Abstract
In this work, we study the direct and inverse problems arising from electromagnetic shaping in applications such as continuous casting processes. The magnetic field produces a surface pressure which forces a molten metal to change its shape until it reaches an equilibrium state between the magnetic pressure and the surface tension. The arising direct problem is a free boundary problem which is to determine the shape of molten metals for a given magnetic field. On the other hand, the inverse problem is to seek a configuration of electromagnetic field generators (i.e. inductors) in order that molten metals have prescribed shapes. A level set method will be presented to determine an equilibrium shape formed by a given configuration of magnetic fields. Also a computational method as well as uniqueness results for the inverse problem will be introduced and illustrated with examples.
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