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.

Note#

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

References#

• [1] - J. Erhel, K. Burrage and B. Pohl, Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996).

• [2] - 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: KSP: Linear System Solvers, 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