Topological-shape sensitivity method: Theory and applications

Abstract

The topological derivative allow us to quantify the sensitivity of a given cost function when the domain of definition of the problem is perturbed by introducing a hole or an inclusion. This concept has been successfully applied in the context of topology design and inverse problems. In order to find close expressions for the topological derivative several methods can be achieved in the literature. In particular, we have proposed the Topological-Shape Sensitivity Method, whose main feature is that all mathematical framework (and results), already developed for shape sensitivity analysis, can be used in the calculation of the topological derivative. In this paper we present the Topological-Shape Sensitivity Method and use it as a systematic methodology for computing the topological derivative for holes and inclusions in problems governed by Poisson's and Navier's equations. © 2006 Springer.