Interface for multigrid solver (via solve) that iteratively performs standard vcycles. More...

#include <multigrid.hpp>

Public Member Functions
	~Multigrid ()

	Multigrid ()=delete

	Multigrid (AMG::InterpolatorBase< EleType > interpolator_, AMG::SmootherBase< EleType > smoother_, const Eigen::SparseMatrix< EleType > &A, const Eigen::Matrix< EleType, -1, 1 > &b, size_t n_levels_, EleType tolerance_=1e-9, size_t compute_error_every_n_iters_=10, size_t n_iters_=100)
	Construct a new Multigrid object.

void	vcycle ()
	A single multigrid vcycle.

const Eigen::Matrix< EleType, -1, 1 > &	solve ()
	Solve a linear system of equations via vcycle.

const Eigen::SparseMatrix< EleType > &	get_coefficient_matrix (size_t level) const

const Eigen::Matrix< EleType, -1, 1 > &	get_soln (size_t level) const

const Eigen::Matrix< EleType, -1, 1 > &	get_rhs (size_t level) const

const size_t	get_n_dofs (size_t level) const

const EleType	get_tolerance () const

void	display_error_on ()

void	display_error_off ()

Private Member Functions
size_t	n_H_dofs_from_n_h_dofs (size_t h_dofs)
	Return number of next coarsest dofs given finer dofs.

Private Attributes
InterpolatorBase< EleType > *	interpolator
	Interpolator providing restriction and prolongation operations.

AMG::SmootherBase< EleType > *	smoother

Eigen::SimplicialLDLT< Eigen::SparseMatrix< EleType > >	coarse_direct_solver

EleType	tolerance
	Tolerance below which a smoother is considered to have converged.

size_t	compute_error_every_n_iters
	Compute the error every `n` iterations during smoothing.

size_t	n_iters
	Maximum number of iterations before smoothing termination.

size_t	n_fine_nodes

size_t	n_levels
	Number of multigrid levels where level 0 is finest.

size_t	finest_grid_ix = 0
	Index of the finest grid.

size_t	coarsest_grid_ix
	Index of the coarsest grid.

std::vector< size_t >	level_to_n_dofs
	Map multigrid level to number of degrees of freedom for that level.

std::vector< Eigen::SparseMatrix< EleType > >	level_to_coefficient_matrix
	Map multigrid level to coefficient matrix A.

std::vector< Eigen::Matrix< EleType, -1, 1 > >	level_to_rhs
	Map multigrid level to right hand side (forcing) vector.

std::vector< Eigen::Matrix< EleType, -1, 1 > >	level_to_soln
	Map multigrid level to solution (u) vector.

std::vector< Eigen::Matrix< EleType, -1, 1 > >	level_to_residual
	Map multigrid level to residual (e) vector.

bool	display_error {false}

Detailed Description

template<class EleType>
class AMG::Multigrid< EleType >

Interface for multigrid solver (via solve) that iteratively performs standard vcycles.

Template Parameters

EleType

Constructor & Destructor Documentation

◆ ~Multigrid()

template<class EleType >

AMG::Multigrid< EleType >::~Multigrid ( )

inline

◆ Multigrid() [1/2]

template<class EleType >

AMG::Multigrid< EleType >::Multigrid ( )

delete

◆ Multigrid() [2/2]

template<class EleType >

AMG::Multigrid< EleType >::Multigrid	(	AMG::InterpolatorBase< EleType > *	interpolator_,
		AMG::SmootherBase< EleType > *	smoother_,
		const Eigen::SparseMatrix< EleType > &	A,
		const Eigen::Matrix< EleType, -1, 1 > &	b,
		size_t	n_levels_,
		EleType	tolerance_ = 1e-9,
		size_t	compute_error_every_n_iters_ = 10,
		size_t	n_iters_ = 100 )

inline

Construct a new Multigrid object.

Parameters

interpolator_	Provide prolongation and restriction operators.
smoother_	Smooth high frequency errors in post/pre relaxation.
A	Coefficients matrix for discretized governing equations.
b	Right hand side of linear system `Au = b`.
n_levels_	Desired number of levels where level 0 is finest level.
tolerance_	Minimum tolerance residual must be leq to converge.
compute_error_every_n_iters_	Compute convergence on this interval.
n_iters_	Max number of iterations for stopping solution via vcycles.

Member Function Documentation

◆ display_error_off()

template<class EleType >

void AMG::Multigrid< EleType >::display_error_off ( )

inline

◆ display_error_on()

template<class EleType >

void AMG::Multigrid< EleType >::display_error_on ( )

inline

◆ get_coefficient_matrix()

template<class EleType >

const Eigen::SparseMatrix< EleType > & AMG::Multigrid< EleType >::get_coefficient_matrix ( size_t level ) const

inline

◆ get_n_dofs()

template<class EleType >

const size_t AMG::Multigrid< EleType >::get_n_dofs ( size_t level ) const

inline

◆ get_rhs()

template<class EleType >

const Eigen::Matrix< EleType, -1, 1 > & AMG::Multigrid< EleType >::get_rhs ( size_t level ) const

inline

◆ get_soln()

template<class EleType >

const Eigen::Matrix< EleType, -1, 1 > & AMG::Multigrid< EleType >::get_soln ( size_t level ) const

inline

◆ get_tolerance()

template<class EleType >

const EleType AMG::Multigrid< EleType >::get_tolerance ( ) const

inline

◆ n_H_dofs_from_n_h_dofs()

template<class EleType >

size_t AMG::Multigrid< EleType >::n_H_dofs_from_n_h_dofs ( size_t h_dofs )

inlineprivate

Return number of next coarsest dofs given finer dofs.

