::get_pre_smoother_list ( ) const

inline

Gets the list of pre-smoother operators.

Returns: the list of pre-smoother operators

◆ parse()

static parameters_type gko::solver::Multigrid::parse	(	const config::pnode &	config,
		const config::registry &	context,
		const config::type_descriptor &	td_for_child = `config::make_type_descriptor<>()`
	)

static

Create the parameters from the property_tree.

Because this is directly tied to the specific type, the value/index type settings within config are ignored and type_descriptor is only used for children configs.

Parameters

config	the property tree for setting
context	the registry
td_for_child	the type descriptor for children configs

Returns: parameters

Note: Multigrid does not support the selector option in file config

◆ set_cycle()

void gko::solver::Multigrid::set_cycle ( multigrid::cycle cycle )

inline

Set the cycle of multigrid.

Parameters

multigrid::cycle the new cycle

References gko::solver::Multigrid::parameters_type::cycle.

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

ginkgo/core/solver/multigrid.hpp

Classes

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Function Documentation

◆ apply_uses_initial_guess()

◆ get_coarsest_solver()

◆ get_cycle()

◆ get_mg_level_list()

◆ get_mid_smoother_list()

◆ get_post_smoother_list()

◆ get_pre_smoother_list()

◆ parse()

◆ set_cycle()