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 [1], use#

-ksp_gmres_restart <m+k> -ksp_lgmres_augment

Note#

Supports both left and right preconditioning, but not symmetric.

Developer Note#

This object is subclassed off of KSPGMRES

Contributed by#

Allison Baker

References#

  • [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).

See Also#

KSP: Linear System Solvers, 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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