Nonlinear solvers - SNES

petsc-3.14.5 2021-03-03
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## 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
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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