Topology design of inductors in electromagnetic casting using level-sets and second order topological derivatives

We propose a new iterative method for the topology design of the inductors in electromagnetic casting. The method is based on a level-set representation of the solution together with first and second order topological derivatives. The optimal design is found by minimizing a Kohn–Vogelius-type functional for the problem. The complete topological expansion of the objective functional, which is herein given, is used to define the iterative step. Results for several numerical examples show that the technique proposed can be efficiently used in the design of suitable inductors.