Algorithm | Matrix types | External Package* |
Parallel |
Complex |
||
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(k) |
aij | Euclid/hypre (LLNL) | X | |||
ILU dt | aij | pilut/hypre (LLNL) | X | |||
Matrix-free | infrastructure | X | X | |||
Multigrid | infrastructure | X | X | |||
geometric structured grid | X | X | ||||
(petsc-dev only) | PFMG from hypre | X | ||||
algebraic | aij | BoomerAMG/hypre (LLNL) | X | |||
aij | ML/Trilinos (SNL) | X | ||||
baij | Prometheus (LBNL) | X | ||||
Approximate inverses | aij | Parasails/hypre (LLNL) | X | |||
aij | SPAI | X | ||||
Substructuring | balancing Neumann-Neumann | is | --- | X | X | |
Direct solvers | LU | LU | seqaij,seqbaij | --- | X | |
LU | seqaij | MATLAB | X | |||
aij | Spooles | X | X | |||
aij | PaStiX | X | X | |||
aij |
SuperLU (BNL) Sequential/Parallel | X | X | |||
aij | MUMPS | X | X | |||
seqaij | ESSL (IBM) | |||||
seqaij | UMFPACK (U. Florida) | |||||
seqaij | LUSOL | |||||
dense | PLAPACK | X | X | |||
Cholesky | Cholesky | seqaij,seqsbaij | --- | X | ||
sbaij | Spooles | X | X | |||
sbaij | PaStiX | X | X | |||
sbaij | MUMPS | X | X | |||
dense | PLAPACK | X | X | |||
QR | matlab | MATLAB | ||||
XXt and XYt | aij | --- | X | |||
Krylov methods | Richardson | --- | X | X | ||
Chebychev | --- | 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 |
*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
This page was inspired by Jack Dongarra's freely available software for linear algebra list