A Hybrid ADI and SBTD Scheme for Unconditionally Stable Time-Domain Solutions of Maxwell's Equations

Based upon the sampling bi-orthogonal algorithm and alternating direction implicit scheme, we present an unconditionally stable time-domain method, SB-ADI. Similar to the ADI scheme, this method is a second-order approximation in temporal discretization. However, theoretically, the new method produces no spatial discretization error due to the sampling property and compact support of the SBTD algorithm. Dispersion and stability analysis are presented. In a numerical example of 2-D electromagnetic bandgap structure, the new method has reduced the error by a factor of 3.5 at 16% increase of CPU time with respect to the standard ADI.

I. Introduction

Since the finite-diffence time-domain (FDTD) algorithm was developed by Yee [1] in the middle 1960s, it has become one of most powerful tools in full-wave analysis for time-domain electromagnetic solutions in device, material, antenna, and scattering simulations [2]–[5]. On many occasions, the FDTD provides accurate results both in time and frequency domains. However, its computational efficiency is limited by two inherent physical constraints: the numerical dispersion and the Courant–Friedrich–Levy (CFL) stability condition. The former requires fine spatial discretization for a particular accuracy, while the latter demands a proper time step for computational stability. Both of them lead to large memory and CPU time consumptions.