Solve using GMRES with multigrid as preconditioner. More...

#include <AMReX_GMRES_MLMG.H>

Public Types
using	VEC = Vector< MF >

using	MG = MLMGT< MF >

using	RT = typename MG::RT

using	GM = GMRES< Vector< MF >, GMRESMLMGT< MF > >

Public Member Functions
	GMRESMLMGT (MG &mlmg)
	Wrap an existing MLMG hierarchy as a GMRES operator/preconditioner.

void	solve (MF &a_sol, MF const &a_rhs, RT a_tol_rel, RT a_tol_abs)
	Solve the linear system.

void	solve (Vector< MF * > const &a_sol, Vector< MF const * > const &a_rhs, RT a_tol_rel, RT a_tol_abs)
	Solve using pointer-to-MultiFab arrays (utility for existing MLMG data).

void	setVerbose (int v)
	Set verbosity level `v` for both GMRES and MLMG components.

void	setMaxIters (int niters)
	Cap the number of GMRES iterations executed per solve to `niters`.

int	getNumIters () const
	Number of iterations executed by the last solve().

RT	getResidualNorm () const
	Final residual 2-norm produced by the last solve().

GM &	getGMRES ()
	Direct access to the underlying GMRES driver for fine-grained tuning.

VEC	makeVecRHS () const
	Return a MultiFab vector without ghost cells for RHS storage.

VEC	makeVecLHS () const

RT	norm2 (VEC const &mf) const
	Return the 2-norm of `mf` using the multigrid operator's weighting.

RT	dotProduct (VEC const &mf1, VEC const &mf2) const
	Return the preconditioner-aware dot product between `mf1` and `mf2`.

void	apply (VEC &lhs, VEC const &rhs) const
	Apply the operator supplied to the constructor.

void	precond (VEC &lhs, VEC const &rhs) const
	Apply the MLMG-based preconditioner: $\text{lhs} = P^{-1}(\text{rhs})$ .

bool	usePrecond (bool new_flag)
	Enable or disable MLMG as a preconditioner.

void	setPrecondNumIters (int precond_niters)
	Adjust how many MLMG smoothing iterations run inside each GMRES iteration.

Static Public Member Functions
static void	scale (VEC &mf, RT scale_factor)
	Scale each component of `mf` by `scale_factor`.

static void	setToZero (VEC &lhs)
	Reset `lhs` to zero on every AMR level.

static void	assign (VEC &lhs, VEC const &rhs)
	Copy `rhs` into `lhs` level by level.

static void	increment (VEC &lhs, VEC const &rhs, RT a)
	Add a scaled vector: $\text{lhs} \mathrel{+}= a\,\text{rhs}$ .

static void	linComb (VEC &lhs, RT a, VEC const &rhs_a, RT b, VEC const &rhs_b)
	Form a linear combination: $\text{lhs} = a\,\text{rhs}_a + b\,\text{rhs}_b$ .

Detailed Description

template<typename MF>
class amrex::GMRESMLMGT< MF >

Solve using GMRES with multigrid as preconditioner.

The linear system to solve is provided by MLMG, which is also being used as the preconditioner.

Member Typedef Documentation

◆ GM

template<typename MF >

using amrex::GMRESMLMGT< MF >::GM = GMRES<Vector<MF>,GMRESMLMGT<MF> >

◆ MG

template<typename MF >

using amrex::GMRESMLMGT< MF >::MG = MLMGT<MF>

◆ RT

template<typename MF >

using amrex::GMRESMLMGT< MF >::RT = typename MG::RT

◆ VEC

template<typename MF >

using amrex::GMRESMLMGT< MF >::VEC = Vector<MF>

Constructor & Destructor Documentation

◆ GMRESMLMGT()

template<typename MF >

amrex::GMRESMLMGT< MF >::GMRESMLMGT ( MG & mlmg )

explicit

Wrap an existing MLMG hierarchy as a GMRES operator/preconditioner.

Parameters

mlmg	Multigrid object that provides apply/precond hooks.

Member Function Documentation

◆ apply()

template<typename MF >

void amrex::GMRESMLMGT< MF >::apply	(	VEC &	lhs,
		VEC const &	rhs
	)		const

Apply the operator supplied to the constructor.

Parameters

lhs	Destination vector receiving $L(\text{rhs})$ .
rhs	Source vector.

◆ assign()

template<typename MF >

void amrex::GMRESMLMGT< MF >::assign	(	VEC &	lhs,
		VEC const &	rhs
	)

static

Copy rhs into lhs level by level.

Parameters

lhs	Destination vector updated in place.
rhs	Source vector.

◆ dotProduct()

template<typename MF >

auto amrex::GMRESMLMGT< MF >::dotProduct	(	VEC const &	mf1,
		VEC const &	mf2
	)		const

Return the preconditioner-aware dot product between mf1 and mf2.

◆ getGMRES()

template<typename MF >

GM & amrex::GMRESMLMGT< MF >::getGMRES ( )

inline

Direct access to the underlying GMRES driver for fine-grained tuning.

◆ getNumIters()

template<typename MF >

int amrex::GMRESMLMGT< MF >::getNumIters ( ) const

inline

Number of iterations executed by the last solve().

