A minimax method in shape and topological derivatives and homogenization: the case of Helmholtz equation

Abstract

In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem  is formulated by introducing cost  functional. We derive first by considering the lagradian method the shape derivative of the functional. It is also proven a topological derivative  with the same approach. An application to several unconstrained shape functions arising from differential geometry are also given.