Summary of Sparse Linear Solvers Available In PETSc#
Preconditioners#
Algorithm |
Associated Type |
Matrix Types |
External Packages |
Parallel |
Complex |
|
---|---|---|---|---|---|---|
Generic |
Jacobi |
— |
X |
X |
||
Point Block Jacobi |
— |
X |
X |
|||
Block Jacobi |
— |
X |
X |
|||
SOR |
— |
X |
||||
Point Block SOR |
|
— |
X |
|||
Additive Schwarz |
— |
X |
X |
|||
Deflation |
All |
— |
X |
X |
||
Incomplete |
ILU |
— |
X |
|||
ILU with drop tolerance |
X |
|||||
Euclid/hypre ( |
X |
|||||
ICholesky |
— |
X |
||||
Matrix Free |
Infrastructure |
All |
— |
X |
X |
|
Multigrid |
Infrastructure |
All |
— |
X |
X |
|
Geometric |
All |
— |
X |
X |
||
Smoothed Aggregation |
— |
X |
X |
|||
Structured Geometric |
X |
|||||
Classical Algebraic |
X |
|||||
Domain Decomposition |
X |
X |
||||
Physics-based Splitting |
Relaxation & Schur Complement |
— |
X |
X |
||
Least Squares Commutator |
|
— |
X |
X |
||
Approximate Inverse |
AIV |
X |
||||
Substructuring |
Balancing Neumann-Neumann |
— |
X |
X |
||
Balancing Domain Decomposition |
— |
X |
X |
Direct Solvers#
Algorithm |
Associated Type |
Matrix Types |
External Packages |
Parallel |
Complex |
|
---|---|---|---|---|---|---|
Direct LU |
LU |
— |
X |
|||
X |
||||||
X |
X |
|||||
X |
X |
|||||
X |
X |
|||||
X |
||||||
X |
||||||
X |
||||||
X |
X |
|||||
X |
X |
|||||
Direct Cholesky |
Cholesky |
— |
X |
|||
X |
X |
|||||
X |
X |
|||||
X |
||||||
X |
X |
|||||
X |
||||||
Direct QR |
QR |
MATLAB |
||||
XXt and XYt |
— |
X |
Krylov Methods#
Algorithm |
Associated Type |
External Packages |
Parallel |
Complex |
---|---|---|---|---|
Richardson |
— |
X |
X |
|
Chebyshev |
— |
X |
X |
|
GMRES |
— |
X |
X |
|
Flexible GMRES |
— |
X |
X |
|
LGMRES |
— |
X |
X |
|
Conjugate Gradient |
— |
X |
X |
|
Conjugate Gradient Squared |
— |
X |
X |
|
Conjugate Gradient for Least Squares |
— |
X |
X |
|
Conjugate Gradient on Normal Equations |
— |
X |
X |
|
Bi-Conjugate Gradient |
— |
X |
X |
|
Stabilized Bi-Conjugate Gradient |
— |
X |
X |
|
Transpose-free QMR |
— |
X |
X |
|
Conjugate Residual |
— |
X |
X |
|
Generalized Conjugate Residual |
— |
X |
X |
|
Generalized Conjugate Residual (with inner normalization and deflated restarts) |
X |
X |
||
Minimum Residual |
— |
X |
X |
|
LSQR |
— |
X |
X |
|
SYMMLQ |
— |
X |
X |