The Allen-Cahn and Cahn-Hilliard equations are used within material science, image processing or chemistry. Both equations are derived by minimizing the well-known Ginzburg-Landau energy. In order to accurately represent many phycical processes it is useful to use non-smooth functions within the problem formulation, which in turn requires the application of non-smooth optimization techniques. Again, we are faced with structured linear systems for which we design robust and cheap-to-apply preconditioners.
- Luise Blank (University of Regensburg)