Summary of Nonlinear Solvers Available In PETSc

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

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