On the Internal Resonant Modes in Marching-on-in-Time Solution of the Time Domain Electric Field Integral Equation

Abstract

Internal resonant modes are always observed in the marching-on-in-time (MOT) solution of the time domain electric field integral equation (EFIE), although “relaxed initial conditions,” which are enforced at the beginning of time marching, should in theory prevent these spurious modes from appearing. It has been conjectured that, numerical errors built up during time marching establish the necessary initial conditions and induce the internal resonant modes. However, this conjecture has never been proved by systematic numerical experiments. Our numerical results in this communication demonstrate that, the internal resonant modes' amplitudes are indeed dictated by the numerical errors. Additionally, it is shown that in a few cases, the internal resonant modes can be made “invisible” by significantly suppressing the numerical errors. These tests prove the conjecture that the internal resonant modes are induced by numerical errors when the time domain EFIE is solved by the MOT method.