Edge Elements and Current Diffusion

Current flow in the neighborhood of sharp conducting edges and corners is encountered in many applications of computational electromagnetics. Some examples include resonant cavities and waveguides of rectangular shape, cracks in metal components in nondestructive testing, and the edges and corners of the rail-armature contact in an electromagnetic launcher. Although the number of analytical solutions to such problems is small, it is generally believed that such solutions often involve singularities, high gradients, or discontinuities in one or more field components near the edge or corner. It has been demonstrated that the so-called edge elements can provide much more accurate predictions of global quantities (like resonant frequencies and scattering parameters) in the case of full-wave electromagnetics when field discontinuities or singularities are present. They have also been shown to better represent field discontinuities at material interfaces in magnetostatics and reentrant corners in low-frequency electromagnetics. This feature of edge elements is due to their ability to allow necessary jumps in field components at geometric or material discontinuities, as opposed to nodal elements, with the Coulomb gauge enforced, which can overconstrain the fields in certain situations. The main question of interest in this paper is whether edge elements give a similar advantage in the representation of current diffusion around a sharp edge. Both edge- and node-based formulations are considered, and the results are discussed.