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 baij, bs = 2,3,4,5 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
Incomplete factorizations ILU(k) seqaij,seqbaij --- X
ICC(k) seqaij,seqbaij --- X
ILU dt aij pilut/hypre (LLNL) X
Matrix-free infrastructure X X
Multigrid infrastructure X X
geometric (DMDA for structured grid) X X
geometric/algebraic X X
structured geometric hyprestruct PFMG from hypre X
classical algebraic aij BoomerAMG/hypre (LLNL) X
aij ML/Trilinos (SNL) X
unstructured geometric and smoothed aggregation baij 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 (petsc-master only) X X
Direct solvers LU LU seqaij,seqbaij --- X
LU seqaij MATLAB X
aij PaStiX (INRIA) X X
aij SuperLU (BNL) SuperLU Sequential LU solver / SuperLU_DIST Parallel LU solver X X
aij MUMPS X X
seqaij ESSL (IBM)
seqaij UMFPACK Part of SuiteSparse X
seqaij KLU Part of SuiteSparse X
seqaij LUSOL
dense X X
Cholesky Cholesky seqaij,seqsbaij --- X
sbaij PaStiX (INRIA) X X
sbaij MUMPS X X
seqaij, seqsbaij CHOLMOD Part of SuiteSparse X
dense X 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 --- X X
SYMMLQ --- X X
LGMRES --- X X
GCR --- X X
Conjugate gradient on the normal equations --- X X

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