The next coarsest dofs formula follows from the following (see ref [1]):

nc = n/2 - 1
nf = n - 1
# nc in terms of nf
nc = (nf + 1)/2 - 1

References:

[1] : Briggs2000. "A Multigrid Tutorial, 2ed". pp. 34.

Returns: size_t

◆ solve()

template<class EleType >

const Eigen::Matrix< EleType, -1, 1 > & AMG::Multigrid< EleType >::solve ( )

inline

Solve a linear system of equations via vcycle.

◆ vcycle()

template<class EleType >

void AMG::Multigrid< EleType >::vcycle ( )

inline

A single multigrid vcycle.

Ref [1] was used for the main algorithm (non-recursive) while refs [2-4] were used to verify that coarse solutions need to be zeroed at each vcycle.

References:

[1] : Algebraic Multigrid from amgcl

[2] : Kostler2008. "Multigrid HowTo: simple Multigrid solver in C++ in less than 200 lines of code"

[3] : Pawar2019. "CFD Julia: A Learning Module Structuring an Introductory Course on Computational Fluid Dynamics "

[4] : AlgebraicMultigrid.jl solve

Member Data Documentation

◆ coarse_direct_solver

template<class EleType >

Eigen::SimplicialLDLT<Eigen::SparseMatrix<EleType> > AMG::Multigrid< EleType >::coarse_direct_solver

private

◆ coarsest_grid_ix

template<class EleType >

size_t AMG::Multigrid< EleType >::coarsest_grid_ix

private

Index of the coarsest grid.

◆ compute_error_every_n_iters

template<class EleType >

size_t AMG::Multigrid< EleType >::compute_error_every_n_iters

private

Compute the error every n iterations during smoothing.

◆ display_error

template<class EleType >

bool AMG::Multigrid< EleType >::display_error {false}

private

◆ finest_grid_ix

template<class EleType >

size_t AMG::Multigrid< EleType >::finest_grid_ix = 0

private

Index of the finest grid.

◆ interpolator

template<class EleType >

InterpolatorBase<EleType>* AMG::Multigrid< EleType >::interpolator

private

Interpolator providing restriction and prolongation operations.

◆ level_to_coefficient_matrix

template<class EleType >

std::vector<Eigen::SparseMatrix<EleType> > AMG::Multigrid< EleType >::level_to_coefficient_matrix

private

Map multigrid level to coefficient matrix A.

◆ level_to_n_dofs

template<class EleType >

std::vector<size_t> AMG::Multigrid< EleType >::level_to_n_dofs

private

Map multigrid level to number of degrees of freedom for that level.

Note that n_dofs==n_nodes*n_nodes

◆ level_to_residual

template<class EleType >

std::vector<Eigen::Matrix<EleType, -1, 1> > AMG::Multigrid< EleType >::level_to_residual

private

Map multigrid level to residual (e) vector.

◆ level_to_rhs

template<class EleType >

std::vector<Eigen::Matrix<EleType, -1, 1> > AMG::Multigrid< EleType >::level_to_rhs

private

Map multigrid level to right hand side (forcing) vector.

◆ level_to_soln

template<class EleType >

std::vector<Eigen::Matrix<EleType, -1, 1> > AMG::Multigrid< EleType >::level_to_soln

private

Map multigrid level to solution (u) vector.

◆ n_fine_nodes

template<class EleType >

size_t AMG::Multigrid< EleType >::n_fine_nodes

private

◆ n_iters

template<class EleType >

size_t AMG::Multigrid< EleType >::n_iters

private

Maximum number of iterations before smoothing termination.

◆ n_levels

template<class EleType >

size_t AMG::Multigrid< EleType >::n_levels

private

Number of multigrid levels where level 0 is finest.

◆ smoother

template<class EleType >

AMG::SmootherBase<EleType>* AMG::Multigrid< EleType >::smoother

private

◆ tolerance

template<class EleType >

EleType AMG::Multigrid< EleType >::tolerance

private

Tolerance below which a smoother is considered to have converged.

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

include/amg/multigrid.hpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ ~Multigrid()

◆ Multigrid() [1/2]

◆ Multigrid() [2/2]

Member Function Documentation

◆ display_error_off()

◆ display_error_on()

◆ get_coefficient_matrix()

◆ get_n_dofs()

◆ get_rhs()

◆ get_soln()

◆ get_tolerance()

◆ n_H_dofs_from_n_h_dofs()

◆ solve()

◆ vcycle()

Member Data Documentation

◆ coarse_direct_solver

◆ coarsest_grid_ix

◆ compute_error_every_n_iters

◆ display_error

◆ finest_grid_ix

◆ interpolator

◆ level_to_coefficient_matrix

◆ level_to_n_dofs

◆ level_to_residual

◆ level_to_rhs

◆ level_to_soln

◆ n_fine_nodes

◆ n_iters

◆ n_levels

◆ smoother

◆ tolerance