A Hybrid Scheme With Nyström Discretization for Solving Transient Electromagnetic Scattering by Conducting Objects

The interaction of transient electromagnetic (EM) waves 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 combining the method of moments (MoM) in spatial domain and a march-on-in-time (MoT) scheme in temporal domain. The MoM usually requires conforming meshes with a well-designed basis function and the MoT may suffer from a stability problem. 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 basis and testing functions is employed with a march-on-in-degree (MoD) manner in the temporal domain. The Nyström method does not require any basis and testing functions and can use nonconforming meshes in spatial domain, whereas the MoM with Laguerre function as basis and testing functions can fully eliminate the stability problem in temporal domain. Numerical examples for EM scattering by typical conducting objects are presented to demonstrate the scheme and its merits have been verified.