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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 許文翰(Tony Wen-Hann Sheu) | |
| dc.contributor.author | Chia-Min Mei | en |
| dc.contributor.author | 梅嘉敏 | zh_TW |
| dc.date.accessioned | 2021-06-13T04:36:33Z | - |
| dc.date.available | 2012-08-01 | |
| dc.date.copyright | 2011-08-01 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-07-27 | |
| dc.identifier.citation | [1] Yee KS, Numerical solution of initial boundary value problems involving Maxwell’s
equations in isotropic media, IEEE. Trans. Antenn. Propag. 1966; AP4: 302-307. [2] M. Born, E. Wolf, Principles of Optics,Pergamon, Oxford,1964. [3] B. Cockburn, F. Y. Li, C. W. Shu, Locally divergence-free discontinuous Galerkin methods for the Maxwell’s equations, J. Comput. Phys. 194, 588-610, 2004. [4] B. N. Jiang, J.Wu, L. A. Povinelli, The origin of spurious solutions in computational electromagnetics, J. Comput. Phys. 125, 104-123, 1996. [5] R. A. Nicolaides, D. Q. Wang, Convergence analysis of a covolume scheme for Maxwell’s equations in three dimensions, Mathematics of Computation 67, 947-963, 1998. [6] N. Anderson, A.M. Arthurs, Helicity and variational principles forMaxwell’s equations, Int. J. Electron. 54, 861-864, 1983. [7] J. S. Kole, M. T. Figge, De Raedt, Higher-order unconditionally stable algorithms to solve the time-dependent Maxwell’s equations, Phys. Rev. E 65, 0667051 1-12, 2002. [8] R. Holland and J. W. Williams, Total-Field verus Scattered-Field Finite-Difference Codes: A Comparative Assessment, IEEE Trans. Nuclear Science, NS-30, 4583-4588, 1983. [9] J. P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114, 185-200, 1994. [10] Z. S. Sack, D. M. Kingsland, R. Lee, J. F. Lee, A perfectly matched anisotropic absorber for use as an absorbing boundary condition, IEEE Trans. Antennas Propagat. 43, 1460-1463, 1995. [11] S. D. Gedney, An Anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices, IEEE Trans. Antennas Propagat. 44, 1630-1639, 1996. [12] R. Holland, APitfalls of staircase meshing, IEEE Trans. Electromagn. Comput. 35, 434-439, 1993. [13] M. S. Rodrigo, UPML formulation for truncating conductive media in curvilinear coordinates, Numer Algor, 46, 259-319, 2007. [14] Y. Shi and C.-H. Liang, Multidomain pseudospectral time-Domain alogorihm in curvilinear coordinates system, Microwave And Optical Technology Letters, 49, No. 10, 2007. [15] B. Cockburn, F. Li, C.W. Chi, Locally divergence-free discontinuous Galerkin methods for the Maxwell equations, J. Comput phys, 194, 588-610, 2004. [16] J. U. Brackbill, D.C. Barnes, The effect of nonzero $ ablacdot B$ on numerical solution of the magnetohydrodynamic equations, J. Comput Phys, 35, 426-430, 1980. [17] C. R. Evans, J.F. Hawley, Simulation of magnetohydrodynamic flows: A constrained transport method, Astrophys. J, 332, 659-677, 1998. [18] K. G. Powell, An Approximate Riemann Solver for Magnetohydrodynamics That Works in More Than One Dimension, Tech. Report, ICASE, Langley, VA. 94-95, 1994. [19] F. Assous, P. Degond, E. Heintze, P.A. Raviart and J. Serger, On a finite-element method for solving the three-dimensional Maxwell equations, J. Comput. Phys, 109, 222-237, 1993. [20] Tony W. H. Sheu, Y. W. Hung, M. H. Tsai, J. H. Li, On the development of a triple-preserving Maxwell's equations solver in non-stroggered grids, Int. J. Numerical Meths. in Fluids, 63, 1328-1346, 2010. [21] P. J. Morrison, The Maxwell-Vlasov equations as a continuous Hamiltonian system, Phys. Lett, 80, 383-386, 1980. [22] J. E. Marsden, A. Weinsten, The Hamiltonian structure of the Maxwell-Vlasov equations, Physica D, 4, 394-406, 1982. [23] X. W. Lu, R. Schmid, Symplectic algorithms for Maxwell's equations,Proc. for International Conference on New Applications of Multisymplectic Field Theories, Salamanca, Spain, Sept, 10-25, 1999. [24]Z. X. Huang, X. L. Wu, Symplectic