KSPGMRES#

Implements the Generalized Minimal Residual method [SS86] with restart

Options Database Keys#

  • -ksp_gmres_restart - the number of Krylov directions to orthogonalize against

  • -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

Note#

Left and right preconditioning are supported, but not symmetric preconditioning.

References#

SS86

Y. Saad and M. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 44:856–869, 1986.

See Also#

KSP: Linear System Solvers, KSPCreate(), KSPSetType(), KSPType, KSP, KSPFGMRES, KSPLGMRES, KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

Level#

beginner

Location#

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

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