KrylovGMRES< T > Class Template Reference

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

#include <CD_KrylovGMRES.H>

Inheritance diagram for KrylovGMRES< T >:

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, measured against m_residualScale.
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 = 0.0
	Norm that both the printed residual and the convergence test are measured against.

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
	A*K^{-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 = 0.0

Norm that both the printed residual and the convergence test are measured against.

The driver sets this to the zero-residual ||r_zero|| = ||rhs - L(0)||, which is the scale the hosting solver itself uses to decide whether a solution has converged. Measuring the exit test on that same scale is what makes m_eps mean the same thing here as it does to the caller, and is also what lets a warm start pay for itself: scaling the tolerance by this solve's own initial residual instead would demand the same reduction factor no matter how good the initial guess was. A non-positive value falls back to this solve's initial residual norm, which is the right scale when there is no host to agree with.

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

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