I’m working on a problem which, morally, can be posed as a system of coupled
semi linear elliptic PDEs together with unknown nonlinear eigenvalue
parameters, loosely, of the form
-\Delta u_1 + f(u_1, u_2) = lam * u1 - mu * du2/dx
-\Delta u_2 + g(u_1, u_2) = lam * u2 + mu * du1/dx
Currently, I have it set up with a DMComposite with two sub da’s, one for the
parameters (lam, mu), and one for the vector field (u_1, u_2) on the mesh. I
have had success in solving this as a fully coupled system with SNES + sparse
direct solvers (MUMPS, SuperLU).
Lately, I am finding that, when the mesh resolution gets fine enough (i.e.
10^6-10^8 lattice points), my SNES gets stuck with the function norm =
O(10^{-4}), eventually returning reason -6 (failed line search).
Perhaps there is another way around the above problem, but one thing I was
thinking of trying would be to get away from direct solvers, and I was hoping
to use field split for this. However, it’s a bit beyond what I’ve seen
examples for because it has 2 types of variables: scalar parameters which
appear globally in the system and vector valued field variables. Any
suggestions on how to get started?
-gideon
