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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/36918完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 顏瑞和 | |
| dc.contributor.author | Li-Hsin Hung | en |
| dc.contributor.author | 洪立昕 | zh_TW |
| dc.date.accessioned | 2021-06-13T08:22:41Z | - |
| dc.date.available | 2005-07-28 | |
| dc.date.copyright | 2005-07-28 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-07-17 | |
| dc.identifier.citation | 參考文獻
1. Karniadakis, G..E. and Sherwin S. J., Spectral/hp element methods for CFD, Oxford University Press, New York, 1999 2. T.C. Warbutron., Spectral/hp Methods on Polymorphic Multi-Domains:Algorithms and Applications. PhD thesis,Brown University,1998 3. J.T. Oden. Plate beam structures. PhD thesis,Oklahoma State University,1962 4. D. Gottlieb and S.A. Orszag. Numerical Analysis of Spectral Methods:Theory and Applications. SIAM-CMBS,1997 5. T.C. Warbutron, Spencer J. Sherwin, and G.E. Karniadakis. Spectral basis functions for 2d hybrid hp elements. SIAM J. Sci. Comp.,1997 6. S.A. Orszag and G. S. Patterson, Numerical simulation of the three dimensional homogeneous isotropic turbulence, Phy. Rev. Letter., 28-76, (1972) 7. A. T. Patera, A spectral element method for fluid dynamics: Laminar flow in a channel expansion, J. Comp. Physics., 54-68, (1984) 8. Josep Sarrate and Antonio Huerta, Efficient Unstructured quadrilateral mesh Generation, Int. J. Numer. Meth. Engng 2000; 49:1327-1350. 9. M. Dubiner, spectral methods on triangles and other domains, J. Sci. Comp., v. 6, pp.345,1991 10. S. J. SHERWIN AND G. E. KARNIADAKIS, Tetrahedral hpFinite Elements: Algorithms and Flow Simulations, JOURNAL OF COMPUTATIONAL PHYSICS 124, 14–45 (1996) 11. S. J. SHERWIN AND G. E. KARNIADAKIS, A triangular spectral elements: Application to incompressible Navier-Stokes equations, Computer methods in applied mechanics and engineering, 123, 189-225,(1995) 12. Richard Pasquetti, Francesca Rapetti, Spectral element methods on triangles and quadrilaterals: comparisons and applications, Journal of Computational Physics 198 (2004) 349–362 13. J. S. Hesthaven, T. Warburton, HIGH-ORDER UNSTRUCTURED GRID METHODS FOR TIME-DOMAIN ELECTROMAGNETICS, BrownSC-2001-19, Division of Applied Mathematics, Brown University, 2001 14. Ali Beskok§;1 and Timothy C. Warburtony; An Unstructured hpFinite-Element Scheme for Fluid Flow and Heat Transfer in Moving Domains, Journal of Computational Physics 174, 492–509 (2001) 15. Thomas, S.J., R.D. Loft, 2002: Parallel Semi-Implicit Spectral Element Atmosphere Model, Journal of Scitific Computing, 15, no 4, 499-518. 16. http://www.homme.ucar.edu/: HOMME on the IBM BlueGene/L 17. Dupont, Frédéric and Charles A. Lin, The Adaptive Spectral Element Method and Comparisons with More Traditional Formulations for Ocean Modeling, Journal of Atmospheric and Oceanic Technology, 21, 135--147, 2004. 18. Qing Huo Liu , Candong Cheng, and Hisham Z. Massoud, The Spectral Grid Method: A Novel Fast Schrödinger-Equation Solver for Semiconductor Nanodevice Simulation, IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 23, NO. 8, AUGUST 2004 19. New Perspectives for Spectral and High Order Methods, SIAM News, Volume 37, Number 1, January/February 2004 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/36918 | - |
