請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/63748
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 許文翰(Wen-Hann Sheu) | |
dc.contributor.author | Rih-Yang Chung | en |
dc.contributor.author | 張日陽 | zh_TW |
dc.date.accessioned | 2021-06-16T17:18:06Z | - |
dc.date.available | 2013-08-20 | |
dc.date.copyright | 2012-08-20 | |
dc.date.issued | 2012 | |
dc.date.submitted | 2012-08-17 | |
dc.identifier.citation | [1] K. S. Yee, 'Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,' IEEE Trans. Antennas Propagat., AP4 (1966) 302-307.
[2] G. Mur, 'Absorbing boundary conditions for the nite-di erence approximation of the time-domain electromagnetic- eld equations,' IEEE Trans. Electromagnetic Compatibility., 23 (1981) 377-382. [3] J. P. Berenger, 'A perfectly matched layer for the absorption of electromagnetic waves,' J. Com. Physics., 114 (1994) 185-200. [4] J. P. Berenger, 'Perfectly matched layer for the FDTD solution of wavestructure interaction problems,' IEEE Trans. Antennas Propagat., 44 (1996) 110-117. [5] J. A. Roden and S. D. Gedney, 'Convolutional PML(CPML): An e cient FDTD implementation of the CFS-PML for arbitrary media,' Microwave Optical Tech. Lett., Vol. 27, 2000, pp. 334-339. [6] R. J. Luebbers, F. Hunsberger, and K. S. Kunz, et al., 'A frequency dependent finite-di erence time-domain formulation ofr dispersive material,' IEEE Transactions on Electromagnetic Compatibility., 1990, 32(3): 222-227. [7] D. F. Kelley and R. J. Lubbers, 'Piecewise linear recursive convolution for dispersive media using FDTD,' IEEE Transactions on Antennas Propagat., 1996, 44(6): 792-797. [8] R. Siushansiana and J. Lovetri, 'A comparison of numerical techniques for modeling electromagnetic dispersive media,' IEEE Microwave and Guided Wave Letters., 1995, 5(12): 426-428. [9] Y. Takayama and W. Klaus, 'Reinterpretation of the auxiliary di erential equation method for FDTD,' IEEE Microwave Wireless Components Lett., 2002, 12(3):102-104. [10] M. Born and E. Wolf, Princioles of Optics. Pergamon, Oxford, 1964. [11] B. Cockburn, F. Y. Li, and C. W. Shu, 'Locally divergence-free discontinuous Galerkin methods for the Maxwell's equations,' J. Comput. Phys., 194 (2004) 588-610. [12] S. D. Gedney, 'An Anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,' IEEE Trans. Antennas Propagat., 44 (1996) 1630-1639. [13] S. Abarbanel, D. Gottlieb, and J. S. Hesthaven, 'Non-linear PML equations for time dependent electromagnetics in three dimensions,' J. Sci. Comput., 28 (2006) 125-136. [14] Kuzuoglu, M. and R. Mittra, 'Frequency dependence of the constitutive parameters of causal perfectly matched antisotropic absorbers,' IEEE Microwave Guided Wave Lett., Vol. 6, 1996, pp.164-168. [15] Bing Wei, Shi-quan Zhang, Fei Wang, and Debiao Ge, 'A novel UPML FDTD absorbing boundary condition for dispersive media,' Waves in Random and Complex Media., Vol. 20, No. 3, Auguest 2010, 511-527. [16] Tony W. H. Sheu, R. K. Lin, 'An incompressible Navier-Stokes model implemented on nonstaggered grids,' Numer. Heat Transfer., B 44 (2003) 277-294. [17] P. H. Chiu, Tony W. H. Sheu, and R. K. Lin, 'Development of a dispersionrelation-preserving upwinding scheme for incompressible