Fast solution of the inverse electromagnetic casting problem

• Published in: Structural and multidisciplinary optimization Vol. 57; no. 6; pp. 2447 - 2455
• Main Authors: Machado, T. J., Canelas, A., Novotny, A. A., Roche, J. R.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2018; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Core wire; Engineering; Engineering Design; Inductors; Inverse problems; Iterative methods; Levitation casting; Liquid metals; Mathematics; Numerical Analysis; Optimization; Research Paper; Theoretical and Applied Mechanics; Non-iterative second order method; Point-wise inductors; Electromagnetic casting; Kohn-Vogelius based criterion
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-017-1874-2

In this paper we deal with an inverse electromagnetic casting problem, which consists in designing a set of inductors in such a way that a liquid metal achieves a given shape. The inductors are assumed to be made of single solid-core wires with a negligible cross-section area. The inverse problem is rewritten in the form of an optimization problem. In particular, a Kohn-Vogelius based functional is minimized with respect to a set of admissible inductors, leading to a non-iterative second order optimization algorithm. Finally, several numerical examples are presented showing that the proposed approach is effective to design suitable inductors.