Shape and topology optimal design problems in electromagnetic casting

Purpose In this paper the authors review the recent numerical techniques proposed to solve the forward and inverse problems concerning the electromagnetic casting and electromagnetic levitation techniques of the metallurgical industry. In addition, the authors present a new topology optimization method to solve the inverse axisymmetric electromagnetic levitation problem. Design/methodology/approach The proposed method is based on an exact second-order topological expansion of a Kohn-Vogelius-like functional specially devised for this problem. Findings Through some examples the authors show that it can find suitable solutions efficiently. Originality/value The new method completes the set of efficient methods available to solve the inverse electromagnetic casting and the inverse axisymmetric electromagnetic levitation problems.