KSPPIPEFGMRES#

Implements the Pipelined (1-stage) Flexible Generalized Minimal Residual method. 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
-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 What steps are necessary to make the pipelined solvers execute efficiently?

Developer Note#

This class is subclassed off of KSPGMRES.

Contributed by#

P. Sanan and S.M. Schnepp

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