petsc-3.4.2 2013-07-02

# 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 Database Keys: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against . -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 DGMRES Options Database Keys: -ksp_dgmres_eigen <neig> - 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 <0, 1> - Use the deflation at each restart; switch off the adaptive strategy.

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

### References

[1]Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996), 303-318. [2]On the performance of various adaptive preconditioned GMRES strategies, 5(1998), 101-121. [3] 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 (for list of available types), KSP, KSPFGMRES, KSPLGMRES, KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(), KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

Level:beginner
Location:src/ksp/ksp/impls/gmres/dgmres/dgmres.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages