Topology optimization in electromagnetic casting via quadratic programming

Abstract

A new optimization method is proposed for solving an inverse problem concerning the shape and topology of the inductors used in the electromagnetic casting technique of the metallurgical industry. The method is based on an sparse convex quadratic programming version of a recently proposed topology optimization formulation of the inverse electromagnetic casting problem. Regular 0–1 solutions are found by adding to the original Kohn–Vogelius objective function an appropriate penalty term that preserves the quadratic programming structure of the problem, allowing the use of efficient interior-point algorithms. Results for some numerical examples are presented, showing that the technique proposed is effective and can successfully find inductors of optimal shape and topology.