Investigations on the Solution of the Magnetic Field Integral Equation with Rao-Wilton-Glisson Basis Functions

Abstract

In computational electromagnetics, surface integral equations are a flexible and computationally efficient tool. The low-order Rao-Wilton-Glisson (RWG) functions are a very common choice of basis functions since they capture the natural div-conformity of surface current densities [1]. The evaluation of the surface fields should be performed in its dual space from a mathematical point of view [2], [3]. However, this is not the only issue to take care of; the testing function also should exhibit a similar direction as the field vector. For the electric field of an electric current, it is obvious that curl-conforming rotated RWGs fulfill these two criteria. However, the magnetic field of an electric current is approximately orthogonal, rendering the equation system obtained by these testing functions ill-conditioned. Therefore, the magnetic field integral equation (MFIE) is classically constructed with div-conforming RWG testing functions for the sake of a well-conditioned system matrix, but this MFIE shows strong inaccuracies [4], [5]. For high-frequency problems, the reason seems to lie in the “strong singularity” of the identity operator [6], while for low frequencies the situation is clearly more related to the lack of dual-space testing functions [3], [7]. The accuracy issues are highly relevant, since the combination of the MFIE with the electric field integral equation (EFIE) to the combined field integral equation is the most common method to simulate large perfect electrically conducting objects with boundary integral equations, and the combination of MFIE and EFIE operators is, furthermore, also required for the dielectric case.