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

Abstract

SUMMARYIn this paper, an original alternative method to compute the current density J 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 density J0, and the second step computes an electric vector potential T. Finally, the current density J is computed using J = J0 + curl T. The first step ensures the conservation of the normal component of J0 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 of J. 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.

Special Issue: The 9th International Symposium on Electric and Magnetic Fields (EMF 2013)

“…Using a B ( H ) curve defined by five random parameters, Sobol indices are used to determine the sensitivity for each state of magnetization, in order to investigate where the experimental characterization process should focus to improve the accuracy of the linkage flux computation. Ferrouillat et al present a numerical scheme to solve three‐dimensional electric conduction problems using facet finite elements. The goal of the proposed scheme is to ensure the conservation of the normal component of the current density across the facets of the mesh.…”