請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/42811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 | Ming-Hong Tsai | en |
| dc.contributor.author | 蔡明宏 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:24:21Z | - |
| dc.date.available | 2010-07-24 | |
| dc.date.copyright | 2009-07-24 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-23 | |
| dc.identifier.citation | [1] Y. Liu, Fourier analysis of numerical algorithms for the Maxwell’s equations, J.
Comput. Phys. 124 (1996) 396-416. [2] C. W. Trowbridge, J. K. Sykuski, Some key developments in computational electromagnetics and their attribution, IEEE Trans. Magn. 42 (2006) 503-508. [3] R. Rieben, D. White, G. Rodrigue, High-Order Symplectic Integration Methods for Finite Element Solutions to Time Dependent Maxwell Equations, IEEE Trans. Antenn. Propag. 52 (2004) 2190-2195. [4] Le-Le Jiang, Jun-Fa Mao, and Xian-Liang Wu, Symplectic Finite-Difference Time- Domain Method for Maxwell Equations, IEEE Trans. Magn. 42 (2006) 1991-1995. [5] Jiaxiang Cai, Yushun Wang, Bin Jiang, New multisymplectic self-adjoint scheme and its composition scheme for the time-domain Maxwell’s equations, J. Math. Phys. 47 (2006) 123508 1-18. [6] M. Born, E. Wolf, Principles of Optics, 7th edition, Cambridge University Press, 1999. [7] B. Cockburn, F. Y. Li, C. W. Shu, Locally divergence-free discontinuous Galerkin methods for the Maxwell’s equations, J. Comput. Phys. 194 (2004) 588-610. [8] B. N. Jiang, J.Wu, L. A. Povinelli, The origin of spurious solutions in computational electromagnetics, J. Comput. Phys. 125 (1996) 104-123. [9] R. A. Nicolaides, D. Q. Wang, Convergence analysis of a covolume scheme for Maxwell’s equations in three dimensions, Mathematics of Computation 67 (1998) 947-963. [10] B. Engquist, A.Majda, Absorbing boundary conditions for the numerical simulation of waves, Mathematics of Computation 31 (1977) 629-651. [11] G. Mur, Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations, IEEE Trans. Electromagn. Compat. 23 (1981) 377-382. [12] R. L. Higdon, Absorbing boundary conditions for difference approximations to the multidimensional wave equation, Mathematics of Computation 47 (1986) 437-459. [13] X. Feng, Absorbing boundary conditions for electromagnetic wave propagation, Mathematics of Computation 68 (1999) 145-168. [14] J. P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994) 185-200. [15] S. Abarbanel, D. Gottlieb, On the construction and analysis of absorbing layers in CEM, Appl. Numerical Mathematics 27 (1998) 331-340. [16] S. Abarbanel, D. Gottlieb, J. S. Hesthaven, Non-linear PML equations for time dependent electromagnetics in three dimensions, J. Sci. Comput. 28 (2006) 125-136. [17] 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 (1995) 1460-1463. [18] S. D. Gedney, An Anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices, IEEE Trans. Antennas Propagat. 44 (1996) 1630-1639. [19] N. Anderson, A.M. Arthurs, Helicity and variational principles forMaxwell’s equations, Int. J. Electron. 54 (1983) 861-864. [20] 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 (2002) 0667051 1-12. [21] S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16-42. [22] P. J. Morrison, The Maxwell-Vlasov equations as a continuous Hamiltonian system, Phys. Lett. 80 (1980) 383-386. [23] J. E.Marsden, A.Weinsten, The Hamiltonian structure of theMaxwell-Vlasov equations, Physica D 4 (1982) 394-406. [24] 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 [25] Z. X. Huang, X. L. Wu, Symplectic partitioned Runge-Kutta scheme for Maxwell’s equations, Int. J. Quantum Chem. 106 (2006) 839-842. [26] J. De Frutos, J. M. Sanz-Serna, An easily implementable fourth-order method for the time integration of wave problems, J. Comput. Phys. 103 (1992) 160-168. [27] J. David Brown, Midpoint rule as a variational-symplectic integrator: Hamiltonian systems, Phys. Rev. D 73 (2006) 024001024001 1-11. [28] Jiaxiang Cai, Yushun Wang, Bin Jiang, New multisymplectic self-adjoint scheme and its composition scheme for the time-domain Maxwell’s equations, J. Math. Phys. 47 (2006) 123508 1-18. [29] Tony W. H. Sheu, R. K. Lin, An incompressible Navier-Stokes model implemented on nonstaggered grids, Numer. Heat Transfer, B 44 (2003) 277-294. [30] P. H. Chiu, Tony W. H. Sheu, R. K. Lin, Development