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 byPetscOptionsGetViewer()
. 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
See Also#
KSP: Linear System Solvers, 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