Finite Elements for Magnetostatic Fields With Distributed Current Densities

This paper presents a general finite element method for the solution of fields due to general three-dimensional vector-valued sources in terms of the magnetic scalar potential, between boundaries of axisymmetric shape. In the space occupied by the sources, and there only, a correction field defined by a vector quantity must be added. This correction field is obtained by using a vector potential Ā, subject to the Coulomb convention. The latter convention may be relaxed to allow Ā to be divergenceless in the mean. In many magnetic field problems, the sources (current-carrying coils), occupy only a small part of the problem region. Since the correction field is non-zero only in the current-carrying space, it is computationally relatively cheap to find. Use of the procedure is illustrated by the end winding model of an electric machine.