**petsc-main 2021-04-20**

## Nonlinear solvers - SNES: Examples

The Scalable Nonlinear Equations Solvers (SNES) component provides an
easy-to-use interface to Newton-type, quasi-Newton, full approximation scheme (FAS) multigrid, and other methods for solving systems of
nonlinear equations. SNES users can set various algorithmic options
at runtime via the options database (e.g., specifying a trust region
method via
-snes_type newtontr
).
SNES internally employs KSP for the solution of
its linear systems.
SNES users can also set KSP options directly in application
codes by first extracting the KSP context from the SNES context via
SNESGetKSP()
and then directly calling various KSP (and PC) routines (e.g.,
PCSetType()
).

ex1.c: Newton's method for a two-variable system, sequential

ex2.c: Newton method to solve u'' + u^{2} = f, sequentially

ex3.c: Newton methods to solve u'' + u^{2} = f in parallel

ex5.c: Bratu nonlinear PDE in 2d

ex6.c: Newton method to solve u'' + u^{2} = f, sequentially

ex9.c: Solves obstacle problem in 2D as a variational inequality\n\

ex12.c: Poisson Problem in 2d and 3d with simplicial finite elements

ex14.c: Bratu nonlinear PDE in 3d

ex15.c: p-Bratu nonlinear PDE in 2d

ex17.c: Linear elasticity in 2d and 3d with finite elements

ex18.c: Nonlinear Radiative Transport PDE with multigrid in 2d

ex19.c: Nonlinear driven cavity with multigrid in 2d

ex21.c: Solves PDE optimization problem using full-space method, treats state and adjoint variables separately

ex22.c: Solves PDE optimization problem using full-space method, interlaces state and adjoint variables

ex25.c: Minimum surface problem in 2D

ex28.c: 1D multiphysics prototype with analytic Jacobians to solve individual problems and a coupled problem

ex30.c: Steady-state 2D subduction flow, pressure and temperature solver

ex33.c: Multiphase flow in a porous medium in 1d

ex35.c: -Laplacian u = b as a nonlinear problem

ex42.c: Newton's method to solve a two-variable system that comes from the Rosenbrock function

ex46.c: Surface processes in geophysics

ex48.c: Toy hydrostatic ice flow with multigrid in 3D

ex56.c: 3D, tri-quadratic hexahedra (Q1), displacement finite element formulation\n\

ex58.c: Parallel version of the minimum surface area problem in 2D using DMDA

ex59.c: Tries to solve u`` + u^{2} = f for an easy case and an impossible case

ex62.c: Stokes Problem discretized with finite elements,\n\

ex70.c: Poiseuille flow problem

ex77.c: Nonlinear elasticity problem in 3d with simplicial finite elements

ex78.c: Newton methods to solve u'' = f in parallel with periodic boundary conditions

ex47cu.cu: Solves -Laplacian u - exp(u) = 0, 0 < x < 1 using GPU\n\n

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