An Explicit MOT-TD-VIE Solver for Time Varying Media

Abstract

An explicit marching on-in-time (MOT) scheme for solving the time domain electric field integral equation enforced on volumes with time varying dielectric permittivity is proposed. Unknowns of the integral equation and the constitutive relation, i.e., flux density and field intensity, are discretized using full and half Schaubert-Wilton-Glisson functions in space. Temporal interpolation is carried out using band limited approximate prolate spherical wave functions. The discretized coupled system of integral equation and constitutive relation is integrated in time using a PE(CE)(m) type linear multistep scheme. Unlike the existing MOT methods, the resulting explicit MOT scheme allows for straightforward incorporation of the time variation in the dielectric permittivity.