Asymptotic formula for detecting inclusions via boundary measurements

Abstract

In this article, we are concerned with a geometric inverse problem related to the Laplace operator in a three-dimensional domain. The aim is to derive an asymptotic formula for detecting an inclusion via boundary measurement. The topological sensitivity method is applied to calculate a high-order topological asymptotic expansion of the semi-norm Kohn-Vogelius functional, when a Dirichlet perturbation is introduced in the initial domain.

Keywords

• Laplace operator
• asymptotic analysis
• topological gradient
• Kohn-Vogelius functional