partitioned Runge-Kutta scheme for Maxwell's equations,Int. J. Quantum Chem, 106, 839-842, 2006. [25] J. De Frutos, J. M. Sanz-Serna,An easily implementable fourth-order method for the time integration of wave problems, J. Comput. Phys, 103, 160-168, 1992 [26] J. David Brown, Midpoint rule as a variational-symplectic integrator: Hamiltonian systems, Phys. Rev. D, 73, 024001024001 1-11, 2006 [27] J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations, John Wiley and Sons, Chichester, 1987. [28] Tony W. H. Sheu, R. K. Lin, An incompressible Navier-Stokes model implemented on nonstaggered grids, Numer. Heat Transfer, B, 44, 277-294, 2003 [29] P. H. Chiu, Tony W. H. Sheu, R. K. Lin, Development of a dispersion-relation-preserving upwinding scheme for incompressible Navier-Stokes equations on non-staggered grids, Numer. Heat Transfer, B, 48, 543-569, 2005 [30] C. K. Tam ,J. C. Webb, Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys, 107, 262-281, 1993 [31] S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys, 103, 16-42, 1992 [32] P. H. Chiu, Tony W. H. Sheu, R. K. Lin, Development of a dispersion-relation-preserving upwinding scheme for incompressible Navier-Stokes equations on non-staggered grids, Numer. Heat Transfer, B, 48, 543-569, 2005 [33] J. X. Cai, Y. S. Wang, B. Jiang, New multisymplectic self-adjoint scheme and its composition scheme for the time-domain Maxwell's equations, J. Math. Phys, 47 123508 1-18, 2006 [34] A. Taflove, S. C. Hagness, Computational electrodynamics: The Finite-Difference Time-Domain Method, 2nd edition, Artech House, 2000. [35] J. S. Heshaven, Spectral penalty methods, Appl. Numerical Mathematics, 33, 23-41, 2000. [36] C. H. Teng, B. Y. Lin, H. C. Chang, H. C. Hsu, C. N. Lin, K. A. Feng, A legendre pseudospectral penalty scheme for solving time-domain Maxwell's equations, J. Sci Comput 36, 351-390, 2008. [37] E. Olsson, G. Kreiss, A conservative level set method for two phase flow, J. Comput. Phys, 210, 225-246, 2005. [38] Tony W. H. Sheu, C. H. Yu, P. H. Chiu, Development of a dispersively accurate conservative level set scheme for capturing interface in two-phase flows,J. Comput. Phys, 228, 661-686, 2009. [39] C. M. Furse, S. P. Mathur, O. P. Gandi, Improvements to the finite-difference time-domain method for calculating the radar and cross section of a perfectly conducting target, IEEE Trans. Microwave Teory and Tech, 38, 919-927, 1990. [40] D. M. Sullivan, Mathematical methods for treatment planning in deep regional hyperthermia, IEEE Trans. Microwave Teory and Tech, 39, 864-872, 1991. [41] R. Harrington, Time-harmonic electromagnetic fields. New York, McGraw-Hill, 1961. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/33362 | - |
| dc.description.abstract | 本論文發展時域有限差分(Finite-difference time domain)方法在非正交曲線座標下求解馬克斯威爾方程式，
理論上，在時域和非交錯網格系統下，能維持零散度以及最佳波數保持特性。在時間離散上，因考慮馬斯威爾方程的漢米爾頓性質， 使用半隱式之具辛結構離散格式，在計算時間上能維持其能量守恆性質。此外針對複雜外型，使用面積比(Jacobian)保持緊緻格式來降低因座標轉換所造成之誤差。 由以上完整的時域有限差分方法，求解非正交曲線座標下之二維馬克斯威爾方程， 證實本論文所提出之求解程序的準確性及可行性。 並由測試問題得知本論文提出之格式能保持相當好的收斂斜率以及維持其能量守恆。 最後分析真實電磁波的問題， 本論文使用同軸性完美匹配層(UPML)來模擬無限域問題， 並且使用全場/散射場(TF/SF)和等位函數等數值方法求解非均勻介值之電磁問題 (二維TM模態米氏電磁波散射問題）， 經由測試題目可知，本論文與前人所模擬的結果有相當好的一致性。 最後，再以相同的方法應用在其他外型之散射體問題上。 | zh_TW |
| dc.description.abstract | In this thesis, a finite-difference time domain solver is presented for solving the Maxwell's equations in curvilinear coordinates.The scheme formulated in time domain and non-staggered grid system can
