KSPPIPEFGMRES#

Implements the Pipelined (1-stage) Flexible Generalized Minimal Residual method [SSM16]. Pipelined Krylov Methods. Flexible Krylov Methods

Options Database Keys#

  • -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_pipefgmres_shift - the shift to use (defaults to 1. See KSPPIPEFGMRESSetShift()

  • -ksp_gmres_krylov_monitor - plot the Krylov space generated

Notes#

Compare to KSPPGMRES and KSPFGMRES

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 What steps are necessary to make the pipelined solvers execute efficiently?

Developer Note#

This class is subclassed off of KSPGMRES, see the source code in src/ksp/ksp/impls/gmres for comments on the structure of the code

Contributed by#

P. Sanan and S.M. Schnepp

References#

SSM16

P. Sanan, S. M. Schnepp, and D. A. May. Pipelined, flexible Krylov subspace methods. SIAM Journal on Scientific Computing, 38(5):C441–C470, 2016. doi:10.1137/15M1049130.

See Also#

KSP: Linear System Solvers, What steps are necessary to make the pipelined solvers execute efficiently?, Pipelined Krylov Methods, Flexible Krylov Methods, KSPCreate(), KSPSetType(), KSPType, 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