of a dispersion-relationpreserving upwinding scheme for incompressible Navier-Stokes equations on nonstaggered grids, Numer. Heat Transfer, B 48 (2005) 543-569. [31] P. H. Chiu, Tony W. H. Sheu, R. K. Lin, An effective explicit pressure gradient scheme implemented in the two-level non-staggered grids for incompressible Navier-Stokes equations, J. Comput. Phys. 227 (2008) 4018-4037. [32] J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations, John Wiley and Sons, Chichester, 1987. [33] K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE. Transactions on Antenna Propagation, AP4 (1996) 302-307. [34] C. K. Tam ,J. C. Webb, Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys., 107 (1993) 262-281. [35] S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., 103 (1992) 16-42. [36] C. Bogry, C. Bailly, A family of low dispersive and low dissipative explicit schemes for flow and noise computations, J. Comput. Phys., 194 (2004) 194-214. [37] W. Chen, X. Li, D. Liang, Energy-conserved splitting FDTD schemes forMaxwell’s equations, Numer. Math 108 (2008) 445-485. [38] W. Chen, X. Li, D. Liang, Symmetric Energy-conserved splitting FDTD schemes for Maxwell’s equations, Numer. Math 6 (2009) 804-825. [39] L. M. Brekhovskikh, Waves ib Layerd Media, 2nd edition, Academic Press, 1980. [40] L. Eyges, The classical electromagnetic fields, Addison-Wesley, 1972. [41] A. Taflove, S. C. Hagness, Computational electrodynamics: The Finite-Difference Time-Domain Method, 2nd edition, Artech House, 2000. [42] K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas Propag 14 (1966) 302-327. [43] J. S. Heshaven, Spectral penalty methods, Appl. Numerical Mathematics 33 (2000) 23-41. [44] 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-domainMaxwell’s equations, J. Sci Comput 36 (2008) 351-390. [45] E. Olsson, G. Kreiss, A conservative level set method for two phase flow, J. Comput. Phys., 210 (2005) 225-246. [46] 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 (2009) 661-686. [47] C. M. Furse, S. P. Mathur, O. P. Gandi, Improvements to the finite-difference timedomain method for calculating the radar and cross section of a perfectly conducting target, IEEE Trans. Microwave Teory and Tech., 38 (1990) 919-927. [48] D. M. Sullivan, Mathematical methods for treatment planning in deep regional hyperthermia, IEEE Trans. Microwave Teory and Tech., 39 (1991) 864-872. [49] R. Harrington, Time-harmonic electromagnetic fields. New York, McGraw-Hill, 1961. [50] E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electrons, Phys. Rev. Lett., 58 (1987) 2059-2062. [51] E. Yablonovitch, Photonic band-gap structures, J. Opt. Soc. Am. B, 10 (1993) 283- 295. [52] R. D. Meade, A. Devenvi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, K. Kash, Novel applications of photonic band gap materials: Low-loss bends and high Q cavities, J. App. Phys., 75 (1994) 4753-4755. [53] A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, High transmission through sharp bends inbends in photonic crystal waveguides, Phys. Rev. Lett., 77 (1996) 3787-3790. [54] A. Mekis, S. Fan, J. D. Joannopoulos, Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides, IEEE Microwave Guide Wave Lett, 9 (1999) 502-504. [55] G. S. Almasi, A. Gottlieb, Highly Parallel Computing. Benjamin-Cummings publishers, Redwood City, CA., 1989. [56] D. A. Patterson, J. L. Hennessy, Computer Organization and Design. 2nd edition, Morgan Kaufmann Publishers, 1998. [57] B.Wilkinson,M. Allen, Parallel Programming: Techniques and Applications Using Networked Workstations and Parallel Computers. 2nd edition, Prentice Hall, 1998. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/42811 | - |
| dc.description.abstract | 對於光電電磁波，為了能夠解決奇、偶震盪的問題並得以節省計算時間，本論文中在空間內使用一種準確且有效率得以保持光波傳遞頻散關係Dispersion- relation -preserving (DRP) 的非交錯有限差分格式來離散一次微分項。針對長時間之數值模擬，為了保持其漢米爾頓的結構，使用一有效率守恆物理量的具辛 (Symplectic) 性質的差分格式，並將此一Symplecitic DRP的差分方法其運用於離散光電磁學方程Maxwell’s equations，以求解空間中包含散射體之電磁問題。
藉由求解二維及三維的光電電磁波方程，證實本論文所提出之求解程序的準確性及可行性，由測試問題可知，本論文所提出之格式，在所有的測試問題中均能保有相當好的收斂斜率及能量守恆性。 為了模擬無限域問題，本文中使用了完美匹配層(PML)、全場/散射場(TF/SF)與等位函數法(Level Set)等數值技巧，求解包含非均勻介質之電磁問題(包括二維TM模態米氏電磁散射問題和三維米氏電磁散射問題，以及二維TM模態複雜非均勻介質光子晶體波導問題)，經由測試題目可以得知，本論文所提出的方法可以得到相當好的準確性，且與前人所模擬之結果均呈相當的吻合性。 最後，針對三維米氏電磁散射問題，本文使用叢集式電腦及訊息溝通介面 (message passing interface MPI) 函式庫，將序列程式平行化，藉由使用區域分割法及本論文所提出的平行差分格式，本論文均求得不錯的平行加速比及效能比的結果。 | zh_TW |
