Numerical methods for a shape optimization problem
vendredi 15 juin 2012, 9h45 - 10h45
In this lecture we consider the problem of the optimal distribution of two conducting materials with given volume inside a fixed domain, in order to minimize the first eigenvalue of a Dirichlet operator. We present two numerical approaches to deal with this problem-one based on an asymptotic analysis when the gap in conductivity is small and the other, a descent algorithm which is valid in any domain. One of the consequences of these numerical studies is that we are able to disprove an earlier conjecture concerning the optimal distribution of the materials in a ball. It was earlier supposed that optimal solution consists in putting the material with the highest conductivity in the shape of a ball around the center. We show that this is not true in general. When the amount of the material with the higher density is large enough, the optimal solution is the union of a ball and an outer ring.
Salle : Cordier D