Topology optimization methods with gradient-free perimeter approximation

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.