Higher-order topological sensitivity analysis for the Laplace operator
Maatoug Hassine, Khalifa Khelifi · Comptes Rendus Mathématique · 2016
This paper deals with higher-order topological sensitivity analysis for the Laplace operator with respect to the presence of a Dirichlet geometry perturbation. Two main results are presented in this work. In the first one, we discuss the influence of the considered geometry perturbation on the Laplace solution. The second one is devoted to the higher-order topological derivatives. We derive a higher-order topological sensitivity analysis for a large class of shape functions.