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 [2006], a recycled Krylov method which is similar to KSPLGMRES, see [2016] for a comparison. ex75.c shows how to reproduce the results from the aforementioned paper [2006]. 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 [2021].

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 - any of left, right, or flexible (this option is superseded by KSPSetPCSide())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#

1980 - The block conjugate gradient algorithm and related methods. O’Leary. Linear Algebra and its Applications.
2006 - Recycling Krylov subspaces for sequences of linear systems. Parks, de Sturler, Mackey, Johnson, and Maiti. SIAM Journal on Scientific Computing
2013 - A modified block flexible GMRES method with deflation at each iteration for the solution of non-Hermitian linear systems with multiple right-hand sides. Calandra, Gratton, Lago, Vasseur, and Carvalho. SIAM Journal on Scientific Computing.
2016 - Block iterative methods and recycling for improved scalability of linear solvers. Jolivet and Tournier. SC16.
2017 - A breakdown-free block conjugate gradient method. Ji and Li. BIT Numerical Mathematics.
2021 - KSPHPDDM and PCHPDDM: extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners. Jolivet, Roman, and Zampini. Computer & Mathematics with Applications.