Consider a problem where space is filled with a liquid and a solid phase, with a large, complicated geometry. On each of the phases, there's an electrical potential/poisson equation. The equations are coupled by a nonlinear surface current through the phase boundary.Currently, an FEM is constructed for both phases and assembled into one large Jacobian which is then solved as a black-box in a Newton method. This leads to bad matrix condition and bad performance.To improve performance, I plan to use PETSc. For multi-physics problems, they suggest the usage of nested matrices and then to use a separate preconditioner for each of the equations. BUT, for all the examples I found so far, there's one big difference: The examples always consider different physical equations on one phase which are coupled in all points in space. In my case, I have just one equation per phase, but a coupling only on the boundaries of the phase, and nonlinear.How would you deal with that kind of problem in PETSc? (Emphasis on the combination of matrices, solvers and preconditioners.)
How to deal with multi-region problems (in PETSc)
finite element;petsc;multiphysics