◆ getResidualNorm()

template<typename MF >

RT amrex::GMRESMLMGT< MF >::getResidualNorm ( ) const

inline

Final residual 2-norm produced by the last solve().

◆ increment()

template<typename MF >

void amrex::GMRESMLMGT< MF >::increment	(	VEC &	lhs,
		VEC const &	rhs,
		RT	a
	)

static

Add a scaled vector: $\text{lhs} \mathrel{+}= a\,\text{rhs}$ .

Parameters

lhs	Accumulation target.
rhs	Source vector.
a	Scalar multiplier applied to `rhs`.

◆ linComb()

template<typename MF >

void amrex::GMRESMLMGT< MF >::linComb	(	VEC &	lhs,
		RT	a,
		VEC const &	rhs_a,
		RT	b,
		VEC const &	rhs_b
	)

static

Form a linear combination: $\text{lhs} = a\,\text{rhs}_a + b\,\text{rhs}_b$ .

Parameters

lhs	Destination vector written in place.
a	Scalar applied to `rhs_a`.
rhs_a	First source vector.
b	Scalar applied to `rhs_b`.
rhs_b	Second source vector.

◆ makeVecLHS()

template<typename MF >

auto amrex::GMRESMLMGT< MF >::makeVecLHS ( ) const

Return a MultiFab vector with one layer of ghost cells for LHS storage. Also set the data in the ghost cells to zero.

◆ makeVecRHS()

template<typename MF >

auto amrex::GMRESMLMGT< MF >::makeVecRHS ( ) const

Return a MultiFab vector without ghost cells for RHS storage.

◆ norm2()

template<typename MF >

auto amrex::GMRESMLMGT< MF >::norm2 ( VEC const & mf ) const

Return the 2-norm of mf using the multigrid operator's weighting.

◆ precond()

template<typename MF >

void amrex::GMRESMLMGT< MF >::precond	(	VEC &	lhs,
		VEC const &	rhs
	)		const

Apply the MLMG-based preconditioner: $\text{lhs} = P^{-1}(\text{rhs})$ .

Parameters

lhs	Destination vector, zeroed before solving when the preconditioner is enabled.
rhs	Source vector passed to the preconditioner.

◆ scale()

template<typename MF >

void amrex::GMRESMLMGT< MF >::scale	(	VEC &	mf,
		RT	scale_factor
	)

static

Scale each component of mf by scale_factor.

◆ setMaxIters()

template<typename MF >

void amrex::GMRESMLMGT< MF >::setMaxIters ( int niters )

inline

Cap the number of GMRES iterations executed per solve to niters.

◆ setPrecondNumIters()

template<typename MF >

void amrex::GMRESMLMGT< MF >::setPrecondNumIters ( int precond_niters )

inline

Adjust how many MLMG smoothing iterations run inside each GMRES iteration.

Parameters

precond_niters Number of MLMG iterations per GMRES iteration.

◆ setToZero()

template<typename MF >

void amrex::GMRESMLMGT< MF >::setToZero ( VEC & lhs )

static

Reset lhs to zero on every AMR level.

Parameters

lhs	Per-level vector that will be zeroed in place.

◆ setVerbose()

template<typename MF >

void amrex::GMRESMLMGT< MF >::setVerbose ( int v )

inline

Set verbosity level v for both GMRES and MLMG components.

◆ solve() [1/2]

template<typename MF >

void amrex::GMRESMLMGT< MF >::solve	(	MF &	a_sol,
		MF const &	a_rhs,
		RT	a_tol_rel,
		RT	a_tol_abs
	)

Solve the linear system.

Parameters

a_sol	unknowns, i.e., x in A x = b.
a_rhs	RHS, i.e., b in A x = b.
a_tol_rel	relative tolerance.
a_tol_abs	absolute tolerance.

◆ solve() [2/2]

template<typename MF >

void amrex::GMRESMLMGT< MF >::solve	(	Vector< MF * > const &	a_sol,
		Vector< MF const * > const &	a_rhs,
		RT	a_tol_rel,
		RT	a_tol_abs
	)

Solve using pointer-to-MultiFab arrays (utility for existing MLMG data).

Parameters

a_sol	Per-level solution MultiFabs (single component).
a_rhs	Per-level RHS MultiFabs (single component).
a_tol_rel	Relative tolerance.
a_tol_abs	Absolute tolerance.

◆ usePrecond()

template<typename MF >

bool amrex::GMRESMLMGT< MF >::usePrecond ( bool new_flag )

inline

Enable or disable MLMG as a preconditioner.

Parameters

new_flag Set true to enable, false to disable.

Returns: Previous flag value.

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

/home/runner/work/amrex/amrex/Src/LinearSolvers/AMReX_GMRES_MLMG.H

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ GM

◆ MG

◆ RT

◆ VEC

Constructor & Destructor Documentation

◆ GMRESMLMGT()

Member Function Documentation

◆ apply()

◆ assign()

◆ dotProduct()

◆ getGMRES()

◆ getNumIters()

◆ getResidualNorm()

◆ increment()

◆ linComb()

◆ makeVecLHS()

◆ makeVecRHS()

◆ norm2()

◆ precond()

◆ scale()

◆ setMaxIters()

◆ setPrecondNumIters()

◆ setToZero()

◆ setVerbose()

◆ solve() [1/2]

◆ solve() [2/2]

◆ usePrecond()