Unified treatment of scalar and vector potential fields with lorentz gauge condition by spatial network expression (invited article)

Abstract In the analysis of electromagnetic fields, the vector potential has important roles especially when sources exist and quantum effects occur. We have recently proposed a new numerical method for vector analysis of three‐dimensional electromagnetic fields in the time domain. This is known as the Spatial Network Method (SNM). I have already shown that SNM can be expanded to the vector potential fields with Coulomb's gauge condition by using not only the magnetic vector potential but also the electric vector potential. In this article, the unified formulation in the spatial network expression for both the vector potential and the scalar potential fields is proposed by using the Lorentz gauge condition including loss term. In the formulation, new “F” and “F*” variables are defined to utilize the correspondence between the electromagnetic scalar potential and the velocity potential in the acoustic field. As an example, the difference of internal magnetic fields in the substance with perfect conductivity or perfect diamagnetism in the scalar magnetic field is simulated. © 1993 John Wiley & Sons, Inc.