跳到主要內容

臺灣博碩士論文加值系統

(44.200.171.74) 您好!臺灣時間:2022/08/12 07:14
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:林信吉
研究生(外文):Shin-Chi Lin
論文名稱:以時域平面波展開法加速多區域時域有限差分法之計算法
論文名稱(外文):Multi-Region FDTD(Finite-Difference Time-Domain) enhanced by PWTD(Plane-Wave Time-Domain) Method
指導教授:林俊華林俊華引用關係
指導教授(外文):J.H. Lin
學位類別:碩士
校院名稱:國立海洋大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:103
中文關鍵詞:時域平面波展開法柯西荷夫積分公式全域積分吸收邊界多區域時域有限差分法全幅角展開式時域有限差分法
外文關鍵詞:PWTDKirchhoff Integral FormulaIRBCMR/FDTDWhittaker-type field expansionFDTD
相關次數:
  • 被引用被引用:0
  • 點閱點閱:123
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
本篇論文首先介紹「多區域時域有限差分法」的構想,其藉由「柯西荷夫積分公式」與「時域有限差分法」於各子區域的使用來進行問題的解析。藉此我們得以免除某些「時域有限差分法」的問題,諸如具備細微結構問題區域的網格分割限制,以及各子區域間空白區域的額外的記憶體耗費等。然而,取而代之,點對點的積分運算卻留下另一待解決的難題。也因此,本篇論文引入「時域平面波展開法」的架構,其基於Whittaker-type的平面波展開式的概念,得以將時域的場函數以各方向行進平面波來展開。我們可以發現,相較於使用「柯西荷夫積分公式」直接計算所耗費的O(NtNs^2)計算量,使用二階層的「時域平面波展開法」加強計算的方法,將僅需要O(NtNs^1.5logNs)計算量。

The thesis, first, introduces the concept of multi-region FDTD scheme based on the combination of using Kirchhoff Integral Formula and FDTD method in each sub-region. By this approach, some problems of FDTD method, such as the strict on the grid for total problem domain with some fine structure and the additional memory cost of white space between each sub-region, can be avoided. However, another difficulty about the heavy burden on computational requirement appears because of calculating the integral formula contribution from each point to point. Therefore, the plane wave time domain algorithm (PWTD), relying on a Whittaker-type expansion of transient fields in terms of propagating plane wave, is presented. Opposed to O(NtNs^2) cost by calculating Kirchhoff Integral Formula directly, it is shown that, the algorithm enhanced by two-level PWTD, only requires O(NtNs^1.5logNs) computational resource.

摘 要................................................Ⅰ
Abstract...................................................Ⅱ
目 錄................................................Ⅲ
第一章 緒論............................................... 1
1-1 研究動機............................................... 1
1-2 文獻回顧............................................... 2
1-3 章節概述............................................... 3
第二章 多區域時域有限差分法與時域平面波展開法之基本理論.... 4
2-1 簡介................................................... 4
2-2 多區域時域有限差分法之基本理論......................... 5
2-2.1 等效原理及積分公式................................. 5
2-2.2 全域積分吸收邊界................................... 9
2-2.3 多區域時域有限差分法.............................. 10
2-2.4 使用「柯西荷夫積分公式」的實現觀點................ 14
2-3 時域平面波展開法...................................... 18
2-3.1 時域平面波的展開型式.............................. 18
2-3.2 三階段的時域平面波展開法.......................... 21
2-3.3 「柯西荷夫積分公式」的平面波展開式................ 26
2-3.4 「時域平面波展開法」的實現觀點.................... 29
第三章 實現與程式化的過程................................. 36
3-1 簡介.................................................. 36
3-2 柯西荷夫積分公式的實現與程式化觀點.................... 36
3-2.1封閉面存取場值的考量............................... 36
3-2.2多維動態陣列的使用................................. 39
3-2.3 時間延遲項的內插處理.............................. 42
3-2.4 「柯西荷夫積分公式」直接計算的程式架構............ 43 3-3 時域平面波展開法的實現及程式化觀點................... 49
3-3.1準備工作........................................... 49
3-3.2 三階段的實現...................................... 52
第四章 模擬的結果與分析................................... 59
4-1 簡介.................................................. 59
4-2 「柯西荷夫積分公式」直接計算的結果.................... 59
4-3 「柯西荷夫積分公式」直接計算的複雜度分析.............. 65
4-4「時域平面波展開法」加強「柯西荷夫積分公式」........... 65
4-4.1 單一觀察點、高斯脈衝激發源........................ 66
4-4.2 單一觀察點、多重餘弦激發源........................ 72
4-4.3 平面觀察點的結果(準確性測試).................... 77
4-4.4 單一段「分段訊號」之場源的計算結果................ 85
4-4.5 改善「第一階段」後的計算結果...................... 88
4-5 以「時域平面波展開法」加強計算的複雜度分析............ 91
4-6 整理與討論............................................ 94
第五章 結論.............................................. 98
參 考 文 獻.............................................. 101

