# KSPDGMRES#

Implements the deflated GMRES as defined in [1,2]. In this implementation, the adaptive strategy allows to switch to the deflated GMRES when the stagnation occurs.

## GMRES Options (inherited)#

-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

## DGMRES Options Database Keys#

-ksp_dgmres_eigen

number of smallest eigenvalues to extract at each restart

-ksp_dgmres_max_eigen <max_neig>

maximum number of eigenvalues that can be extracted during the iterative process

-ksp_dgmres_force

use the deflation at each restart; switch off the adaptive strategy.

-ksp_dgmres_view_deflation_vecs

View the deflation vectors, where viewerspec is a key that can be parsed by PetscOptionsGetViewer(). If neig > 1, viewerspec should end with “:append”. No vectors will be viewed if the adaptive strategy chooses not to deflate, so -ksp_dgmres_force should also be given. The deflation vectors span a subspace that may be a good approximation of the subspace of smallest eigenvectors of the preconditioned operator, so this option can aid in understanding the performance of a preconditioner.

## Notes#

Left and right preconditioning are supported, but not symmetric preconditioning. Complex arithmetic is not yet supported

## References#

: J. Erhel, K. Burrage and B. Pohl, Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996).

: D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids, In Press, http://dx.doi.org/10.1016/j.compfluid.2012.03.023

Contributed by: Desire NUENTSA WAKAM,INRIA

.seealso: KSPCreate(), KSPSetType(), KSPType, KSP, KSPFGMRES, KSPLGMRES, KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

beginner

## Location#

src/ksp/ksp/impls/gmres/dgmres/dgmres.c

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