Topological sensitivity analysis for the inverse electromagnetic casting problem

International audienceThe industrial technique of electromagnetic casting allows for contactless heating, shaping and controlling of chemical aggressive, hot melts. The inverse electromagnetic casting problem consists in looking for a suitable set of electric wires such that the electromagnetic field induced by an alternating current passing through them makes a given mass of liquid metal acquire a predefined shape. The number of inductors and their positions are unknowns of the problem. In this work we introduce a new formulation for the inverse problem using a shape functional based on the Kohn-Vogelius criterion. We also present a topology optimization procedure that computes the topological derivatives and locates new inductors in the right position. Several examples are presented showing that the proposed technique is effective to design suitable inductors