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- Samuel Amstutz
- Asymptotic Analysis
- 2006

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)

- Samuel Amstutz, Imene Horchani, Mohamed Masmoudi, Ben Abda, Ben Ameur
- 2008

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)

- Bessem Samet, Samuel Amstutz, Mohamed Masmoudi
- SIAM J. Control and Optimization
- 2003

- SAMUEL AMSTUTZ
- 2005

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)

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)

- Samuel Amstutz, Heiko Andrä
- J. Comput. Physics
- 2006

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)

- Samuel Amstutz
- Optimization Methods and Software
- 2011

- SAMUEL AMSTUTZ
- 2006

The aim of the topological sensitivity analysis is to determine an asymptotic expansion 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… (More)

- Samuel Amstutz, Marc CiligotTravain
- SIAM J. Control and Optimization
- 2010

- S. Amstutz, N. Dominguez, B. Samet
- 2004

In the present work, the topological asymptotic analysis is extended to the case of the insertion of small inhomogeneities in the domain. As a model example, we consider solutions to the Helmholtz equation in two and three dimensions: div (α ε ∇u ε) + β ε u ε = 0, where (α ε , β ε) are the piecewise constant functions equal to (α 1 , β 1) inside the… (More)