臺灣博碩士論文加值系統

本論文是藉由數值模擬無限長直角金屬條在不同入射角電磁脈衝的電磁散射問題，觀察電磁場的分佈圖、直角金屬條結構中心點電磁場的時間函數圖、反射與透射電磁場的時間函數圖、以及各金屬條中心點感應電流的時間函數圖，為學習電磁學的學生提供一套可進一步了解電磁場散射行為的材料。觀察比較數值模擬結果得到直角金屬條各表面上的電場分量不連續；磁場在金屬條表面上不具有垂直分量，但具有平行分量；反射電磁場的Hy分量與Ez分量在行為上較為類似；透射電場行為上在對應的入射角度顯示相似性；在直角金屬條結構中心點的電場分量在強度上有顯著的差異，入射角度負的越多，主峰的強度越強，入射角度正的越多，主峰的強度越弱；金屬表面的感應電流以迎面又垂直照射下具有較大的值，得到的數值模擬結果與理論相符。

The purpose of this these is to numerically simulate the EM scattering from right angle metal strip and to study the EM behavior through the investigation on the EM filed distributions over the entire computational domain, the reflected EM fields, the transmitted EM fields, the EM fields at the center of the right angle metal strip and the induced current in the middle point of every metal strip surface. With an aim also to provide electromagnetics learners a close look of the EM fields behaviors for a better gain of understanding. Observations and comparisons of the numerical results lead to the followings: on the metal surfaces the electric field components are zero in magnitude; there exists no magnetic field components that are normal to the metal surface but the tangential components; the Hy and Ez components of the reflected bear similar trends, the transmitted electric fields are comparable with same angle but regardless of sign; the electric field components at the center of the structure have significant differences in intensity which is the more negative the incident angle, the stronger the intensity of the main peak, the more positive the incident angle, the weaker the intensity of the main peak; and he induced current on the metal surface has a large value under the head-on and vertical irradiation, and the numerical simulation results obtained are consistent with the theory.

摘要 I
Abstract I
誌謝 II
目錄 III
圖目錄 VII
第一章 緒言 VII
1.1 數值電磁學 2
1.2 直角金屬條的電磁散射問題 3
1.3 感應電流 4
第二章 Maxwell方程式與數值方法 5
2.1 自由空間中的Maxwell方程式 5
2.2 光速與真空的特性阻抗 7
2.3 時變電磁場 8
2.4 Euler方程式形式的Maxwell方程式 9
2.5 曲線坐標系中的Maxwell方程式 11
2.6 TE模式的入射電磁場 14
2.7 有限差分法 16
2.8 電磁邊界條件與感應電流 18
第三章 問題的定義與數值模型 20
3.1 問題的定義 20
3.2 數值高斯脈衝 22
3.3 取樣點的設置 25
第四章 數值模擬結果 27
4.1 電磁場的分佈圖 27
4.2 反射電磁場 32
4.3 透射電磁場 35
4.4 直角金屬條結構中心點電磁場 39
4.5 各金屬條表面中心點的感應電流 42
第五章 結論 47
參考文獻 48

[1]Mingtsu Ho (1997) Application of Computational Fluid Dynamics Algorithms to the Solutions of Maxwell’s Equations, A Dissertation submitted to the faculty of Mississippi State University, Starkville, Mississippi, USA.
[2]J. P. Donohoe, J. H. Beggs, MingTsu Ho, “Comparison of finite difference time-domain results for scattered EM fields: Yee algorithm vs. a characteristic based algorithm,” 27th IEEE Southeastern Symposium on System Theory, pp 325-328, March 1995.
[3]K. S. Yee (1966) Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Transactions on Antennas and Propagation (AP-14) 302-307.
[4]David B. Davidson, Computational Electromagnetics for RF and Microwave Engineering, Second Edition, Cambridge University Press, 2010.
[5]R.N.Simpsona et al., "A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis," Computer Methods in Applied Mechanics and Engineering 2012, 209–212, 87.
[6]Y. J. Liu et al., "Recent Advances and Emerging Applications of the Boundary Element Method," Appl. Mech. Rev. May 2011, 64(3).
[7]Stephen Kirkup, "The Boundary Element Method in Acoustics: A Survey," Applied Sciences 2019, 9(8), 1642.
[8]J.N. Reddy (2006) An Introduction to the Finite Element Method, McGraw-Hill. ISBN 9780071267618.
[9]Daryl L. Logan (2011), A first course in the finite element method, Cengage Learning, ISBN 978-0495668251.
[10]Roger F. Harrington (1968) Field Computation by Moment Methods, IEEE Press 1993, ISBN 0780310144.
[11]C. A. Brebbia and R. Magureanu, "The boundary element method for electromagnetic problems," Engineering Analysis 4(4), 178-185, December 1987.
[12]D. L. Whitfield and M. Janus, “Three-dimensional Unsteady Euler Equations Solution Using Flux Vector Splitting,” AIAA Paper No. 84-1552, June 1984.
[13]S. A. Tokareva and E. F. Toro, "A flux splitting method for the Baer–Nunziato equations of compressible two-phase flow," Journal of Computational Physics, 323, 45-74, 2016.
[14]W. Briley, S. Neerarambam, and D. Whitfield. "Implicit Lower-Upper /Approximate- Factorization Algorithms for Viscous Incompressible Flows", 12th Computational Fluid Dynamics Conference, Fluid Dynamics and Co-located Conferences, A95-36593, San Diego, CA, U.S.A., 1995.
[15]Michael B. Cohen, el at, "Solving Directed Laplacian Systems in Nearly-Linear Time through Sparse LU Factorizations," 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), October 2018.