Free boundary problems in electromagnetic levitation melting and continuous casting

Two applications of the melting in cold crucibles are presented: continuous casting and levitation melting. These processes are typical examples of coupled phenomena. A free boundary problem has to be solved to determine the equilibrium shape of molten metal with respect to the electrical and geometrical parameters of the system. The magnetic field distribution is calculated by using a boundary integral method. The free surface can be deduced from a global analysis, that is based on the minimization of the total energy of the system. The derivation with respect to the domain leads to a rapid convergence toward the solution