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- Samuel Amstutz
- Asymptotic Analysis
- 2006

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… (More)

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

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

Abstract: 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 asymptotic expansion is obtained for the Laplace equation with respect to the insertion of a short… (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)

- S. Amstutz, B. Vexler, T. Takahashi
- 2006

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
- 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
- SIAM J. Control and Optimization
- 2013

Abstract. The perimeter functional is known to oppose serious difficulties when it has to be handled within a topology optimization procedure. In this paper, a regularized perimeter functional Perε, defined for 2d and 3d domains, is introduced. On one hand, the convergence of Perε to the exact perimeter when ε tends to zero is proved. On the other hand, the… (More)

- SAMUEL AMSTUTZ
- 2005

Abstract. 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) + ku = 0 in dimensions 2 and 3. For that problem, the topological asymptotic expansion is obtained for a large… (More)

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

- Samuel Amstutz
- Optimization Methods and Software
- 2011