# Shape and Topology Optimization of Systems Governed by External Bernoulli Free Boundary Problems

Jaroslav Haslinger^{*}, Jukka I. Toivanen and Raino A.E. Mäkinen

This talk deals with the shape and topology optimization of systems governed by free boundary problems of Bernoulli type. Instead of the direct free boundary problem we shall consider the inverse like problem. It consists in finding the shape of the inner (non-free) component of the boundary of a doubly connected domain for which the resulting free boundary (the outer component of the boundary of ) is as close as possible to a-priori given target shape. It is well-know that the classical approach based only on boundary variations of the inner boundary (i.e. without changing the topology of) does not give satisfactory results for many "reasonable" target shapes. To get better results, one has to change the topology of. This will be done by using a level set technique. The scalar function defining the level sets will be expressed as a linear combination of radial basis functions. This approach enables us to solve the problem by tools of parametric optimization. Numerical results of several model examples will be presented. For more details we refer to [1]. \begin{thebibliography}{99} \bibitem{eins} J. I. Toivanen, R. A. E. Mäkinen, J. Haslinger: Topology optimization in Bernoulli free boundary problems, J. Eng. Math. (2013) 80: 173-188 \end{thebibliography}

Mathematics Subject Classification: 49N45

Keywords: topology optimization, shape optimization, Bernoulli free boundary problem

Minisymposion: Material and Topology Optimization: Theory, Methods and Applications