From Differential Calculus to 0‐1 Topological Optimization

Abstract

The topological asymptotic expansion gives the variation of a cost function when a small hole is created in a domain. This approach leads to very powerful algorithms in topological optimization. Unfortunately, these asymptotic expansions are obtained with the use of complicated mathematical tools. The goal of this paper is to provide a straightforward way to derive a topological asymptotic expansion using a classical gradient. We will illustrate this general approach by some numerical experiments for the elasticity and the Stokes problems.