Francesc Levrero-Florencio <f.levrero-floren...@onscale.com> writes: > Hi Barry, > > I believe that what you are referring to is what Jed is referring to in > this thread, am I right? > https://scicomp.stackexchange.com/questions/3298/appropriate-space-for-weak-solutions-to-an-elliptical-pde-with-mixed-inhomogeneo/3300#3300
Yeah, that's the scaling. Are you decoupling the interior in the way I described, so the matrix columns for essential boundary conditions are also zeroed? Also note that line searches can prevent a rootfinding method from converging, as in this example. https://scicomp.stackexchange.com/a/2446/119 There is -snes_linesearch_type cp ("critical point"), which has a surrogate that looks like aWolfe conditions when your rootfinding problem happens to be the first order optimality conditions for a minimization problem. There's also SNESSetObjective(), if your problem has an explicit objective. In practice, cp usually works well if your problem is "almost" coming from a minimization principle, and poorly otherwise. > We do set the rows/cols of the Jacobian to zero except the diagonal > component which is set to one, as you mention. I understand that in the > case of only homogeneous Dirichlet BCs it is generally a good idea to scale > that diagonal component so that the condition number of the Jacobian > improves. I assume that what Jed mentions is the inhomogeneous Dirichlet BC > version of this scaling, which also acts on the corresponding indices of > the residual, not just the Jacobian. My question is the following, since > the case we are encountering problems with is a system with only > homogeneous Dirichlet BCs, how does it apply? Also, would this scaling > affect the convergence of the NEWTONLS with "bt" line-search? Without any > scaling we can solve this example with "basic" (with a very reasonable > convergence rate), but not with "bt" line-search.
