A Nyström method for solving time-domain volume integral equations

Electromagnetic (EM) analysis for inhomogeneous penetrable structures relies on the formulation of volume integral equations (VIEs) in integral equation approach and time-domain VIEs (TDVIEs) are required for transient interaction with the structures. The TDVIEs are usually solved by combining the method of moments (MoM) with well-designed basis function in spatial domain and a march-on-in-time (MOT) scheme in temporal domain. We propose a different approach in which the Nyström method is used in the spatial domain and the MoM with Laguerre basis and testing functions is employed in the temporal domain. The proposed approach can simplify the numerical implementation and fully solve the stability problem as in the traditional approach. A numerical example is presented to illustrate the approach and good results have been observed.