A New Efficient Unconditionally Stable Finite-Difference Time-Domain Solution of the Wave Equation

Abstract

This paper presents a new 2-D unconditionally stable finite-difference time-domain (FDTD) method based on the Crank–Nicolson (CN) scheme. Unlike other CN-based unconditionally stable FDTD algorithms, the CN scheme in the proposed method applies only to one of Maxwell curl equations. In fact, the proposed scheme is essentially a finite-difference solution of the vector wave equation in time domain. Therefore, only one of the electric or magnetic fields needs to be updated during the iterations of the algorithm. Most importantly, the implicit updating equations of the proposed methods can be solved simultaneously thereby significantly reducing run time. The stability of the proposed method is proved analytically. For the validation and demonstration of the accuracy of the proposed method and its efficiency, numerical examples are presented and the results are compared with those obtained by analytic solutions and other FDTD methods.