Navier-Stokes equations on non-staggered grids,' Numer. Heat Transfer., B 48 (2005) 543-569. [18] L. Gao, B. Zhang, and D. Liang, 'The splitting nite-di erence time-domain methods for Maxwell's equations in two dimensions,' J. Comput. Applied Math., 205 (2007), pp. 207-230. [19] P. J. Morrison, 'The Maxwell-Vlasov equations as a continuous Hamiltonian system,' Phys. Lett., 80 (1980) 383-386. [20] J. E. Marsden and A. Weinsten, 'The Hamiltonian structure of the Maxwell-Vlasov equations,' Physica., D 4 (1982) 394-406. [21] X. W. Lu and R. Schmid, 'Symplectic algorithms for Maxwell's equations, Proc. for International Conference on New Applications of Multisymplectic Field Theories,' Salamanca, Spain, Sept. (1999) 10-25. [22] Z. X. Huang and X. L. Wu, 'Symplectic partitioned Runge-Kutta scheme for Maxwell's equations,' Int. J. Quantum Chem., 106 (2006) 839-842. [23] I. Saitoh, Y. Suzuki, and N. Takahashi, 'The symplectic nite di erence time domain method,' IEEE Trans. Magn., 37(5) (2001) 3251-3254. [24] C. K. Tam and J. C. Webb, 'Dispersion-relation-preserving nite di erence schemes for computational acoustics,' J. Comput. Phys., 107 (1993) 262-281. [25] L. Gao, B. Zhang, and D. Liang, 'The splitting nite-di erence time-domain methods for Maxwell's equations in two dimensions,' J. Comput. and A. Math., 205 (2007) 207-230. [26] R. L. Luebbers, Forrest P. Hunsberger, Karl S. Kunz, Ronald B. Standler, and Michael Schneider, 'A Frequency-Dependent Finite-Di erence Time-Domain Formulation for Dispersive Materials,' IEEE transactions on electromagnetic compatibility., Vol. 37, No. 32, August. 1990. [27] Bing Wei, Xiao-Yong Li, Fei Wang, and De-Biao Ge, 'A nite di erence time domain absorbing boundary condition for general frequency-dispersive media,' Acta Physica Sinica., Vol.58, No.7, pp : 6174-6178,2009. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/63748 | - |
dc.description.abstract | 本論文是在交錯網格上發展一具最佳數值色散關係之馬克斯威爾方程組的時域有限差分法。本文的目的是在進行長時間的模擬時,於非色散性介值空間仍能保持電場與磁場的零散度條件及維持其能量守恆之性質于時間離散使用了具辛結構(Symplectic) 二級二階之Runge-Kutta;而在半離散式之法拉第及安培旋度方程的空間微分項上,依數值角頻率與波數之間相依的觀念,引入了色散關係方程(Dispersion relation equation, DRE),以期在空間離散上具最佳數質色散的空間微分近似。為了達到最佳數值色散,我們提出減少實解與數值解色散關係方程之誤差的方式,並在空間上得到四階準確之中央差分離散格式。最後,我們把重點放在三種典型代表性之色散介質Debye、Lornetz、Drude 介質模型的電磁波模擬。透過計算上的運用,證明了文中所發展之數值方法於馬克斯威爾方程組在與頻率獨立和頻率相依上的有效性及在長時間模擬下的準確度。 | zh_TW |
dc.description.abstract | In this paper an explicit nite-di erence scheme is developed in staggered grids for solving the Maxwell's equations in time domain. It is aimed to preserve the discrete zero-divergence condition in the electrical and magnetic
elds and conserve some inherent laws in non-dispersive media all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta temporal scheme. The spatial derivative terms in the resulting semi-discretized Faraday's and Ampere's equations are approximated to get an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumber for the Maxwell's equations in a domain of two space dimensions. To achieve the goal of getting the best dispersive characteristics, a fourth-order accurate space centered scheme with the ability of minimizing the di erence between the exact and numerical dispersion relation equations is proposed. The emphasis of this study is placed on the accurate modelling of EM waves in the dispersive media of the Debye, Lorentz and Drude types. Through the computational exercises, the proposed dualpreserving solver is computationally demonstrated to be e cient for use to predict the long-term accurate Maxwell's solutions for the media of frequency independent and dependent types. | en |
