petsc-3.5.4 2015-05-23

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

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), pp. 962-984.

Developer Notes: This object is subclassed off of KSPGMRES

Contributed by: Allison Baker

KSPLGMRES

Options Database Keys

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

References

See Also