Speaker
Description
We present a general framework for PDE constrained shape optimization which combines the phase field method with a sharp interface approach based on the method of Lipschitz mappings. On the one hand, phase field methods are very well suited to numerically determine the shape, size and topology of a sought domain, but on the other hand, they have problems to sharpen out domains where they e.g. should develop corners. This, however is the strength of a sharp-interface approach developed in our group, which provides shape updates in the Lipschitz topology. This leads to a two-stage process that first determines an optimal shape numerically using the phase field method discretized with the finite element method. The resulting domain is the starting solution for the finite element-based sharp interface shape optimization method. We describe the underlying construction process in detail and investigate the performance of our method on a selection of test problems from the literature and from applications.
