A new method for inverse electromagnetic casting problems based on the topological derivative

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. In this paper we propose a new method for the topology design of such inductors. The inverse electromagnetic casting problem is formulated as an optimization problem, and topological derivatives are considered in order to locate new wires in the right position. Several numerical examples are presented showing that the proposed technique is effective to design suitable inductors.