ALOP-Colloquium with Prof. Samuel Amstutz, CMAP – Ecole Polytechnique

On Monday, January 10, 2022, at 16:00 c.t., Prof. Samuel Amstutz of CMAP – Ecole Polytechnique will speak about his recent work regarding

Topology optimization and optimal partitioning with non-local perimeter approximation

Topology optimization deals with the optimal design of shapes of unknown topology. For such problems, the perimeter may be considered as penalization to regularize the boundaries and ultimately favor the existence of optimal shapes, but it is difficult to handle directly within algorithms because it is highly sensitive to topology changes. A classical remedy is to use approximate versions of the perimeter in the sense of Gamma-convergence. In this talk, after reviewing the context, I will present a (relative or total) perimeter approximation which is built upon the solution of an elliptic boundary value problem. I will discuss the advantages and drawbacks of this approach compared with alternative functionals, and show in particular how the variational formulation of the boundary value problem can be exploited to design alternating minimizations schemes. Then I will explain how those results and methods, through combinatorial and convex analysis techniques, can be adapted to multiphase optimal partitioning problems with an energy term consisting of a weighted sum of Hausdorff measures of interfaces. Problems of image classification and of hydrostatics with surface tensions will be shown as examples. If time allows, I will also discuss anisotropic variants.

This presentation will take place via ZOOM. A link will be e-mailed prior to the event.