Nyström method solution for time-domain electric field integral equations

The interaction of transient electromagnetic (EM) wave with objects can be formulated by the integral equation approach in time domain. For conducting objects or homogeneous penetrable objects, the time-domain surface integral equations (TDSIEs) can be applied. Traditionally, the TDSIEs are solved by the method of moments (MoM) in spatial domain and a march-on in time (MOT) scheme in temporal domain. In this work, we propose a hybrid scheme in which the Nyström method is used in spatial domain while the MoM with Laguerre function as a basis function in the time domain is employed. The numerical example for EM scattering by a conducting sphere is presented to demonstrate the scheme and its merits can be observed.