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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 周謀鴻(Mo-Hong Chou) | |
dc.contributor.author | Mau-Ling Hsu | en |
dc.contributor.author | 徐茂霖 | zh_TW |
dc.date.accessioned | 2021-06-13T04:29:43Z | - |
dc.date.available | 2009-07-24 | |
dc.date.copyright | 2006-07-24 | |
dc.date.issued | 2006 | |
dc.date.submitted | 2006-07-20 | |
dc.identifier.citation | [ 1 ] Kato,T.(1958), “ Perturbation theory for nullity. ” 261-322.
[ 2 ] Ciarlet, P.G. and Lions J.L.(1991), “ Handbook of numerical analysis. ” 683-699. [ 3 ] Babuska, I. and A. Aziz (1973) “ Survey lectures on the mathematical foundations of the finite element method. ” 5-359 [ 4 ] William G. Kolata(1978) “ Approximation in variationally posed eigenvalue problems. ” Numer. Math. 29, 159-171 [ 5 ] Ciarlet, P.G.(2002) “ The finite element method for elliptic problem.” [ 6 ] Francoise Chatelin (1983) “ Spectral approximation of linear operators. ” [ 7 ] Darrell W. Pepper, Juan C. Heinrich (1973) “The finite element method : basic concepts and application. ” [ 8 ] O. Axelsson and V. A. Barker(1984) “Finite element solution of Boundary value Problems.” | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/33217 | - |
dc.description.abstract | This Helmholtz equation occurs frequently in dynamic meteorology. In classical physics it is the equation of the vibrating membrane. Time-harmonic wave propagation, either elastic waves or electromagnetic waves, is a common phenomenon that appears in many applications such as acoustic wave scattering from submarines, noise reduction in silencers and mufflers, earthquake wave propagation.
First, the Helmholtz equation reduces to that of solving a generalized eigenvalue problem. In the chapter 2, it shows that the order of the error of eigenvalue is O(h^2) by the application of the spectral theory. In the latest chapter, the Helmholtz equation can be solved via finite element methods. In these numerical results, the eigenvalues are solved throughout a linear triangular element is recognized as approximation. The eigenvalue are solved throughout a quadratic triangular element is recognized as exact solution, since this numerical method has much higher rate of convergence. In addition, we compare the difference between linear triangular element and quadratic triangular element by refining the mesh. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T04:29:43Z (GMT). No. of bitstreams: 1 ntu-95-R91221021-1.pdf: 255849 bytes, checksum: 2c1d275b47fe621bb57849cea14553d6 (MD5) Previous issue date: 2006 | en |
dc.description.tableofcontents | Chapter 1. Basic conception 1
1.1 Introduction 1 1.2 Helmholtz Equation 2 Chapter 2. Spectral theory 3 2.1 Basic of the spectral theory 3 2.2 Survey of spectral theory for compact operator 4 2.3 Spectral projection 5 2.4 Fundamental results on the spectral approximation 6 2.5 The analysis of estimation of eigenvalues 8 Chapter 3. Finite element method with triangular element 12 3.1 Discretize the eigenvalue problem 12 3.2 Linear shape functions 13 3.3 Quadratic shape functions 16 Chapter 4. Numerical results and discussions 19 Appendix. The properties of mesh generation 25 References 27 | |
dc.language.iso | en | |
dc.title | 有限元素法之固有值問題在多邊形鼓膜上之誤差分析 | zh_TW |
dc.title | The finite element method of the eigenvalue problem for the analysis of error with polygonal membrane | en |
dc.type | Thesis | |
dc.date.schoolyear | 94-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 陳宜良(I-Liang Chern),王偉成(Wei-Cheng Wang) | |
dc.subject.keyword | 有限元素法,固有值, | zh_TW |
dc.subject.keyword | finite element method,eigenvalue, | en |
dc.relation.page | 27 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2006-07-21 | |
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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