PETSc version 3.15.4
KSPPIPEGCR
Implements a Pipelined Generalized Conjugate Residual method.
Options Database Keys
 ksp_pipegcr_mmax <N>   the max number of Krylov directions to orthogonalize against

 ksp_pipegcr_unroll_w   unroll w at the storage cost of a maximum of (mmax+1) extra vectors with the benefit of better pipelining (default: PETSC_TRUE)

 ksp_pipegcr_nprealloc <N>   the number of vectors to preallocated for storing Krylov directions. Once exhausted new directions are allocated blockwise (default: 5)

 ksp_pipegcr_truncation_type <standard,notay>   which previous search directions to orthogonalize against

Notes
The PIPEGCR Krylov method supports nonsymmetric matrices and permits the use of a preconditioner
which may vary from one iteration to the next. Users can can define a method to vary the
preconditioner between iterates via KSPPIPEGCRSetModifyPC().
Restarts are solves with x0 not equal to zero. When a restart occurs, the initial starting
solution is given by the current estimate for x which was obtained by the last restart
iterations of the PIPEGCR algorithm.
The method implemented requires at most the storage of 4 x mmax + 5 vectors, roughly twice as much as GCR.
Only supports left preconditioning.
The natural "norm" for this method is (u,Au), where u is the preconditioned residual. This norm is available at no additional computational cost, as with standard CG. Choosing preconditioned or unpreconditioned norm types involves a blocking reduction which prevents any benefit from pipelining.
Reference
P. Sanan, S.M. Schnepp, and D.A. May,
"Pipelined, Flexible Krylov Subspace Methods,"
SIAM Journal on Scientific Computing 2016 38:5, C441C470,
DOI: 10.1137/15M1049130
See Also
KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
KSPPIPEFGMRES, KSPPIPECG, KSPPIPECR, KSPPIPEFCG,KSPPIPEGCRSetTruncationType(),KSPPIPEGCRSetNprealloc(),KSPPIPEGCRSetUnrollW(),KSPPIPEGCRSetMmax()
Level
intermediate
Location
src/ksp/ksp/impls/gcr/pipegcr/pipegcr.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages