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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 王偉仲(Weichung Wang) | |
dc.contributor.author | Weichien Liao | en |
dc.contributor.author | 廖為謙 | zh_TW |
dc.date.accessioned | 2021-06-17T07:18:23Z | - |
dc.date.available | 2022-07-17 | |
dc.date.copyright | 2019-07-17 | |
dc.date.issued | 2019 | |
dc.date.submitted | 2019-07-10 | |
dc.identifier.citation | L. V. Ahlfors. Complex analysis: an introduction to the theory of analytic functions of one complex variable. New York, London, page 177, 1953.
A. C. Aitken. Determinants and matrices. Read Books Ltd, 2016. R.-L. Chern, H.-E. Hsieh, T.-M. Huang, W.-W. Lin, and W. Wang. Singular value decompositions for single-curl operators in three-dimensional Maxwell’s equations for complex media. SIAM Journal on Matrix Analysis and Applications, 36(1):203– 224, 2015. Y. Futamura, H. Tadano, and T. Sakurai. Parallel stochastic estimation method of eigenvalue distribution. JSIAM Letters, 2:127–130, 2010. G. H. Golub and C. F. Van Loan. Matrix computations, volume 3. JHU Press, 2012. T.-M.Huang, H.-E.Hsieh, W.-W.Lin, and W. Wang. Eigendecomposition of the dis- crete double-curl operator with application to fast eigensolver for three-dimensional photonic crystals. SIAM Journal on Matrix Analysis and Applications, 34(2):369– 391, 2013. T. Ikegami and T. Sakurai. Contour integral eigensolver for non-Hermitian systems: a Rayleigh-Ritz-type approach. Taiwanese Journal of Mathematics, pages 825–837, 2010. A. Imakura, L. Du, and T. Sakurai. Accuracy analysis on the Rayleigh-Ritz type of the contour integral based eigensolver for solving generalized eigenvalue problems. Technical report, Citeseer, 2014. V. Klimov. Nanoplasmonics. Pan Stanford, 2014. S. Lang. Complex analysis, volume 103. Springer Science & Business Media, 2013. S. A. Maier. Plasmonics: fundamentals and applications. Springer Science & Busi- ness Media, 2007. L. Novotny and B. Hecht. Principles of nano-optics. Cambridge university press, 2012. A. Raman and S. Fan. Photonic band structure of dispersive metamaterials formu- lated as a Hermitian eigenvalue problem. Physical review letters, 104(8):87401, 2010. T. Sakurai and H. Sugiura. A projection method for generalized eigenvalue problems using numerical integration. Journal of computational and applied mathematics, 159(1):119–128, 2003. T. V. Shahbazyan and M. I. Stockman. Plasmonics: theory and applications. Springer, 2013. K. Yee. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Transactions on antennas and propagation, 14(3):302–307, 1966. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/73120 | - |
dc.description.abstract | 數值模擬是研究表面電漿特性的重要方法。本文以馬克士威方程式建模,將此方程用 K.S.Yee 提出的時域有限差分法進行離散化 (discretization),接著將離散後的方程做適當的相似變換 (similarity transformation),使原始的問題轉換為特徵值問題 (eigenvalue problem)。此特徵值問題的矩陣為非共軛對稱 (non-Hermitian) 的方陣,並且其特徵值分佈呈現高度叢集性。因此為克服現有方法在解此問題所需特定區域特徵值的困難,而發展了一個高效的周道積分法應用於求解此問題。此方法結合了周道積分、快速矩陣向量乘法以及高效的線性系統求解。由數據結果可驗證本文提出之方法能高效求解線性系統以及特徵值。 | zh_TW |
dc.description.abstract | Numerical simulations play a significant role for studying the properties of surface plasmon. The surface plasmon problem is first modelled by the Maxwell equations, and the equations is then discretized by the widely-used Yee’s scheme. After applying certain similarity transformations to the discretized system, the original simulation problem becomes a clustered non-Hermitian eigenvalue problem. An efficient contour integral (CI) based eigensolver is developed to overcome the difficulties of applying current existing methods to solve eigenvalues in particular designated regions for this problem. This efficient method combines the contour integral, the fast matrix-vector multiplication and efficient linear system solving. The numerical results can show the efficiency of solving linear systems and eigenvalues with the efficient CI eigensolver. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T07:18:23Z (GMT). No. of bitstreams: 1 ntu-108-R05246012-1.pdf: 1859113 bytes, checksum: 9048d2b788e88c8aba8b52beccc9d431 (MD5) Previous issue date: 2019 | en |
dc.description.tableofcontents | 誌謝 i
Acknowledgements ii 摘要 iii Abstract iv 1 Introduction 1 2 The Model Equation 4 3 Solving the Eigenvalue Problem by the Contour Integral 8 3.1 EstimatingtheNumberofEigenvalues................................................. 11 3.2 ComputingtheEigenpairs ................................................................. 12 3.3 TheOrthogonalizationofSˆ............................................................... 14 3.4 IterationTechnique ........................................................................... 15 4 Fast Matrix-Vector Multiplication 16 4.1 Thematrix-vectormultiplicationAx.................................................... 16 4.2 Thematrix-vectormultiplication(A−σI)−1x. . . . . . . . . . . . . . ............. 17 4.3 TheSVDoftheDiscreteCurlOperatorC .............................................. 20 4.4 TheLinearSystem ............................................................................ 23 5 Numerical Results 25 5.1 TheSparsityPatternoftheMainMatrix ............................................... 25 5.2 EfficiencyofLinearSolver................................................................. 27 5.3 Efficiency of the Contour Integral Eigenvalue Solver . . . . . . . . . . . 30 5.4 Parallelization.................................................................................. 35 6 Conclusion 37 Bibliography 38 | |
dc.language.iso | en | |
dc.title | 高效能周道積分法模擬表面電漿特徵值問題 | zh_TW |
dc.title | An Efficient Contour Integral Based Eigensolver for Surface Plasmon Simulations | en |
dc.type | Thesis | |
dc.date.schoolyear | 107-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 黃聰明(Tsung-Ming Huang),謝世峰(Shih-Feng Shieh) | |
dc.subject.keyword | 馬克士威方程式,周道積分法,快速矩陣向量乘法,表面電漿, | zh_TW |
dc.subject.keyword | the Maxwell equation,discrete double-curl operator,contour integral based eigensolver,fast matrix-vector multiplication,surface plasmon, | en |
dc.relation.page | 39 | |
dc.identifier.doi | 10.6342/NTU201900986 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2019-07-10 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
顯示於系所單位: | 應用數學科學研究所 |
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