DOLFIN User Manual - FEniCS Project

Chapter 8Nonlinear solver◮ Developer’s note: This chapter is currently being written. . .DOLFIN provides tools for solving nonlinear equations of the formF (x) = 0 (8.1)where F : R n → R n . The nonlinear solvers are based on Newton’s methodand utilise functions from PETSc [11].To use the nonlinear solver, a nonlinear function must be defined. The nonlinearsolver is then initialised with this function and a solution computed.8.1 Nonlinear functionsTo solve a nonlinear problem, the user must defined a class which . The classshould be derived from the DOLFINclass NonlinearFunction. The classshould contain the necessary functions to form the function F (u) and theJacobian matrix J = ∂F/∂u. The precise form of the user defined class willdepend on the PDE being solved and the numerical method. The structu ofa user defined class MyNonlinearFunction is shown below.53