Numerical Solution of Time-Domain Volume Integral Equations for Transient Electromagnetic Scattering by Dielectric Objects

Electromagnetic (EM) interaction with penetrable objects can be described by volume integral equations (VIEs) in integral equation approach and time-domain VIEs (TDVIEs) are required for formulating transient EM problems with such objects. The TDVIEs are usually solved by combining the method of moments (MoM) with well-designed basis function in space domain and a march-on-in-time (MOT) scheme in time domain. The space-domain MoM requires conforming meshes in geometric discretization and twofold numerical integrations in matrix generation while the MOT in time domain suffers from a late-time instability problem. In this communication, we propose an alternative approach that uses the Nystrom method to discretize the VIEs in space domain while employing the MoM with Laguerre basis and testing functions to discretize the equations in time domain. The proposed approach can simplify the numerical implementation and produce a march-on-in-degree procedure similar to that in frequency-domain approaches. Numerical examples are presented to illustrate the approach and good results have been observed.