Summary of Nonlinear Solvers Available In PETSc#

Algorithm	Associated Type	Notes
Newton’s method	`SNESNEWTONLS`	Use `-snes_mf` for matrix-free linear solvers
Newton’s method with trust region	`SNESNEWTONTR`
Newton with Arc Length Continuation	`SNESNEWTONAL`
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`
Multi-stage smoothers	`SNESMS`
Preconditioned nonlinear solver	—	See `SNESGetNPC()`/ `SNESSetNPC()`, can be combined to accelerate many of the solvers