Nonlocal approximation of the anisotropic perimeter and application to topology optimization

We present a Γ−convergence approximation of a class of anisotropic perimeter functionals. In contrast to other works on the topic, the construction relies on the solution of possibly nonlinear elliptic boundary value problems. We discuss theoretical and algorithmic aspects. We also show various applications in topology optimization, including multiphase partitioning and overhang penalization in a mechanical framework related to additive manufacturing.