Summary
We describe a numerical method to compute free surfaces in electromagnetic shaping and levitation of liquid metals. We use an energetic variational formulation and optimization techniques to compute, a critical point. The surfaces are represented by piecewise linear finite elements. Each step of the algorithm requires solving an elliptic boundary value problem in the exterior of the intermediate surfaces. This is done by using an integral representation on these surfaces.
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Pierre, M., Roche, J.R. Numerical simulation of tridimensional electromagnetic shaping of liquid metals. Numer. Math. 65, 203–217 (1993). https://doi.org/10.1007/BF01385748
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DOI: https://doi.org/10.1007/BF01385748