Sensitivity analysis with respect to a local perturbation of the material property

Article type: Research Article

Authors: Amstutz, Samuel

Affiliations: Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria E-mail: samuel.amstutz@oeaw.ac.at

Abstract: In the present work, the notion of topological sensitivity is extended to the case of a local perturbation of the properties of the material constitutive of the domain. As a model example, we consider the problem −div(αεA∇uε)+βεuε=Fε in two and three dimensions, where A is a symmetric positive definite matrix and αε,βε,Fε are functions whose values inside a small subdomain ωε are different from those of the background medium. An adjoint method is used to determine an asymptotic expansion of a given criterion when the diameter of ωε goes to zero.

Keywords: topology optimization, topological sensitivity analysis, detection of inclusions

Journal: Asymptotic Analysis, vol. 49, no. 1-2, pp. 87-108, 2006