Samuel Amstutz

Learn 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)
Sensitivity analysis with respect to a local perturbation of the material property Powered by TCPDF ( 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)
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)
  • 1