一种高稳定的复杂色散介质分析FDTD方法

doi:10.3969/j.issn.1001-2400.2018.04.021

摘要/Abstract

摘要：

针对复杂色散介质电磁特性分析问题，提出一种新的、高稳定通用时域有限差分法．该方法从二阶复有理函数形式的极化率函数入手，将纽马克算法同时作用于极化矢量与电场的时域关系式两边，得到显式时域有限差分时域递推公式，并从理论和数值两方面对该算法的稳定性进行了分析．该方法不仅可作为处理包括复共轭极点-留数、临界点、修正洛伦兹以及二阶复有理函数等复杂色散介质问题的通用时域有限差分方法，而且具有更高的稳定性．

关键词: 复杂色散模型, 纽马克算法, 时域有限差分法, 稳定性分析

Abstract:

A novel finite-difference time-domain (FDTD) approach for analyzing a complicated dispersion model is presented. Starting from the susceptibility in the quadratic rational function form, the explicit FDTD time-step formula is obtained by applying the Newmark algorithm to both sides of the relation equation with the polarization vector and electric field in the time domain. Then, the stability of the presented algorithm is investigated from two aspects of theory and numerical computation. It is observed that this method has the advantages of generality and high stability and can thus be applied to the treatment of many complicated dispersion models, including the complex conjugate pole residue model, the critical point model, the modified Lorentz model, the complex quadratic rational function, etc.

Key words: complicated dispersive model, Newmark algorithm, finite-difference time-domain (FDTD) method, stability analysis

张玉强;葛德彪. 一种高稳定的复杂色散介质分析FDTD方法[J]. 西安电子科技大学学报, 2018, 45(4): 118-122+173.

ZHANG Yuqiang;GE Debiao. Highly stable FDTD method for complicated dispersive medium[J]. Journal of Xidian University, 2018, 45(4): 118-122+173.

参考文献

［1］ HAN M, DUTTON R W, FAN S. Model Dispersive Media in Finite-difference Time-domain Method with Complex-conjugate Pole-residue pairs［J］. IEEE Microwave and Wireless Components Letters, 2006, 16(3): 119-121.
［2］ PROKOPIDIS K P, ZOGRAFOPOULOS D C. Efficient FDTD Algorithms for Dispersive Drude-critical Points Media Based on Bilinear z-transform［J］. Electronics Letters, 2013, 49(8): 534-536
［3］ PROKOPIDIS K P, ZOGRAFOPOULOS D C. Investigation of the Stability of ADE-FDTD Methods for Modified Lorentz Media［J］. IEEE Microwave and Wireless Components Letters, 2014, 24(10): 659-661.
［4］ PARK S M, KIM E K, PARK Y B, et al. Parallel Dispersive FDTD Method Based on the Quadratic Complex Rational Function［J］. IEEE Antennas and Wireless Propagation Letters, 2016, 15: 425-428.
［5］ CHO J, HA S G, PARK Y B, et al. On the Numerical Stability of Finite-difference Time-domain for Wave Propagation in Dispersive Media Using Quadratic Complex Rational Function［J］. Electromagnetics, 2014, 34(8): 625-632.
［6］ RAMADAN O. Stability Considerations for the Direct FDTD Implementation of the Dispersive Quadratic Complex Rational Function Models［J］. IEEE Transactions on Antennas and Propagation, 2016, 64(11): 4929-4932.
［7］ ZIENKIEWICZ O C. A New Look at the Newmark, Houbolt and Other Time Stepping Formulas: a Weighted Residual Approach［J］. Earthquake Engineering and Structural Dynamics, 1977, 5(4): 413-418.
［8］ JIAO D, JIN J M. A General Approach for the Stability Analysis of the Time-domain Finite-element Method for Electromagnetic Simulations［J］. IEEE Transactions on Antennas and Propagation, 2002, 50(11): 1624-1632.
［9］李林茜, 魏兵, 杨谦, 等. 二维DGTD方法中UPML吸收边界的实现［J］. 西安电子科技大学学报, 2016, 43(6): 86-90.
LI Linqian,WEI Bing,YANG Qian,et al. Implementation of UPML Absorbing Boundary Conditions in DGTD Method［J］. Journal of Xidian University, 2016, 43(6): 86-90.
［10］ WEI B, CAO L, WANG F, et al. Frequency-dependent FDTD Algorithm Using Newmarks Method［J］. International Journal of Antennas and Propagation, 2014, 2014: 216763.
［11］王飞, 魏兵, 杨谦, 等. 色散手征介质FDTD分析的Newmark方法［J］. 西安电子科技大学学报, 2017, 44(1): 44-50.
WANG Fei, WEI Bing, YANG Qian, et al. FDTD Formulation for Dispersive Chiral Media Using Newmark Algorithm［J］. Journal of Xidian University, 2017, 44(1): 44-50.
［12］ PEREDA J A, VIELVA L A, VEGAS A, et al. Analyzing the Stability of the FDTD Technique by Combining the Von Neumann Method with the Routh-Hurwitz Criterion［J］. IEEE Transactions on Microwave Theory and Techniques, 2001, 49(2): 377-381.
［13］ RAMADAN O. On the Derivation of the Numerical Permittivity and Stability of the CDS-FDTD Implementation of High-order Constitutive relations［J］. IEEE Transactions on Antennas and Propagation, 2017, 65(3): 1486-1489.
［14］ LIN Z, THYLEN L. On the Accuracy and Stability of Several Widely Used FDTD Approaches for Modeling Lorentz Dielectric［J］. IEEE Transactions on Antennas and Propagation, 2009, 57(10): 3378-3381.

