DFG-Forschungszentrum "Mathematik für Schlüsseltechnologien - MATHEON": Control of phase separation phenomena with applications to structure formation during cooling of binary alloys and phase inversion processes in polymetric membrane production.

Controlling phase separation processes in material science allows to influence the quality, functionality or life time expectancy of materials. Utilizing a phase field approach coupled with relevant physical phenomena such as either the Navier-Stokes system or the Navier-Lame system the project work aims at deriving first and second order optimality characterizations for the associated optimal control problems and efficient numerical solution algorithms relying on adaptive discretization and Newton-type solvers. The derivation of optimality conditions is challenged by the nature of the free energy involved in the phase field model, and the solver design has to cope with potentially involved non-differentiabilities and the large scale of the discretized systems.