Abstract

In the numerical study of shape optimization problems the choice of the parametrization of shapes is an important aspect. An explicit parametrization can give direct access to geometric quantities related to the shape and can allow us to compute explicitly the cost function or use more precise techniques to solve the partial differential equations needed in the optimization process. In this talk I will show some examples where the use of a radial parametrization allows us to find precise approximations of solutions of some optimization problems regarding spectral quantities. In a second part I will show how using a parametrization based on the support function may lead to efficient ways of incorporating non-standard constraints, like diameter inequalities, constant-width or convexity into the optimization procedure. The results presented in the second part of the talk are in collaboration with Pedro Antunes.