petsc-master 2019-12-10
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Summary of Sparse Linear Solvers Available from PETSc

Summary of Sparse Linear Solvers Available from PETSc

Requests and contributions welcome

Algorithm Matrix types External Package* Parallel Complex

* External Package If this column is filled in you must install the external package indicated to use this feature. See instructions

** A "block Jacobi" style SOR with lits local smoothing followed by update of ghost points from other processors, see MatSOR()

*** Use PCType of PCSOR

Preconditioners Jacobi aij, baij, sbaij, dense --- X X
point block Jacobi aij, baij, baij, kaij, mpisell, is --- X X
SOR seqdense, seqaij, seqsbaij, mpiaij ** --- X
point block SOR*** seqbaij, bs = 2,3,4,5 --- X
block Jacobi aij, baij, sbaij --- X X
additive Schwarz aij, baij, sbaij --- X X
deflation --- X X
Incomplete factorizations ILU(k) seqaij, seqbaij --- X
ICC(k) seqaij, seqbaij, seqsbaij --- X
ILU dt aij pilut/hypre (LLNL) Deprecated. Use euclid/hypre instead X
Matrix-free infrastructure X X
Multigrid infrastructure X X
geometric (DMDA for structured grid) X X
smoothed aggregation aij --- X X
structured geometric hyprestruct PFMG from hypre X
classical algebraic aij BoomerAMG/hypre (LLNL) X
aij ML/Trilinos (SNL) X
domain decomposition-based aij, baij, sbaij, is HPDDM (CNRS) X X
Physics-based splitting relaxation and Schur-complement aij, baij, nest --- X X
least squares commutator schurcomplement --- X X
Approximate inverses aij Parasails/hypre (LLNL) X
aij SPAI X
Substructuring balancing Neumann-Neumann is --- X X
BDDC is --- X X
Direct solvers LU LU seqaij, seqbaij --- X
seqaij MATLAB X
aij PaStiX (Inria) X X
aij SuperLU (BNL) SuperLU Sequential LU solver / SuperLU_DIST Parallel LU solver X X
aij, baij MUMPS (CERFACS, CNRS, ENS Lyon, INP Toulouse, Inria, Mumps Technologies, University of Bordeaux) X X
seqaij ESSL (IBM)
seqaij UMFPACK Part of SuiteSparse X
seqaij KLU Part of SuiteSparse X
seqaij LUSOL
seqaij, seqbaij MKL Pardiso (Intel) X
mpiaij, mpibaij MKL CPardiso (Intel) X X
dense --- X X
Cholesky Cholesky seqaij, seqsbaij --- X
sbaij PaStiX (Inria) X X
sbaij MUMPS (CERFACS, CNRS, ENS Lyon, INP Toulouse, Inria, Mumps Technologies, University of Bordeaux) X X
seqaij, seqsbaij CHOLMOD Part of SuiteSparse X
dense --- X X
seqsbaij MKL Pardiso (Intel)
mpisbaij MKL CPardiso (Intel) X
QR matlab MATLAB
XXt and XYt aij --- X
Krylov methods Richardson --- X X
Chebyshev --- X X
conjugate gradients --- X X
GMRES --- X X
bi-CG-stab --- X X
transpose free QMR --- X X
conjugate residuals --- X X
conjugate gradient squared --- X X
bi-conjugate gradient --- X X
MINRES --- X X
flexible GMRES --- X X
LSQR (supports rectangular matrices) --- X X
CG for least squares (supports rectangular matrices) --- X X
SYMMLQ --- X X
LGMRES --- X X
GCR --- X X
conjugate gradient on the normal equations --- X X
GCR with inner orthogonalization and deflated restarting HPDDM (CNRS) X X

This page was inspired by Jack Dongarra's freely available software for linear algebra list