A Marching-on-in-Time Method of Moments for Transient Modeling of a Vertical Electrode Buried in a Lossy Medium

This article proposes a full-wave time-domain method for analyzing the transient behavior of a grounding electrode buried vertically in a lossy soil. In this method, the electrode is first approximated by a thin wire, and the modified image theory is utilized to account for the soil-air interface. The governing electric field integral equation (EFIE) is then derived with the current distribution along the electrode being the unknown quantities. Finally, the EFIE is solved by the time-domain method of moments based on a marching-on-in-time (MOT) procedure. This is done by expanding the unknown currents in terms of a finite linear combination of products of appropriate spatial and temporal basis functions, and adopting the Galerkin method in space and the point matching method in time. The MOT procedure makes the proposed method more efficient computationally than its rival frequency-domain method of moments (FD-MoM). The efficiency of the proposed method is demonstrated by comparing the lightning ground potential rise of various grounding electrodes with those obtained using the FD-MoM and a commercial numerical code.