petsc-3.10.5 2019-03-28
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# Summary of Nonlinear Solvers Available from PETSc

### See the paper Composing Scalable Nonlinear Algebraic Solvers or the PETSc users manual for details on the algorithms

### Requests and contributions welcome

Algorithm | Name of solver
--- | ---
* Does not support a line search
Newton's method | newtonls | Use -snes_mf for matrix-free linear solvers
Newton's method with trust region* | newtontr |
Single linearization* | ksponly | Essentially one step of Newtwon without a line search
Quasi-Newton method (BFGS) | qn |
Nonlinear CG | ncg | Requires nearly symmetric Jacobian for good convergence
Nonlinear GMRES | ngmres |
Anderson mixing | anderson |
Nonlinear Richardson | nrichardson |
Nonlinear Gauss-Siedel* | ngs |
Full Approximation Scheme (nonlinear multigrid) | fas |
Nonlinear additive Schwarz method* | nasm |
Nonlinear additive Schwarz preconditioned inexact Newton (ASPIN) methods | aspin |
Composite; combine several nonlinear solvers | composite |
Preconditioned nonlinear solver/td> | SNESGetNPC() | Can be combined to accelerate many of the solvers