On solving connexity problems within modeling massive conductors

This paper deals with the three-dimensional modeling of massive conductors carrying a total imposed current and involving multiply connected regions. Both stationary motion and time harmonic eddy current problems are consider ed. The aim of the modeling is to determine the current distribution and th e eddy current's effects inside the conductor, as well as to calculate the Lorentz force acting on a conducting region. The choice of a suitable formu lation based on solving the current vector potential T and the magnetic sca lar potential phi is argued, then various methods for the restoration of th e Ampere law in the multiply connected regions are presented Two methods fo r calculating an auxiliary vector potential T-0 are applied in order to cal culate the force acting on the armature of a railgun and the repulsion betw een the electrodes of a vacuum circuit breaker, then the results are compar ed.