Simulation of Electromagnetic Wave Propagation in Plasma Using Matrix Exponential FDTD Method
- PDF / 176,893 Bytes
- 7 Pages / 439.37 x 666.142 pts Page_size
- 33 Downloads / 217 Views
Simulation of Electromagnetic Wave Propagation in Plasma Using Matrix Exponential FDTD Method Song Liu & Shaobin Liu
Received: 20 April 2009 / Accepted: 20 May 2009 / Published online: 2 June 2009 # Springer Science + Business Media, LLC 2009
Abstract The electromagnetic propagation in plasma media can be conveniently modeled using finite difference time domain method based on the matrix exponential (ME-FDTD) method. The Maxwell’s curl equations and the constitutive relations between the flux density and the electric field can be looked as a first order differential matrix system. The fundamental solution to such a system is derived in terms of matrix exponential and the update equations can be extracted conveniently from the solution. This has the advantages of presenting a more concise formulation. The ME-FDTD algorithm is validated by comparing the simulation results with the analytical values. Numerical results show that the ME-FDTD can acquire high efficiency with less computer consumption and has a good performance of flexibility and simplicity. Keywords Plasma . Finite difference time domain (FDTD) . Matrix exponential (ME) method . Electromagnetic wave
1 Introduction The finite difference time domain method (FDTD) has been widely used to simulate the interaction of the electromagnetic wave with the various nondispersive media. To allow modeling the electromagnetic propagation in dispersive media, the conventional FDTD requires additional treatments due to the frequency-dependent permittivity or permeability of the media. 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 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 School of Sciences, Nanchang University, Nanchang Jiangxi 330031, People’s Republic of China
J Infrared Milli Terahz Waves (2009) 30:1020–1026
1021
[7], direct integration (DI) methods [8, 9], piecewise linear current density recursive convolution (PLCDRC) method [10], exponential time differencing (ETD) method[11], and Runge-Kutta exponential time differencing (RKETD)[12] and so on. In all above mentioned methods, the discretizations are applied independently to the Maxwell’s curl equations and the constitutive relations between the flux density and the electric field. In this paper, we present a novel formulation whereby all equations and relations are cast in a first order differential matrix system. The fundamental solution to such a system is derived in terms of matrix exponential and the update equations can be extracted conveniently from the solution. The formulation of the ME-FDTD schemes to simulate electromagnetic wave propagation in plasma is developed. The high efficiency and accuracy of the method are confirmed by computing the tran
Data Loading...
