petsc-3.10.5 2019-03-28
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# KSPLGMRES

Augments the standard GMRES approximation space with approximations to the error from previous restart cycles.

### Options Database Keys

| -ksp_gmres_restart <restart> | - total approximation space size (Krylov directions + error approximations)
| -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
| -ksp_lgmres_augment <k> | - number of error approximations to augment the Krylov space with
| -ksp_lgmres_constant | - use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)

### To run LGMRES(m, k) as described in the above paper, use

-ksp_gmres_restart <m+k> -ksp_lgmres_augment <k>

### Notes

Supports both left and right preconditioning, but not symmetric.

### References

1. -A. H. Baker, E.R. Jessup, and T.A. Manteuffel. A technique for accelerating the convergence of restarted GMRES. SIAM Journal on Matrix Analysis and Applications, 26 (2005).

### Developer Notes

This object is subclassed off of KSPGMRES

Contributed by: Allison Baker

### See Also

KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPGMRES,
KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPLGMRESSetAugDim(), KSPGMRESSetConstant()

### Level

beginner

### Location

src/ksp/ksp/impls/gmres/lgmres/lgmres.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages