petsc-3.10.2 2018-10-09
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KSPGMRES

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

Options Database Keys

-ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
-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 <never,ifneeded,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

1. -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.

See Also

KSPCreate(), KSPSetType(), KSPType (for list of available types), 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

Examples

src/ksp/ksp/examples/tutorials/ex7.c.html
src/ksp/ksp/examples/tutorials/ex8.c.html
src/ksp/ksp/examples/tutorials/ex62.c.html
src/tao/pde_constrained/examples/tutorials/hyperbolic.c.html

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