Analysis of electromagnetic force for shaping the free surface of a molten metal in a cold crucible

An inverse problem in which the currents in the induction coils are to be calculated to obtain the given free surface of a molten metal in a cold crucible is solved by using the boundary-integral equation method and the least-squares method (LSM). To formulate the problem of the free surface as an inverse problem may be promising since the inverse problem has fewer iteratively determined parameters than the direct method. The inverse approach may be considered to be complementary to the direct approach. Combining the direct problem with the inverse problem gives an efficient and accurate approach to the free-surface problem of a molten metal in a cold crucible