Refining Transient Electromagnetic Scattering Analysis: A new approach based on the magnetic field integral equation

The magnetic field integral equation (MFIE) in a timedomain form is used to describe transient electromagnetic (EM) scattering by conductors. The MFIE is a second kind of integral equation that can help improve the conditioning of the matrix equation but is less widely addressed in the time domain. The time-domain MFIE (TDMFIE) is generally solved by the spatial-domain method of moments (MoM) at each time step, after being discretized in the time domain with a march-on-in-time (MOT) scheme. The MoM is inconvenient in implementation due to its special basis and testing functions, and, in addition, the MOT will produce the well-known instability problem. This article proposes a novel solving approach by incorporating a spatial-domain Nystr?m scheme with a robust singularity treatment that has a temporal-domain Galerkin method (TDGM) with Laguerre basis and testing functions. The Nystr?m scheme has several advantages, as demonstrated in the frequency domain, but it has not been used for the TDMFIE. The TDGM can fully overcome the drawback of the MOT and simplify the implementation by deriving closed-form formulations. Numerical examples for transient EM scattering by conductors including a concave object are presented here to illustrate the approach and its robust results.