The inverse electromagnetic shaping problem

Abstract

The inverse problem concerning electromagnetic casting of molten metals consists of looking for an electric current density distribution such that the induced electromagnetic field makes a given mass of liquid metal acquire a predefined shape. This problem is formulated here as an optimization problem where the positions of a finite set of inductors are the design variables. Two different formulations for this optimization problem for the two-dimensional case are proposed. The first one minimizes the difference between the target and the equilibrium shapes while the second approach minimizes the L2 norm of a fictitious surface pressure that makes the target shape to be in mechanical equilibrium. The optimization problems are solved using Feasible Arc Interior Point Algorithm, a line search interior-point algorithm for nonlinear optimization. Some examples are presented to show the effectiveness of the proposed approaches.