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> SNESGetPC() Can be combined to accelerate many of the solvers