| dc.description.abstract | In this thesis, the electromagnetic wave equation
is discretized in non-staggered grids. To avoid even-odd spurious oscillations, the first-order spatial derivative terms will be approximated by the explicit compact scheme to save the computational time. 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 integrity of the finite difference time domain method for solving the Maxwell's equations involving scatters will be verified by solving several problems in two- and three-dimensional 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, including 2-D (TM) Mie scattering problem, 3-D Mie scattering problem and modeling of PC-based L-shaped waveguide problem. The results simulated from the proposed method agree well with other numerical and experimental results for the chosen problems. Finally, the present Maxwell's equation solver for the 3-D Mie scattering problem are solved in MPI parallel platforms. With the domain decomposition methods combined with the proposed scheme, the speed-up and efficiency are both good in the simulated scattering problem. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:24:21Z (GMT). No. of bitstreams: 1 ntu-98-R96525007-1.pdf: 11543952 bytes, checksum: c42c1fa0821efa7aff9f12d7c94be3bb (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
1 Introduction 1 1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Outlines of the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Electromagnetic wave equations - Maxwell’s equations 7 2.1 Physical and Mathematical properties . . . . . . . . . . . . . . . . . . . 7 2.2 Uniaxial Perfectly Matched Layer Absorbing Boundary Condition . . . . 10 3 Discretization method : Dual-preserving numerical schemes 21 3.1 Symplecticity-preserving temporal scheme . . . . . . . . . . . . . . . . . 21 3.2 Dispersion relation preserving spatial scheme in nonstaggered grids . . . 25 3.2.1 Analysis of the proposed scheme in Fourier space . . . . . . . . 28 3.3 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3.1 TE wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3.2 TM wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3.3 3D Maxwell’s equations . . . . . . . . . . . . . . . . . . . . . . 34 4 Simulation of propagated electromagnetic waves 43 4.1 Source Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Total-Field/Scattered-Field technique . . . . . . . . . . . . . . . . . . . . 44 4.3 Level Set scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.4 Numerical results of simulations . . . . . . . . . . . . . . . . . . . . . . 47 4.4.1 Numerical error discussion . . . . . . . . . . . . . . . . . . . . . 48 4.4.2 Modeling of PC-based L-shaped waveguide . . . . . . . . . . . . 48 5 Parallel computing 63 5.1 Open Multi Processing - OMP . . . . . . . . . . . . . . . . . . . . . . . 64 5.1.1 Shared memory programing . . . . . . . . . . . . . . . . . . . . 64 5.2 Message Passing Interface - MPI . . . . . . . . . . . . . . . . . . . . . . 65 5.2.1 Parallelized domain decomposition method . . . . . . . . . . . . 66 5.3 Parallel efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.4 Numerical results-verification study . . . . . . . . . . . . . . . . . . . . 67 6 Conclusion remarks 77 A Comparison of Maxwell’s equations of PML and free space 79 B Normalization of Maxwell’s equations 81 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 | |
| dc.language.iso | zh-TW | |
| dc.subject | 辛結構 | zh_TW |
| dc.subject | 馬克斯威爾方程 | zh_TW |
| dc.subject | 頻散保持 | zh_TW |
| dc.subject | symplecticity | en |
| dc.subject | dispersion relation preserving | en |
| dc.title | 具辛結構及頻散保持性質之平行馬克斯威爾方程算則 | zh_TW |
| dc.title | On a symplecticity and dispersion relation preserving parallel solver for Maxwell's equations | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李佳翰(jiahan@ntu.edu.tw),曾雪峰(Snow H Tseng),邱奕鵬(Yih-Peng Chiou) | |
| dc.subject.keyword | 馬克斯威爾方程,頻散保持,辛結構, | zh_TW |
| dc.subject.keyword | dispersion relation preserving,symplecticity, | en |
| dc.relation.page | 90 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-24 | |
| 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-98-1.pdf 未授權公開取用 | 11.27 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。