KSPFGMRES#
Implements the Flexible Generalized Minimal Residual method, flexible GMRES. Flexible Krylov Methods
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
-ksp_fgmres_modifypcnochange - do not change the preconditioner between iterations
-ksp_fgmres_modifypcksp - modify the preconditioner using
KSPFGMRESModifyPCKSP()
Notes#
See KSPFGMRESSetModifyPC() for how to vary the preconditioner between iterations
GMRES requires that the preconditioner used is a linear operator. Flexible GMRES allows the preconditioner to be a nonlinear operator. This
allows, for example, Flexible GMRES to use GMRES solvers or other Krylov solvers (which are nonlinear operators in general) inside the preconditioner
used by KSPFGMRES. For example, the options -ksp_type fgmres -pc_type ksp -ksp_ksp_type bcgs -ksp_view -ksp_pc_type jacobi make the preconditioner
(or inner solver) be bi-CG-stab with a preconditioner of PCJACOBI. KSPFCG provides a flexible version of the preconditioned conjugate gradient method.
Only right preconditioning is supported.
The following options -ksp_type fgmres -pc_type ksp -ksp_ksp_type bcgs -ksp_view -ksp_pc_type jacobi make the preconditioner (or inner solver)
be bi-CG-stab with a preconditioner of PCJACOBI
Developer Note#
This object is subclassed off of KSPGMRES, see the source code in src/ksp/ksp/impls/gmres for comments on the structure of the code
Contributed by#
Allison Baker
See Also#
KSP: Linear System Solvers, Flexible Krylov Methods, KSPCreate(), KSPSetType(), KSPType, KSP, KSPGMRES, KSPLGMRES, KSPFCG,
KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPFGMRESSetModifyPC(),
KSPFGMRESModifyPCKSP()
Level#
beginner
Location#
Examples#
src/dm/impls/stag/tutorials/ex4.c
src/ts/tutorials/ex30.c
src/dm/impls/stag/tutorials/ex2.c
src/dm/impls/stag/tutorials/ex8.c
src/ksp/ksp/tutorials/ex7.c
src/dm/impls/stag/tutorials/ex3.c
src/ksp/pc/tutorials/ex4.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages