Numerical Approximation of a Free Boundary Problem Arising in Electromagnetic Shaping

Abstract

This paper deals with the numerical approximation of the section of a column of liquid metal shaped by an external electromagnetic field. The bidimensional model used here leads up to solve, by a spectral method, a nonlinear boundary value problem posed on the exterior of the unit disk to find a convenient conformal mapping. We give accurate bounds on the errors in the approximation process. Some examples of shapes for both exterior and interior shaping are presented.