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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)

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)

In this paper we consider optimal control problems subject to a semilinear elliptic state equation together with the control constraints 0 ≤ u ≤ 1 and u = m. Optimality conditions for this problem are derived and reformulated as a nonlinear, nonsmooth equation which is solved using a semismooth Newton method. A regularization of the nonsmooth equation is… (More)

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)

We provide in this paper a link between two methods of edge detection: edge detection using scale-space analysis, and edge detection using topological asymptotic analysis. More precisely, we show that the topological gradient associated with an image $$u$$ u is given by a combination of the gradients of two smoothed versions of the image $$u$$ u at two… (More)

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