Thursday, September 28

Invited Lecture: Shape Optimization for Free Boundary Problems: Analysis and Numerics

Time: 14:30 - 15:30
Room: L1, Building L
Chair: Kristian Bredies, Universität Graz

In this talk, the solution of Bernoulli type free boundary problems is considered by means of shape optimization. Different formulations are compared from an analytical and numerical point of view. By analyzing the shape Hessian in case of matching data, it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz–Galerkin method is applied for the discretization of the shape optimization problem. In case of well-posedness, existence and convergence of the approximate shapes is proven. Efficient first and second order shape optimization algorithms are obtained by means of modern boundary element methods.

This is joint work with Karsten Eppler

Helmut Harbrecht
Universität Basel