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International Journal of Antennas and Propagation
Volume 2017 (2017), Article ID 5817380, 6 pages
https://doi.org/10.1155/2017/5817380
Research Article

The CFS-PML for 2D Auxiliary Differential Equation FDTD Method Using Associated Hermite Orthogonal Functions

1College of Defense Engineering, PLA University of Science and Technology, Nanjing 210007, China
2Jiangsu Regulatory Bureau of Nuclear and Radiation Safety, Nanjing 210019, China
3National Key Laboratory on Electromagnetic Environmental Effects and Electro-Optical Engineering, PLA University of Science and Technology, Nanjing 210007, China

Correspondence should be addressed to Feng Lu

Received 25 October 2016; Revised 18 February 2017; Accepted 26 March 2017; Published 18 May 2017

Academic Editor: Sotirios K. Goudos

Copyright © 2017 Feng Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The complex frequency shifted (CFS) perfectly matched layer (PML) is proposed for the two-dimensional auxiliary differential equation (ADE) finite-difference time-domain (FDTD) method combined with Associated Hermite (AH) orthogonal functions. According to the property of constitutive parameters of CFS-PML (CPML) absorbing boundary conditions (ABCs), the auxiliary differential variables are introduced. And one relationship between field components and auxiliary differential variables is derived. Substituting auxiliary differential variables into CPML ABCs, the other relationship between field components and auxiliary differential variables is derived. Then the matrix equations are obtained, which can be unified with Berenger’s PML (BPML) and free space. The electric field expansion coefficients can thus be obtained, respectively. In order to validate the efficiency of the proposed method, one example of wave propagation in two-dimensional free space is calculated using BPML, UPML, and CPML. Moreover, the absorbing effectiveness of the BPML, UPML, and CPML is discussed in a two-dimensional (2D) case, and the numerical simulations verify the accuracy and efficiency of the proposed method.