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.
Options Database Keys#
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()
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