Accuracy and stability analysis of a 3D high-order staggered FDTD for Maxwell's equations

With the aim of increasing the numerical methods' precision regarding Maxwell's equations solving, a third order staggered FDTD method is proposed in this paper. The proposed method offers a trade-off between the accuracy and the stability, through the application of a third order staggered backward differentiation for the approximation of the temporal partial derivatives, and a fourth-order central difference approximation for the spatial derivatives approximation. The analysis of the numerical dispersion and the Courant-Friedrichs-Lewy condition demonstrates that the proposed method is more efficient than the traditional FDTD.

I. Introduction

Since it has been introduced by Yee [1], the second-order accurate in both time and space finite difference time domain (FDTD) method has been used to numerically solve a wide range of electromagnetic problems [2]. The FDTDbased algorithms are advantageous through the simplicity of their computation and implementation. Besides, they are very suitable for modeling inhomogeneous geometries. However standard FDTD-based algorithms suffer from the numerical dispersion caused by the low order accuracy in both time and space domains. This fact provokes the necessity of using a fine grid to achieve satisfactory results and consequently a high cost regarding the utilization of the memory and the time of simulation [3].