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