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[2]	江树刚;林中朝;张玉;魏兵;赵勋旺. 国产超级计算机实现10万核FDTD并行计算[J]. J4, 2015, 42(5): 86-91.
[3]	白冰;牛中奇. 时域有限差分法中的GPU加速高效CPML方案[J]. J4, 2015, 42(1): 194-199+212.
[4]	雷继兆;梁昌洪;张玉. 并行FDTD结合服务器分析电大电磁问题[J]. J4, 2009, 36(5): 846-850.
[5]	丁海1;褚庆昕2. TE模式下子域二阶精度FDTD算法 [J]. J4, 2009, 36(1): 162-165.
[6]	陈智慧1;褚庆昕2. 任意线性集总网络FDTD建模新方法 [J]. J4, 2008, 35(2): 262-266.
[7]	王林年;褚庆昕;梁昌洪. 交替方向隐式时域有限差分法中的Berenger理想匹配层[J]. J4, 2006, 33(3): 458-461.
[8]	陈霖;刘其中;纪奕才. 广义正交坐标系中FDTD算法的APML吸收边界[J]. J4, 2004, 31(5): 770-773.
[9]	赵建勋1;鲁德强2. 细胞培皿构形对毫米波辐照剂量的影响[J]. J4, 2004, 31(1): 115-118.
[10]	暂时无作者信息. 介质体曲面的时域有限差分子网格建模[J]. J4, 2003, 30(5): 623-625.
[11]	暂时无作者信息. 填充横向磁化铁氧体矩形波导的时域有限差分法分析[J]. J4, 2002, 29(6): 745-748.
[12]	暂时无作者信息. 有源集成天线的时域有限差分法分析[J]. J4, 2002, 29(3): 360-363.
[13]	暂时无作者信息. 交齿形微带滤波器特性的时域分析[J]. J4, 1999, 26(5): 641-646.
[14]	暂时无作者信息. 时域有限差分法的优化吸收边界条件[J]. J4, 1998, 25(5): 0-0.
[15]	暂时无作者信息. 波导不连续性的时域分析[J]. J4, 1997, 24(4): 0-0.