The topological asymptotic with respect to a singular boundary perturbation

The aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the insertion of a small hole in the domain. The question that we address here is what happens if the hole is located at the boundary of the domain and what happens if the boundary is not regular. The adjoint method and the domain truncation technique are proposed to solve this problem. As a model example, we consider the Laplace equation in a domain with a corner. (C) 2003 Academie des sciences. Published by Editions scientifiques et medicales Elsevier SAS. All rights reserved.