A rigorous solution to the low-frequency breakdown in the electric field integral equation

The low-frequency breakdown problem in electric field integral equation (EFIE) is well recognized and has been extensively studied. However, existing approaches have not rigorously solved the problem yet since they rely on low-frequency approximations. In this work, we present a rigorous method to fundamentally eliminate the problem. In this method, the original frequency dependent problem is rigorously transformed to a generalized eigenvalue problem, from the solution of which the frequency dependence of the EFIE solution can be analytically derived. The rigor of the proposed method has been validated at frequencies as low as DC. As the first rigorous solution to EFIE at low frequencies, the proposed method can be used to benchmark the accuracy of existing low-frequency EFIE-based solvers, quantitatively answer critical design questions such as at which frequency full-wave effects become important, etc.