theoretically preserve zero-divergence condition and optimized numerical wavenumber characteristics. To accommodate the Hamiltonian structure in the Maxwell's equations, the time integrator employed in the current semi-discretization falls into the symplectic category. The inherent local conservation laws are also retained discretely all the time.To reduce the numerical error from the coordinate transformation in complex domain, the Jacobian-preserving compact scheme is used in this thesis. The integrity of the finite difference time domain method for solving the Maxwell's equations in two-dimensional curvilinear coordinates that are amenable to the exact solutions. The results with good rates of convergence are demonstrated for all the investigated problems. For simulating wave problems on open domain, in this thesis, the Perfectly matched layer (PML), Total-field-Scattered-field (TF/SF) and Level Set method are employed for solving scattering problems (2D (TM) Mie scattering problem). The results simulated from the proposed method agree well with other numerical and experimental results for the chosen problems. Finally, this scheme to other scattered structure problems is applied. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T04:36:33Z (GMT). No. of bitstreams: 1 ntu-100-R98525022-1.pdf: 21010048 bytes, checksum: ded475ae29e7dd1edf5f3f9a06a3fc7e (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 目錄
致謝...........................i 摘要......................iii Abstract......................iV 第一章 導論..............................1 1.1 前言.........................1 1.2 研究動機.....................1 1.3 研究目標.....................2 1.4 論文大綱.....................3 第二章 電磁波動方程-馬克斯威爾方程式.............3 2.1 卡式坐標下之馬克斯威爾方程...................4 2.1.1 方程式之物理及數學意義.................4 2.1.2 卡斯坐標下於單軸完美匹配層(Uniaxial perfectly Matched Layer)內之方程式..............6 2.2 非正交坐標下之馬克斯威爾方程.................10 2.2.1 卡式及非正交曲線坐標上方程式之轉換...10 2.2.2 非正交坐標下于單軸完美匹配層(Non-orthogonal Uniaxial perfectly Matched Layer) 之方程式....12 第三章 零散度(divergence-free)............................22 3.1 馬克斯威爾方程中三大定律:安培定律/法拉第定律/高斯定律.22 3.2 馬克斯威爾方程中兩大定律:安培定律、法拉第定律.........23 3.2.1 零散度演算法則運算安培定律/法拉第定律..............23 3.2.2 正交坐標下之零散度演算法則.........................24 3.2.3 非正交曲線坐標下之零散度演算法則...................26 第四章 數值方法...................................37 4.1 具辛結構保持之時間離散格式(Symplecticity-preserving temporal scheme)..............................37 4.2 具波數保持性質之空間離散格式..................39 4.3 具面積比保持之緊緻格式........................42 第五章 電磁波程式之驗證與結果.....................46 5.1 正交坐標下之TM wave傳播問題...................46 5.2 非正交曲線坐標下之TM wave傳播問題.............47 5.3 外型為平行四邊形網格之TM wave.................48 5.3 外型為任意外型網格之TM wave...................49 5.5 測試驗證之結果之與討論........................49 第六章 電磁波實際題目之測試.........................58 6.1 入射波源........................................58 6.2 全場散射場(Total-Field/Scattered-field)設定.....59 6.3 材料性質設定....................................60 6.4 電磁波模擬之數值結果............................61 6.5 電磁波模擬之數值結果討論........................63 第七章 結論.........................................79 7.1 檢視研究目標之達成與否研究結果..................79 7.2 未來工作與展望..................................80 附錄A 正交坐標下的物理量轉成非正交坐標下的物理量之推導.81 附錄B 曲線坐標下之馬克斯威爾方程推導...................83 參考文獻...............................................85 | |
| dc.language.iso | zh-TW | |
| dc.subject | 時域有限差分方法 | zh_TW |
| dc.subject | 非交錯網格 | zh_TW |
| dc.subject | 零散度 | zh_TW |
| dc.subject | 馬克斯威爾方程 | zh_TW |
| dc.subject | 曲線座標 | zh_TW |
| dc.subject | finite-difference time domain | en |
| dc.subject | divergence free | en |
| dc.subject | curvilinear coordinates | en |
| dc.subject | non-staggered grids | en |
| dc.title | 在曲線座標系統下發展一具最佳數值波數的馬克斯威爾方程數值方法 | zh_TW |
| dc.title | Development of an optimized numerical wavenumber Maxwell’s equation solver in curvilinear coordinates | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 吳瑞北(Ruey-Beei Wu),李佳翰(Jia-Han Li),張宏鈞(Hung-Chun Chang) | |
| dc.subject.keyword | 馬克斯威爾方程,時域有限差分方法,非交錯網格,曲線座標,零散度, | zh_TW |
| dc.subject.keyword | finite-difference time domain,non-staggered grids,curvilinear coordinates,divergence free, | en |
| dc.relation.page | 88 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2011-07-27 | |
| 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 | |
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