Numerical Analysis
The topological asymptotic with respect to a singular boundary perturbation
[L'asymptotique topologique par rapport à une perturbation singulière du bord]
Comptes Rendus. Mathématique, Tome 336 (2003) no. 12, pp. 1033-1038.

Le but de la sensibilité topologique est d'obtenir une expression asymptotique d'une fonctionnelle de forme par rapport à l'insertion d'un petit trou dans le domaine. Dans cette Note, nous considérons le cas d'un petit trou situé sur un coin du domaine. La méthode de l'état adjoint et la technique de troncature de domaine sont proposées pour résoudre ce probléme. Nous considérons comme exemple modèle, l'équation de Laplace posée dans un domaine avec un coin.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00258-9
Samet, Bessem 1

1 MIP, UMR 5640, CNRS-Université Paul Sabatier-INSA, 118, route de Narbonne, 31062 Toulouse cedex, France
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Samet, Bessem. The topological asymptotic with respect to a singular boundary perturbation. Comptes Rendus. Mathématique, Tome 336 (2003) no. 12, pp. 1033-1038. doi : 10.1016/S1631-073X(03)00258-9. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00258-9/

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