[1] Yee, K. S., “Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media,” IEEE Trans. on AP, vol. AP-14, pp. 302-307, May 1966.
[2] A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method. Boston: Atech House, 1995.
[3] D. M. Sullivan, Electromagnetic simulation using the FDTD method. New York: IEEE Press, 2000.
[4] Matthew N.O. Sadiku, Numerical techniques in electromagnetics. Boca Raton : CRC Press, 2000.
[5] Andrew F. Peterson, Scott L. Ray, Raj Mittra, Computational methods for electromagnetics. New York : IEEE Press, pp. 495-522, 1998.
[6] J. C. Olivier, “On the Synthesis of Exact Free Space Absorbing Boundary Conditions For the FDTD Method,” IEEE Trans. on AP, vol. 40, no. 4, pp. 456-460, 1992.
[7] J. C. Olivier, “On the Synthesis of Exact Free Space Absorbing Boundary Conditions For the FDTD Method: Numerical Results,” IEEE Trans. on AP, vol. 43, no. 2, pp. 213-215, 1995.
[8] J. De Moerloose and D. De Zutter, “Surface Integral Representation Boundary Condition For the FDTD Method: Numerical Results,” IEEE Trans. on AP, vol. 41, no. 7, pp. 890-896, 1993.
[9] J. M. Johnson and Y. Rahmat-Samii, “MR/FDTD: A Multiple-Region FDTD Method,” Mirco. and Optical Techn. Letts., vol. 14, no. 2, pp. 101-105, 1993.
[10] C. L. Holloway and M. S. Sarto, “On the Use of A Hybrid IE/FDTD Method For the Analysis of Electromagnetic Scattering and Coupling Problems,” IEEE International Symposium on Electromagnetic Compatibility, vol. 2, pp. 801-806, 2000.
[11] R. L. Wagner and W. C. Chew, “A Ray-Propagation Fast Multipole Algorithm,” Mirco. and Optical Techn. Letts., vol. 7, no. 10, pp. 435-438, 1994.
[12] J. M. Song and W. C. Chew, “Fast Multipole Method Solution Using Parametric Geometry,” Mirco. and Optical Techn. Letts., vol. 7, no. 16, pp. 760-765, 1994.
[13] D. Eric, “The Fast Multipole Method: Numerical Implementation,” J. Computational Phys., vol. 160, pp. 195-240, 2000.
[14] B. Hu, W. C. Chew, E. Michielssen, and J. Zhao, “An Improved Fast Steepest Descent Path Algorithm,” IEEE International Symposium on AP Digest, vol. 3, Atlanta, GA, June 21-26, pp. 1542-1545, 1998.
[15] E. Heyman, “Time-dependent multipoles and their application for radiation from volume source distributions,” J. Math. Phys., Vol. 37. pp.682, 1996.
[16] E. Heyman, “Time-dependent plane-wave spectrum representations for radiation from volume source distributions,” J. Math. Phys., vol. 37. pp. 157-180, 1998.
[17] A. Shlivinski, E. Heyman and A. J. Devaney, “Time Domain Radiation By Scalar Sources: Plane Wave To Multipole Transform,” J. Math. Phys., vol. 40. no.12, pp. 5915-5919, 2001.
[18] A. A. Ergin, B. Shanker, K. Aygun, and E. Michielssen, “Computational Complexity and Implementation of Two-Level Plane Wave Time Domain Algorithm for Scalar Wave Equation,” IEEE International Symposium on AP Digest, Vol. 2, Atlanta, GA, June 21-26, pp. 944-947, 1998.
[19] A. A. Ergin, B. Shanker, and E. Michielssen, “Fast Evaluation of Three-Dimensional Transient Wave Fields using Diagonal Translation Operators,” J. Comp. Phys., vol. 146, no.10, pp. 157-180, 1998.
[20] A. A. Ergin, B. Shanker, and E. Michielssen, “The Plane-Wave Time Domain Algorithm for the Fast Analysis of Transient Wave Phenomena,” IEEE Trans. on AP, vol. 41, no.4, pp. 39-51, 1999.
[21] A. A. Ergin, B. Shanker, K. Aygun and E. Michielssen, “Analysis of Transient Electromagnetic Sacttering Phenomena using a Two-Level Plane Wave Time-Domain Algorithm,” IEEE Trans. on AP, vol. 48, no.4, pp. 510-523, 2000.
[22] A. Shlivinski, E. Heyman, and R. Kastner, “Antenna Characterization In the Time Domain,” IEEE Transactions on Antennas and Propagation, AP-45, no. 7, pp. 1140-1149, 1997.
[23] O. M. Bucci and G. Franceschetti, “On the Spatial Bandwidth of Scattered Field,” IEEE Transactions on Antennas and Propagation, AP-35, 12, pp. 1445-1455, 1987.
[24] J. J. Knab, “Interpolation of band-limited functions using the approximate prolate series,” IEEE Transactions on Information Theory, vol. 25, pp.717, 1979.

QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top