Topology optimization methods with gradient-free perimeter approximation

Samuel Amstutz (1) , Nicolas van Goethem (2)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie
2 CMAF - Centro de Matemática e Aplicações Fundamentais

In this paper we introduce a family of smooth perimeter approximating functionals designed to be incorporated within topology optimization algorithms. The required mathematical properties, namely the $\Gamma$-convergence and the compactness of sequences of minimizers, are first established. Then we propose several methods for the solution of topology optimization problems with perimeter penalization showing different features. We conclude by some numerical illustrations in the contexts of least square problems and compliance minimization.

Mots clés: topology optimization; perimeter

Domaines: Optimisation et contrôle [math.OC]

Samuel Amstutz, Nicolas van Goethem. Topology optimization methods with gradient-free perimeter approximation. 2011. ⟨hal-00614818⟩