Summary of Nonlinear Solvers Available In PETSc#
See the paper Composing Scalable Nonlinear Algebraic Solvers for details on the algorithms.
| Algorithm | Associated Type | Notes | 
|---|---|---|
| Newton’s method | Use  | |
| Newton’s method with trust region | ||
| Single linearization | Essentially one step of Newtwon without a line search | |
| Quasi-Newton method (BFGS) | ||
| Nonlinear CG | Requires nearly symmetric Jacobian for good convergence | |
| Nonlinear GMRES | ||
| Anderson mixing | ||
| Nonlinear Richardson | ||
| Nonlinear Gauss-Siedel | ||
| Full Approximation Scheme (nonlinear multigrid) | ||
| Nonlinear additive Schwarz | ||
| Nonlinear additive Schwarz preconditioned inexact Newton (ASPIN) methods | ||
| Composite (combine several nonlinear solvers) | ||
| Preconditioned nonlinear solver | — | See  |