Regularized perimeter for topology optimization

Samuel Amstutz (1)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie

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, defined for 2d and 3d domains, is introduced. On one hand, the convergence to the exact perimeter is proved. On the other hand, the topological differentiability of the regularized functional is analyzed. These features lead to the design of a topology optimization algorithm suitable for perimeter dependent objective functionals. Some numerical results on academic problems illustrate the method.

Mots clés: Topology optimization; Perimeter; Topological derivative; Level set.; Level set

Domaines: Optimisation et contrôle [math.OC]

Samuel Amstutz. Regularized perimeter for topology optimization. 2010. ⟨hal-00542854⟩