Accurate Solution of Volume-Surface Integral Equations at Very Low Frequencies

Electromagnetic (EM) problems with both conducting and penetrable media can be formulated by volume-surface integral equations (VSIEs) in integral equation approach. Traditionally, the electric field integral equation (EFIE) is used to describe the conducting part, but it has a low-frequency breakdown problem because the vector potential and scalar potential are seriously imbalanced at low frequencies and also it belongs to the first kind of integral equation. In this paper, we use the magnetic field integral equation (MFIE) to replace the EFIE for the conducting part and combine the volume integral equations (VIEs) for the penetrable part to form the VSIEs. Both the MFIE and VIEs belong to the second kind of integral equations and the resultant VSIEs will not suffer from the low-frequency breakdown anymore. We present numerical examples to demonstrate the scheme at very low frequencies and good results have been obtained.