Hey all, so I have a nonlinear problem that can be abstractly written as
| F(u,P) | | 0 | | | = | | | G(u,P) | | 0 | Here u is a variable that comes from a discretization of a PDE and P are four scalars that come from some coupled attached ODEs (P = (P1,P2,P3,P4) ) I know abstract how to apply Newton-Raphson in this context as the Jacobian is simply d_u F d_P F d_u G d_P G where d_P F and d_u G are formed from 4 Vecs resp, and d_P G is a 4x4 matrix. So what I have troubles with is how I could squeeze something like this into an SNES context, at the moment I'm doing a Schur-Complement for Solving this problem for each Newton solve. This however entails, that I'm, solving (d_u F)^-1 to a very low tolerance inside the SC. In the End I want to have something that can work with an inexact Newton method, but I don't know which would be the correct tool (MATSHELL for the jacobian maybe?) to squeeze this into an SNES. Any ideas? Best regards Elias -- Dr. Elias Karabelas Research Associate University of Graz Institute of Mathematics and Scientific Computing Heinrichstraße 36 A-8010 Graz Austria Phone: +43 316 380 8546 Email: [email protected]<mailto:[email protected]> Web: https://ccl.medunigraz.at/
