petsc-3.13.6 2020-09-29
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Augments the standard GMRES approximation space with approximations to the error from previous restart cycles.

Options Database Keys

-ksp_gmres_restart <restart> - total approximation space size (Krylov directions + error approximations)
-ksp_gmres_haptol <tol> - 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 <k> - 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 <k>


Supports both left and right preconditioning, but not symmetric.


1. -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 (for list of available types), KSP, KSPFGMRES, KSPGMRES,
KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPLGMRESSetAugDim(), KSPGMRESSetConstant()




Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages