Dear dealii community, I am interested in solving a nonlinear problem with Newton's method. I would describe it as a heat equation with a nonlinear diffusion coefficient, thus building on step-15, 25 and 26. I've found step-15, step-25 and step-57 very helpful for understanding how to set up the linear system for the residual and solve it at each step of the nonlinear iteration.
1) Is that the best approach to take in dealii, i.e. compute the residual manually and manually do the nonlinear iteration until convergence is satisfied? In step-25, the scalar time-dependent system admits a straightforward expression for F'(u, delta_u) from F(u). In step-33, an automatic differentiation package, trilinos::sacado, is used to facilitate the computation of the vector-valued conservation law's "terrible beast" of a Jacobian. For computing the residual, automatic differentiation seems like it can help in certain situations. 2) Are there other options to help "automate" the nonlinear treatment? For example, does anyone have any experience with the petsc nonlinear solvers (snes)? For example, might it allow to easily switch between a Picard (fixed-point) loop, if the Newton loop does not converge? I note that in the PETScWrappers namespace there are no entries related to the snes package. Why/why not? With many thanks, Sean -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
