KSPLGMRES#

Augments the standard GMRES approximation space with approximations to the error from previous restart cycles.

Options Database Keys#

-ksp_gmres_restart

total approximation space size (Krylov directions + error approximations)

-ksp_gmres_haptol

sets the tolerance for “happy ending” (exact convergence)

-ksp_gmres_preallocate

preallocate all the Krylov search directions initially (otherwise groups of vectors are allocated as needed)

-ksp_gmres_classicalgramschmidt

use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)

-ksp_gmres_modifiedgramschmidt

use modified Gram-Schmidt in the orthogonalization (more stable, but slower)

-ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

determine if iterative refinement is used to increase the stability of the classical Gram-Schmidt orthogonalization.

-ksp_gmres_krylov_monitor

plot the Krylov space generated

-ksp_lgmres_augment

number of error approximations to augment the Krylov space with

-ksp_lgmres_constant

use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)

To run LGMRES(m, k) as described in the above paper, use#

-ksp_gmres_restart <m+k> -ksp_lgmres_augment

Notes#

Supports both left and right preconditioning, but not symmetric.

References#

: A. H. Baker, E.R. Jessup, and T.A. Manteuffel. A technique for accelerating the convergence of restarted GMRES. SIAM Journal on Matrix Analysis and Applications, 26 (2005).

Developer Notes#

This object is subclassed off of KSPGMRES

Contributed by: Allison Baker

See Also#

KSPCreate(), KSPSetType(), KSPType, KSP, KSPFGMRES, KSPGMRES, KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPLGMRESSetAugDim(), KSPGMRESSetConstant()

Level#

beginner

Location#

src/ksp/ksp/impls/gmres/lgmres/lgmres.c


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