1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
|
.. _doc_nonlinsolve:
===============================================
Summary of Nonlinear Solvers Available In PETSc
===============================================
See the paper `Composing Scalable Nonlinear Algebraic Solvers
<https://www.mcs.anl.gov/papers/P2010-0112.pdf>`__ for details
on the algorithms.
.. list-table::
:widths: auto
:align: center
:header-rows: 1
* - Algorithm
- Associated Type
- Notes
* - Newton's method
- ``SNESNEWTONLS``
- Use ``-snes_mf`` for matrix-free linear solvers
* - Newton's method with trust region
- ``SNESNEWTONTR``
-
* - Single linearization
- ``SNESKSPONLY``
- Essentially one step of Newtwon without a line search
* - Quasi-Newton method (BFGS)
- ``SNESQN``
-
* - Nonlinear CG
- ``SNESNCG``
- Requires nearly symmetric Jacobian for good convergence
* - Nonlinear GMRES
- ``SNESNGMRES``
-
* - Anderson mixing
- ``SNESANDERSON``
-
* - Nonlinear Richardson
- ``SNESNRICHARDSON``
-
* - Nonlinear Gauss-Siedel
- ``SNESNGS``
-
* - Full Approximation Scheme (nonlinear multigrid)
- ``SNESFAS``
-
* - Nonlinear additive Schwarz
- ``SNESNASM``
-
* - Nonlinear additive Schwarz preconditioned inexact Newton (ASPIN) methods
- ``SNESASPIN``
-
* - Composite (combine several nonlinear solvers)
- ``SNESCOMPOSITE``
-
* - Preconditioned nonlinear solver
- ---
- See ``SNESGetNPC()``/ ``SNESSetNPC()``, can be combined to accelerate many of the solvers
|
