Time-Domain Solution of Volume-Surface Integral Equations Based on Nyström-Laguerre Scheme for Transient Electromagnetic Problems

Abstract

Transient analysis for electromagnetic scattering by the objects with both conducting and penetrable media requires the accurate solution of time-domain volume-surface integral equations in an integral equation approach. Traditionally, the problem is solved by uniting the method of moments (MoM) in the space domain and a marching-on-in-time (MOT) scheme in the time domain. The MoM requires structured conforming meshes for discretizing geometries because of the used divergence-conforming Rao–Wilton–Glisson and Schaubert–Wilton–Glisson basis functions and the implementation will be more inconvenient when incorporated with the MOT scheme that has a well-known late-time instability problem. In this communication, we propose a different scheme to solve the problem and it uses a Nystrom method to discretize the space domain and Galerkin’s method with Laguerre basis and testing functions to discretize the time domain. The Nystrom method has several merits compared to the MoM while Galerkin’s method can result in an unconditional stability in the time domain. Numerical examples are presented to demonstrate the approach, and its good performance has been seen.