petsc-3.10.2 2018-10-09
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KSPPIPEFGMRES

Implements the Pipelined Generalized Minimal Residual method. A flexible, 1-stage pipelined variant of 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
-ksp_pipefgmres_shift - the shift to use (defaults to 1. See KSPPIPEFGMRESSetShift() vectors are allocated as needed)
-ksp_gmres_krylov_monitor - plot the Krylov space generated

Notes

This variant is not "explicitly normalized" like KSPPGMRES, and requires a shift parameter.

A heuristic for choosing the shift parameter is the largest eigenvalue of the preconditioned operator.

Only right preconditioning is supported (but this preconditioner may be nonlinear/variable/inexact, as with KSPFGMRES). MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods. See the FAQ on the PETSc website for details.

Developer Notes

This class is subclassed off of KSPGMRES.

Reference

P. Sanan, S.M. Schnepp, and D.A. May, "Pipelined, Flexible Krylov Subspace Methods," SIAM Journal on Scientific Computing 2016 38:5, C441-C470, DOI: 10.1137/15M1049130

See Also

KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPLGMRES, KSPPIPECG, KSPPIPECR, KSPPGMRES, KSPFGMRES
KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESMonitorKrylov(), KSPPIPEFGMRESSetShift()

Level

intermediate

Location

src/ksp/ksp/impls/gmres/pipefgmres/pipefgmres.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages