KSPHPDDM — PETSc 3.23.0 documentation

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# KSPHPDDM

Interface with the HPDDM library. This `KSP` may be used to further select methods that are currently not implemented natively in PETSc, e.g., GCRODR [PdSM+06], a recycled Krylov method which is similar to `KSPLGMRES`, see [JT16] for a comparison. ex75.c shows how to reproduce the results from the aforementioned paper [PdSM+06]. A chronological bibliography of relevant publications linked with `KSP` available in HPDDM through `KSPHPDDM`, and not available directly in PETSc, may be found below. The interface is explained in details in [JRZ21]. See also [OLeary80], [JL17] and [CGL+13]

## Options Database Keys

- -ksp_gmres_restart <restart, default=30> - see `KSPGMRES`

- -ksp_hpddm_type <type, default=gmres> - any of gmres, bgmres, cg, bcg, gcrodr, bgcrodr, bfbcg, or preonly, see `KSPHPDDMType`

- -ksp_hpddm_precision <value, default=same as PetscScalar> - any of half, single, double or quadruple, see `KSPHPDDMPrecision`

- -ksp_hpddm_deflation_tol <eps, default=-1.0> - tolerance when deflating right-hand sides inside block methods (no deflation by default, only relevant with block methods)

- -ksp_hpddm_enlarge_krylov_subspace <p, default=1> - split the initial right-hand side into multiple vectors (only relevant with nonblock methods)

- -ksp_hpddm_orthogonalization <type, default=cgs> - any of cgs or mgs, see KSPGMRES

- -ksp_hpddm_qr <type, default=cholqr> - distributed QR factorizations with any of cholqr, cgs, or mgs (only relevant with block methods)

- -ksp_hpddm_variant <type, default=left> - any of left, right, or flexible (this option is superseded by `KSPSetPCSide()`)

- -ksp_hpddm_recycle <n, default=0> - number of harmonic Ritz vectors to compute (only relevant with GCRODR or BGCRODR)

- -ksp_hpddm_recycle_target <type, default=SM> - criterion to select harmonic Ritz vectors using either SM, LM, SR, LR, SI, or LI (only relevant with GCRODR or BGCRODR). For BGCRODR, if PETSc is compiled with SLEPc, this option is not relevant, since SLEPc is used instead. Options are set with the prefix -ksp_hpddm_recycle_eps_

- -ksp_hpddm_recycle_strategy <type, default=A> - generalized eigenvalue problem A or B to solve for recycling (only relevant with flexible GCRODR or BGCRODR)

- -ksp_hpddm_recycle_symmetric <true, default=false> - symmetric generalized eigenproblems in BGCRODR, useful to switch to distributed solvers like `EPSELEMENTAL` or `EPSSCALAPACK` (only relevant when PETSc is compiled with SLEPc)

## References

[CGL+13]

Henri Calandra, Serge Gratton, Rafael Lago, Xavier Vasseur, and Luiz Mariano Carvalho. A modified block flexible GMRES method with deflation at each iteration for the solution of non-Hermitian linear systems with multiple right-hand sides. SIAM Journal on Scientific Computing, 35(5):S345–S367, 2013.

[JL17]

Hao Ji and Yaohang Li. A breakdown-free block conjugate gradient method. BIT Numerical Mathematics, 57:379–403, 2017.

[JRZ21]

Pierre Jolivet, Jose Roman, and Stefano Zampini. KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners. Computers and Mathematics with Applications, 84:277–295, 2021.

[JT16]

Pierre Jolivet and Pierre-Henri Tournier. Block iterative methods and recycling for improved scalability of linear solvers. In SC'16: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, 190–203. IEEE, 2016.

[OLeary80]

Dianne P O'Leary. The block conjugate gradient algorithm and related methods. Linear algebra and its applications, 29:293–322, 1980.

[PdSM+06] (1,2)

M.L. Parks, E. de Sturler, G. Mackey, D.D. Johnson, and S. Maiti. Recycling Krylov subspaces for sequences of linear systems. SIAM Journal on Scientific Computing, 28(5):1651–1674, 2006.

## See Also

KSP: Linear System Solvers, Flexible Krylov Methods, `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPGMRES`, `KSPCG`, `KSPLGMRES`, `KSPDGMRES`

## Level

intermediate

## Location

src/ksp/ksp/impls/hpddm/hpddm.cxx

## Examples

src/ksp/ksp/tutorials/ex75.c
src/ksp/ksp/tutorials/ex79.c
src/ksp/ksp/tutorials/ex78.c
src/ksp/ksp/tutorials/ex76f.F90
src/ksp/ksp/tutorials/ex76.c

Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages