KSPGMRES#

Implements the Generalized Minimal Residual method. (Saad and Schultz, 1986) 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

Notes#

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

References#

: YOUCEF SAAD AND MARTIN H. SCHULTZ, GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS. SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986.