dc.description.provenance | Made available in DSpace on 2021-06-16T17:18:06Z (GMT). No. of bitstreams: 1 ntu-101-R99525060-1.pdf: 2982923 bytes, checksum: 7d16fa7204319a925dc2dfb163abf270 (MD5) Previous issue date: 2012 | en |
dc.description.tableofcontents | 目錄
摘要 . . . . . . . . . . . . . . . . . . . . . . . i Abstract . . . . . . . . . . . . . . . . . . . . . ii 符號說明 . . . . . . . . . . . . . . . . . . . . . iii 第一章緒論 1 1.1 前言 . . . . . . . . . . . . . . . . . . . . . 1 1.2 文獻回顧 . . . . . . . . . . . . . . . . . . . 2 1.3 研究動機 . . . . . . . . . . . . . . . . . . . 3 1.4 研究目標 . . . . . . . . . . . . . . . . . . . 4 1.5 論文大綱 . . . . . . . . . . . . . . . . . . . 4 第二章電磁波方程-馬克斯威爾方程式 5 2.1 數學模型 . . . . . . . . . . . . . . . . . . . 5 2.1.1 法拉第/ 安培/ 高斯方程組及其推導 . . . . . . 5 2.1.2 法拉第/ 安培方程組 . . . . . . . . . . . . . 6 2.2 色散介質 . . . . . . . . . . . . . . . . . . . 8 2.3 卷積完美匹配吸收層 . . . . . . . . . . . . . . 9 第三章數值方法 20 3.1 交錯網格系統 . . . . . . . . . . . . . . . . . 20 3.2 具辛結構之PRK 時間離散 . . . . . . . . . . . . 22 3.3 具色散關係之空間離散方程 . . . . . . . . . . . 23 3.3.1 一維離散方程 . . . . . . . . . . . . . . . . 24 3.3.2 二維離散方程 . . . . . . . . . . . . . . . . 28 第四章具色散關係保持性離散方程之數值分析 36 4.1 一維空間離散分析 . . . . . . . . . . . . . . . 36 4.1.1 積分域之影響 . . . . . . . . . . . . . . . . 37 4.1.2 不同Cr之影響 . . . . . . . . . . . . . . . . 38 4.2 二維空間離散分析 . . . . . . . . . . . . . . . 39 4.2.1 角度變化之影響 . . . . . . . . . . . . . . . 40 4.2.2 數值與真實相速度於不同角度之比較 . . . . . . 41 4.3 數值分析之結果討論 . . . . . . . . . . . . . . 42 第五章數值模擬之結果 53 5.1 程式之驗證 . . . . . . . . . . . . . . . . . . 54 5.2 CPML吸收性的驗證 . . . . . . . . . . . . . . . 55 5.3 色散介質-Debye介質模型 . . . . . . . . . . . . 56 5.4 色散介質-Lorentz介質模型 . . . . . . . . . . . 57 5.5 色散介質-Drude介質模型 . . . . . . . . . . . . 57 第六章結論 74 6.1 研究成果與討論 . . . . . . . . . . . . . . . . 74 6.2 未來工作與展望 . . . . . . . . . . . . . . . . 75 參考文獻 . . . . . . . . . . . . . . . . . . . . . 79 | |
dc.language.iso | zh-TW | |
dc.title | 發展一具辛結構及最佳數值色散關係式的方法以求解具色散物質的馬克斯威爾方程 | zh_TW |
dc.title | Development of a symplectic scheme with optimized numerical dispersion-relation equation to solve Maxwell's equations in dispersive media | en |
dc.type | Thesis | |
dc.date.schoolyear | 100-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 吳瑞北(Ruey-Beei Wu),李佳翰(Jia-Han Li),陳瑞琳(Ruey-Lin Chern) | |
dc.subject.keyword | 馬克斯威爾方程,Debye 介質,Lorentz 介質,Drude 介質,色散關 係式,顯式具辛結構,頻率相依, | zh_TW |
dc.subject.keyword | Debye,Lorentz,Drude,dual-preserving solver,dispersion relation equation,frequency dependent, | en |
dc.relation.page | 78 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2012-08-18 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
顯示於系所單位: | 工程科學及海洋工程學系 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-101-1.pdf 目前未授權公開取用 | 2.91 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。