請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/15694完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王偉仲(Wei-Chung Wang) | |
| dc.contributor.author | Kun-Shian Chuang | en |
| dc.contributor.author | 莊坤憲 | zh_TW |
| dc.date.accessioned | 2021-06-07T17:50:11Z | - |
| dc.date.copyright | 2013-02-01 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-01-14 | |
| dc.identifier.citation | [1] C. Kittel. “Introduction to solid state physics.” New York, 2005, Wiley.
[2] A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos. “ High transmission through sharp bends in photonic crystal waveguides.” Phys. Rev. Lett., 77:3787-3790, 1996. [3] K. Yee. “ Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media.” IEEE Trans. Antennas Propag., 14:302–307, 1966. [4] T.-M. Huang, W.-J. Chang, Y.-L. Huang, W.-W. Lin, W.-C. Wang, and W. Wang. “ Preconditioning bandgap eigenvalue problems in three dimensional photonic crystals simulations.” J. Comput. Phys., 229:8684-8793, 2010. [5] P. Arbenz and R. Geus. “ A comparison of solvers for large eigenvalue prob- lems occuring in the design of resonant cavities.” Numer. Linear Algebr. Appl., 6:3–16, 1999. [6] V. Simoncini. “ Algebraic formulations for the solution of the nullspace- free eigen- value problem using the inexact shift-and-invert Lanczos method.” Numer. Linear Algebr. Appl., 10:357–375, 2003. [7] T.-M. Huang, H.-E. Hsieh, W.-W. Lin, and W. Wang. “ Eigendecomposition of The Discrete Double-Curl Operator with Application to Fast Eigensolver for Three Di- mensional Photonic Crystals.” Technical report, National Center for Theoretical Sci- ences, 2012. [8] Y. Saad. “ Iterative methods for sparse linear systems.” PWS Publishing Company, 1996. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/15694 | - |
| dc.description.abstract | 解決大型特徵值問題往往所需大量的時間,尤其在迭代的過程中,矩陣乘向 量更是佔大多數的時間。在本篇論文中,我們的問題來自於光子晶體的馬克斯威 爾方程之鑽石結構。在以往研究中,皆是利用許多不同的方法來加速收斂。這次 發展一個新的方法-投影Lanczos法來解決我們的特徵值問題,其目的是將原本的 問題投影至非零的不變子空間,最後得到新的特徵值問題,而在矩陣乘向量中只 剩傅立葉矩陣與對角矩陣的運算,在此配合傅立葉矩陣乘向量演算法與多線程來 平行剩下的運算將可以快速地收斂到我們要的特徵值。 | zh_TW |
| dc.description.abstract | To solve large-scale eigenvalue problems often require a lot of time, especially in the iterative process, the matrix-vector multiplication accounted for most of the time.In this thesis, our problem is from the three dimension photonic crystals of Maxwell’s equa- tion which is diamond structure.From previous studies in the question, we know that the dimension of null space, and then we will develop a new method for this problem. The purpose is that the original problem is projected to the non-zero invariant space, and us- ing FFT to quickly converge to the non-zero eigenvalues which we want. Finally,we will show the numerical result based on C program. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-07T17:50:11Z (GMT). No. of bitstreams: 1 ntu-102-R99221018-1.pdf: 5878979 bytes, checksum: 55f11909e0312aa71803a85dcdd4c8ba (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 口試委員會審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii 英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Yee’s Discretization and the model eigenvalue problems . . . . . . . 4 3 Invariantsubspaceofzeroandnonzeroeigenvalues . . . . . . . . . . . . . 9 4 Projectiveeigenvalueproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5 NumericalResultswithMulti-CoreCPU . . . . . . . . . . . . . . . . . . . . . 18 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 | |
| dc.language.iso | en | |
| dc.subject | 特徵值問題 | zh_TW |
| dc.subject | 投影Lanczos法 | zh_TW |
| dc.subject | 馬克斯威爾方程 | zh_TW |
| dc.subject | 三維光子晶體 | zh_TW |
| dc.subject | 鑽石結構 | zh_TW |
| dc.subject | Eigenvalue Problem | en |
| dc.subject | Projective Lanczos | en |
| dc.subject | Maxwell’s equations | en |
| dc.title | 以投影Lanczos法解三維光子晶體的特徵值問題 | zh_TW |
| dc.title | Projective Lanczos Method Solve Eigenvalue Problem of Three Dimensional Photonic Crystals | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃聰明(Tsung-Ming Huang),黃楓南(Feng-Nan Hwang) | |
| dc.subject.keyword | 投影Lanczos法,馬克斯威爾方程,三維光子晶體,鑽石結構,特徵值問題, | zh_TW |
| dc.subject.keyword | Projective Lanczos,Maxwell’s equations,Eigenvalue Problem, | en |
| dc.relation.page | 22 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2013-01-14 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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