Topology optimization methods with gradient-free perimeter approximation

Abstract

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 -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. 2010 Mathematics Subject Classification: Primary 49Q10, 49Q20; Secondary 35J05, 35J25. © 2012 European Mathematical Society.