Direct computation of current density to solve 3D electric conduction problems using facet elements with FEM

Abstract

In this paper, an original alternative method to compute the current densityJ in two steps with the FEM is proposed, called the J0-T formulation. The goal of this formulation is to respect the conservation of the normal component of the current density. The first step computes an initial source current densityJ0, and the second step computes an electric vector potential T. Finally, the current densityJ is computed usingJ=J0+curlT. The first step ensures the conservation of the normal component ofJ0 between the facets of the mesh. To reach this condition, J0 is computed with facet finite elements. However, J0 is not unique, which is why a second step is added. In addition to the conditions of the first step, the second step corrects the tangential component ofJ. To reach these conditions, T is computed with edge finite elements. The J0-T formulation is then validated on a right angle conductor with section and direction changes and on a 21-turn copper coil. A conservation of the current is obtained with this formulation that is better than the classical electric scalar potential formulation. Copyright © 2013 John Wiley & Sons, Ltd.