Efficient Solutions of Time-Domain Volume Integral Equations Based on Meshless Discretization

Electromagnetic (EM) interaction with inhomogeneous and/or anisotropic penetrable objects can be formulated by volume integral equations (VIEs) in the integral equation approach. When the EM wave is transient, the time-domain VIEs (TDVIEs) are required to describe the transient behavior. Conventionally, the TDVIEs are solved by discretizing the time domain with the march-on-in-time (MoT) scheme and discretizing the space domain with the method of moments (MoM). However, the time-domain MoT scheme may have a late-time instability while the MoM requires conforming meshes and double-fold numerical integrations which are tedious and expensive. In this paper, we propose a hybrid scheme to solve the TDVIEs, where the time domain is discretized by a Galerkin’s method with Laguerre functions while the space domain is meshed by a truly meshless method (TMM). The proposed scheme can fully eliminate the late-time instability in time domain and greatly reduce the discretization cost in space domain. A numerical example is provided to demonstrate the scheme and its excellent performance has been authenticated.