Solution to the Electric Field Integral Equation at Arbitrarily Low Frequencies

The low-frequency breakdown problem in electric field integral equation (EFIE) has been well recognized and extensively studied. State of the art methods for solving this problem either reformulate the integral equations or introduce a different set of basis functions. The solution to the original full-wave EFIE with the Rao-Wilton-Glisson (RWG)-basis remains unknown at breakdown frequencies. The contribution of this work is the solution to the original RWG-basis based EFIE at an arbitrarily low frequency including DC. This solution is obtained by deriving a closed-form expression of the inverse of the EFIE system matrix, which is rigorous from high down to any low frequency. We also overcome the lowfrequency breakdown caused by the loss of the frequency dependence of the right hand side vector in scattering analysis and the same loss in Green’s function in RCS computation. In addition, we develop a fast solution that eliminates the lowfrequency breakdown of the EFIE in a reduced system of O(1). Instead of introducing additional computational cost to fix the low-frequency breakdown problem, the proposed fast O(1) solution speeds up low-frequency computation. Numerical experiments in inductance, capacitance, and RCS extraction at very low frequencies including DC have demonstrated both accuracy and efficiency of the proposed method.