Three-dimensional magnetic field determination using a scalar potential--A finite element solution

A novel procedure of formulating the three-dimensional magnetic field problem in heterogeneous materials in terms of the unknown scalar potential φ and a known analytical solution for a vector potential which is caused by the specified current densities in a homogeneous domain is presented. The analytical solution to the auxiliary problem is easily determined, and the resulting scalar formulation presents considerable economies against the more obvious but costly direct solution with a three-component vector potential A. Two-and three-dimensional examples assuming linear behavior of the material are given to assess the accuracy of the process, and indication is given of the nature of iterations required for nonlinear properties.