TOPOLOGICAL SENSITIVITY ANALYSIS FOR SOME NONLINEAR PDE SYSTEMS SAMUEL AMSTUTZ Abstract. The aim of the topological sensitivity analysis is to determine an asymptotic ex- pansion of a design functional when creating a small hole inside the domain. In this work, such an expansion is obtained for a certain class of nonlinear PDE systems of order 2 in dimensions 2 and 3 with a Dirichlet condition prescribed on the boundary of an arbitrarily shaped hole. Some examples of such operators are presented. Key words. shape optimization, topological sensitivity, nonlinear PDE. Resume. L'analyse de sensibilite topologique consiste a rechercher un developpement asymp- totique d'une fonctionnelle de forme par rapport a la creation d'un petit trou dans le domaine. Dans ce travail, on etablit un tel developpement pour une certaine famille d'EDP non linires d'ordre 2 en dimensions 2 et 3 et une condition de Dirichlet imposee au bord d'un trou de forme quelconque. Des exemples d'operateurs de ce type sont presentes. Mots-cles. optimisation de forme, sensibilite topologique, EDP non lineaires. 1. Introduction The topological sensitivity analysis aims to provide an asymptotic expansion of a shape functional with respect to the size of a small hole created inside the domain. For a criterion j(?) = J?(u?) where ? ? RN (N = 2 or 3) and u? is the solution of a set of partial differential equations defined over ?, this expansion can be generally written in the form j(? \ (x0 + ??))? j(?) = f(?
- problem reads
- dirichlet condition
- u? ?
- asymptotic expansion
- topological sensitivity
- navier stokes equations
- cost functional