Stable Solutions of Transient Electromagnetic Scattering by Penetrable Objects Based on Time-Domain Muller Equations

Electromagnetic (EM) interaction with homogeneous penetrable objects are usually described by Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equations. The Muller equations (MEs) can also be used to describe the same problem but they are less addressed although they are free of spurious solutions and hypersingularity. For transient problems, the time-domain MEs (TDMEs) are proposed so that the merits of MEs can be explored. Also, the TDMEs are solved by a hybrid scheme in which the Nystrom method is used to discretize the space domain while the Galerkin's method is employed to discretize the time domain. The former can simplify the implementation while the latter can remove the late-time instability. Numerical examples demonstrate the effectiveness and robustness of the approach.