Speaker
Description
We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a scalar valued level set function. The assignment of material at a point in the design domain is then determined by the sign of the level set function which is approximated by a smoothed Heaviside function.
To obtain candidates for local minima, we want to solve the first order optimality system. The typically nonconvex structure of these problems might cause Newton's method with a line search strategy to fail. We therefore opt for a homotopy (continuation) approach which is based on solving a sequence of parameterized problems to approach the solution of the original problem. In addition to the homotopy parameter, the smoothing parameter of the Heaviside function can be used as a continuation parameter. The arising Newton-type method also allows for employing deflation techniques for finding multiple distinct solutions as well as for efficiently tracing Pareto optimal points in multi-objective optimization problems.
First numerical results for PDE-constrained design optimization problems are presented.
