KSPFGMRES — PETSc 3.25.2 documentation

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# KSPFGMRES

Implements the Flexible Generalized Minimal Residual method, flexible GMRES. Flexible Krylov Methods

## Options Database Keys

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

- -ksp_gmres_haptol tol - sets the tolerance for “happy breakdown” (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 `KSPFlexibleModifyPCKSP()`

## Notes

See `KSPFlexibleSetModifyPC()` 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()`, `KSPFlexibleSetModifyPC()`, `KSPFlexibleModifyPCKSP()`

## Level

beginner

## Location

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

## Examples

src/ksp/pc/tutorials/ex4.c
src/dm/impls/stag/tutorials/ex4.c
src/dm/impls/stag/tutorials/ex2.c
src/dm/impls/stag/tutorials/ex8.c
src/dm/impls/stag/tutorials/ex3.c
src/ksp/ksp/tutorials/ex7.c
src/ts/tutorials/ex30.c

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