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Sensitivity analysis with respect to a local perturbation of the material property Powered by TCPDF (www.tcpdf.org) 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(More)
The topological sensitivity analysis consists in studying the behavior of a shape functional when modifying the topology of the domain. In general, the perturbation under consideration is the creation of a small hole. In this paper, the topological asymp-totic expansion is obtained for the Laplace equation with respect to the insertion of a short crack(More)
The topological sensitivity analysis consists in studying the behavior of a given shape functional when the topology of the domain is perturbed, typically by the nucleation of a small hole. This notion forms the basic ingredient of different topology optimization / reconstruction algorithms. From the theoretical viewpoint, the expression of the topological(More)
The level-set method has been recently introduced in the field of shape optimization , enabling a smooth representation of the boundaries on a fixed mesh and therefore leading to fast numerical algorithms. However, most of these algorithms use a Hamilton-Jacobi equation to connect the evolution of the level-set function with the deformation of the contours,(More)
The aim of the topological sensitivity analysis is to determine an asymptotic expansion of a shape functional with respect to the variation of the topology of the domain. In this paper, we consider a state equation of the form div (A∇u) + k 2 u = 0 in dimensions 2 and 3. For that problem, the topological asymptotic expansion is obtained for a large class of(More)
This report has been compiled by the Institute Director Heinz W. Engl based on input by all group leaders and all members of the Institute. Because of the international composition of the Board, it is written in English. Although the report follows the general structure prescribed by the ÖAW, the section about scientific achievements and plans is grouped by(More)