Finite-Difference Time-Domain Algorithm for Dispersive Media Based on Runge-Kutta Exponential Time Differencing Method
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Finite-Difference Time-Domain Algorithm for Dispersive Media Based on Runge-Kutta Exponential Time Differencing Method Song Liu & Shuangying Zhong & Shaobin Liu
Received: 20 December 2007 / Accepted: 10 January 2008 / Published online: 25 January 2008 # Springer Science + Business Media, LLC 2008
Abstract The electromagnetic propagation in dispersive media is modeled using finite difference time domain (FDTD) method based on the Runge-Kutta exponential time differencing (RKETD) method. The second-order RKETD-FDTD formulation is derived. The high accuracy and efficiency of the presented method is confirmed by computing the transmission and reflection coefficients for a nonmagnetized collision plasma slab in one dimension. The comparison of the numerical results of the RKETD and the exponential time differencing (ETD) algorithm with analytic values indicates that the RKETD is more accurate than the ETD algorithm. Keywords Finite difference time domain (FDTD) methods . Runge-Kutta exponential time differencing (RKETD) . Unmagnetized plasma
1 Introduction The finite-difference time-domain method has been widely used to simulate the transient solutions of electromagnetic problems involving the analysis and design of microwave structures, many other engineering applications and the electromagnetic wave propagation in various media. Over the past decade, there have been numerous investigations of FDTD dispersive media formulations. These include the recursive convolution (RC) methods [1, 2], the auxiliary differential equation (ADE) methods [3], frequency-dependent Z transform methods [4, 5], JE convolution (JEC) method [6], piecewise linear recursive convolution (PLRC) method [7], direct integration (DI) methods [8, 9] and piecewise linear current density recursive convolution (PLCDRC) method [10]. S. Liu (*) : S. Liu College of Information Science & Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, People’s Republic of China e-mail: [email protected] S. Liu : S. Zhong School of Sciences, Nanchang University, Nanchang, Jiangxi 330031, People’s Republic of China
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Int J Infrared Milli Waves (2008) 29:323–328
The original exponential time differencing (ETD) algorithm has been used to describe ordinary differential equations and applied to the simulation of electric conductive media and isotropic lossy dielectrics [11–13]. Subsequently, the ETD schemes to simulate wave propagation in nonmagnetized collision plasma is developed [14]. In [14], the original firstorder and second-order accurate of ETD with Taylor series schemes are presented. To develop ETD methods further, in this paper we derive new, more accurate ETD methods with Runge-Kutta time stepping schemes (RKETD) and provide a more succinct derivation of ETD methods than previously given [13]. The propagation of electromagnetic waves through nonmagnetized collision plasma slab is also studied using the RKETD-FDTD method. The high efficiency and accuracy of the method are confirmed by computing the transmission and reflectio
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