Restarted GMRES(m) acting on an AMR hierarchy through AMRMultigridKrylovOp. More...

#include <CD_KrylovGMRES.H>

Inheritance diagram for KrylovGMRES< T >:

[legend]

Public Member Functions
	KrylovGMRES () noexcept=default
	Default constructor. Call define() before use.

	~KrylovGMRES () noexcept
	Destructor. Frees the persistent basis and scratch.

void	define (AMRMultigridKrylovOp< T > a_op, const Vector< LevelData< T > > &a_template) noexcept
	Allocate the persistent basis (m_restart + 1 vectors) and scratch. Call once per regrid.

void	undefine () noexcept
	Free the persistent basis and scratch.

bool	isDefined () const noexcept
	Whether define() has been called.

bool	solve (Vector< LevelData< T > * > &a_phi, const Vector< LevelData< T > * > &a_rhs) noexcept
	Solve a_op(a_phi) = a_rhs (homogeneous operator) with restarted GMRES(m_restart).

Public Attributes
Real	m_eps = 1.E-10
	Relative residual tolerance (against the initial residual norm).

int	m_maxIter = 50
	Maximum number of iterations (total Arnoldi steps across restart cycles).

int	m_restart = 30
	Restart length m in GMRES(m). Must be set before define() (sizes the persistent basis).

bool	m_reorthogonalize = true
	Whether to do one classical Gram-Schmidt reorthogonalization pass (robustness; on by default).

int	m_verbosity = -1
	Verbosity; at >= 4 a terse one-line-per-iteration residual history is printed.

int	m_exitStatus = -1
	Exit status after solve(): 1 = converged, 3 = max iterations, -1 = not run.

Real	m_residualNorm = -1.0
	Final residual norm after solve() (in the adapter inner-product norm).

int	m_iterations = 0
	Number of Arnoldi iterations performed by the last solve().

Real	m_residualScale = 1.0
	Display normalization for printed residuals (set to the zero-residual by the driver; 1 = print absolute).

Protected Attributes
AMRMultigridKrylovOp< T > *	m_op = nullptr
	Operator/adapter (not owned).

bool	m_isDefined = false
	Whether the basis/scratch are allocated.

int	m_allocRestart = 0
	Restart length the persistent storage was sized for.

Vector< Vector< LevelData< T > * > >	m_basis
	Arnoldi basis, size m_allocRestart + 1.

Vector< LevelData< T > * >	m_w
	AK^{-1}v_j scratch.

Vector< LevelData< T > * >	m_z
	K^{-1}*v_j and final preconditioned-update scratch.

Vector< LevelData< T > * >	m_c
	Accumulated unpreconditioned solution update (sum y_k v_k).

Vector< LevelData< T > * >	m_r
	Residual.

Vector< Real >	m_H
	Hessenberg matrix, column-major, leading dimension m_allocRestart + 1.

Vector< Real >	m_cs
	Givens cosines.

Vector< Real >	m_sn
	Givens sines.

Vector< Real >	m_g
	Rotated residual right-hand side.

Vector< Real >	m_y
	Least-squares solution.

Vector< Real >	m_hcol
	Persistent scratch for one Gram-Schmidt projection row (size m_allocRestart).

Vector< Real >	m_corr
	Persistent scratch for the reorthogonalization correction row (size m_allocRestart).

Detailed Description

template<class T>
class KrylovGMRES< T >

Restarted GMRES(m) acting on an AMR hierarchy through AMRMultigridKrylovOp.

A chombo-discharge replacement for Chombo's GMRESSolver on the outer Krylov path, written for scale-out. The Arnoldi basis (m_restart + 1 hierarchies) and the few scratch vectors are allocated once in define() and reused across solves (no per-solve allocation). Orthogonalization uses classical Gram-Schmidt issued through the adapter's batched mDotProduct, so each Arnoldi step costs a single MPI reduction (plus one for the norm) regardless of the AMR level count – as opposed to the modified Gram-Schmidt / per-vector dot products that scale poorly. Right preconditioning keeps the tracked residual the true residual; the preconditioned solution update is formed once per restart cycle (one extra preCond), so the basis vectors need not be stored in preconditioned form.

Note: T is the FAB type (EBCellFAB or MFCellFAB).

Member Function Documentation

◆ define()

template<class T >

void KrylovGMRES< T >::define	(	AMRMultigridKrylovOp< T > *	a_op,
		const Vector< LevelData< T > * > &	a_template
	)

noexcept

Allocate the persistent basis (m_restart + 1 vectors) and scratch. Call once per regrid.

Parameters

[in]	a_op	The (already define()d) operator/adapter to solve against
[in]	a_template	A hierarchy whose layout the work vectors mirror (e.g. the rhs)

◆ isDefined()

template<class T >

bool KrylovGMRES< T >::isDefined ( ) const

noexcept

Whether define() has been called.

Returns: True if defined.

◆ solve()

template<class T >

bool KrylovGMRES< T >::solve	(	Vector< LevelData< T > * > &	a_phi,
		const Vector< LevelData< T > * > &	a_rhs
	)

noexcept

Solve a_op(a_phi) = a_rhs (homogeneous operator) with restarted GMRES(m_restart).

Parameters

[in,out]	a_phi	Solution (in: initial guess; out: solution). Warm starts are honoured.
[in]	a_rhs	Right-hand side.

Returns: True if converged (m_exitStatus == 1).

Member Data Documentation

◆ m_residualScale

template<class T >

Real KrylovGMRES< T >::m_residualScale = 1.0

Display normalization for printed residuals (set to the zero-residual by the driver; 1 = print absolute).

Affects only verbose output, not the convergence test. The printed value is the relative residual ||r|| / ||r_zero||, so progress is comparable across solvers regardless of their internal norm.

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

Source/Elliptic/CD_KrylovGMRES.H
Source/Elliptic/CD_KrylovGMRESImplem.H

Public Member Functions

Public Attributes

Protected Attributes

Detailed Description

Member Function Documentation

◆ define()

◆ isDefined()

◆ solve()

Member Data Documentation

◆ m_residualScale