| dc.description.abstract | 寬頻元素法應用於解非結構性元素Helmholtz方程式
摘要 本文主旨在使用寬頻元素法發展二維的三角形元素，三維的四面體元素組成計算模型的Helmholtz方程式泛用型解程式，程式可解Helmholtz方程式在二維和三維任意幾何外型。在本文中由展開基底的建立到數值的運算，還有演算法的原理均有所研究，完整描述實作程式的理論基礎。程式經過連續邊界條件問題驗證準確性，也實際驗證複雜幾何形狀問題，確定可達到寬頻收斂特性。目前對於移動邊界的研究很多，考慮重新計算元素分布的效率和元素形狀的性質，非結構性元素是較適合採用的元素外型。本研究提供一個有效率的解題核心，作為未來發展非結構性元素流場模擬所需的基礎。 | zh_TW |
| dc.description.abstract | Helmholtz Solver in unstructured mesh with
Spectral Element Method Abstract Due to fast convergence, small diffusion and dispersion errors, higher order numerical methods, such as the spectral element methods have been shown computationally more efficient than the conventional lower order methods in a full Navier Stokes simulations. Traditionally, the element for the spectral element method is in a structured quadrilateral region. The extension from one dimension to higher dimensions is relatively straight forward. In order to broaden the application of spectral element methods to more complex geometries, the use of unstructured elements in the triangular region for two dimensions, and tetrahedral region in three dimensions is to be investigated in this thesis. The objective of this study is to develop an efficient solver to solve a Helmholtz equation in 2D or 3D unstructured meshed domain. A computer code has been developed. The details of algorithms are addressed in this thesis. The code is validated by various examples with complex geometries. Different problems with Dirichlet and Neumann boundary conditions are also tested. . Key Words: spectral element, hp method, finite element, unstructured element, Helmholtz equation | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T08:22:41Z (GMT). No. of bitstreams: 1 ntu-94-R91522120-1.pdf: 521377 bytes, checksum: d35236f93f28e106e61d9cfb0a0b9d52 (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | 目 錄
中文摘要 i 英文摘要 ii 目錄 iii 圖目錄 v 表目錄 viii 符號說明 ix 第一章、緒論 1 第二章、非結構性元素基本觀念 7 2-1、展開基底 9 2-2、元素映射 15 2-3、積分 17 2-4、微分 19 2-5、元素內矩陣計算 22 第三章、Helmholtz 方程式 解程式 28 3-1、展開模式編號和需反相模式設定 28 3-2、元素內矩陣計算、分解 39 3-3、元素組合、求解 41 3-4、一維Helmholtz 方程式測試 44 3-5、二維Helmholtz 方程式測試 45 3-6、三維Helmholtz 方程式測試 47 第四章、結論及建議 52 4-1、結論 52 4-2、未來發展 53 附錄A、實例說明 54 附錄B、程式操作方法 68 參考文獻 74 圖 目 錄 圖2-2-1、三角形和四邊形間轉換關係 15 圖2-2-2、四面體和六面體間轉換關係 16 圖3-1、二維程式運作原理範例 28 圖3-1-1、P=4 三角形展開基底下所有基底展開模式 30 圖3-1-2、三角形邊的編號及方向，展開模式編號 31 圖3-1-3、四面體邊和面的編號及方向 32 圖3-1-4、二個三角形元素，區域編號 32 圖3-1-5、二個三角形元素，整體編號 33 圖3-1-6、二維展開模式排列順序(1) 34 圖3-1-7、二維展開模式排列順序(2) 34 圖3-1-8、P=4 展開模式在特定邊上的貢獻 35 圖3-1-9、P=4，一維元素相接 36 圖3-1-10、四面體面的相接需反相模式 39 圖3-4-1、一維Helmholtz方程式寬頻收斂驗證(1) 44 圖3-4-2、一維Helmholtz方程式寬頻收斂驗證(2) 45 圖3-5-1、二維相同區間下，不同元素個數和分布的情形 46 圖3-5-2、二維不同元素個數和不同多項式階數對誤差取對數後的作圖 47圖3-6-1、三維元素分布(四面體) 48 圖3-6-2、三維Helmholtz方程式寬頻收斂驗證(四面體) 48 圖3-6-3、三維元素分布(六面體) 49 圖3-6-4、三維Helmholtz方程式寬頻收斂驗證(六面體) 49 圖3-6-5、三維元素分布(球體) 50 圖3-6-6、三維Helmholtz方程式寬頻收斂驗證(球體) 50 圖A-1、建立初步邊的串列 56 圖A-2、完成邊的串列設定 57 圖A-3、二維程式運作原理範例-基底矩陣 60 圖A-4、二維程式運作原理範例-權重矩陣(元素一) 60 圖A-5、二維程式運作原理範例-權重矩陣(元素二) 61 圖A-6、二維程式運作原理範例-x方向微分矩陣(元素一) 61 圖A-7、二維程式運作原理範例-y方向微分矩陣(元素一) 62 圖A-8、二維程式運作原理範例-Mass矩陣(元素一) 62 圖A-9、二維程式運作原理範例-Mass矩陣(元素二) 62 圖A-10、二維程式運作原理範例-Laplacian矩陣(元素一) 63 圖A-11、二維程式運作原理範例-Laplacian矩陣(元素二) 63 圖A-12、二維程式運作原理範例-線的Mass矩陣 66 圖A-13、二維程式運作原理範例-調整過的線Mass矩陣 67 圖B-1、二維程式說明範例 68 圖B-2、Element.neu 檔案範例 69 圖B-3、Input.txt 檔案範例 71 圖B-4、function.f90 檔案範例 71 表 目 錄 表3-1-1、四面體面的相接關係 38 | |
| dc.language.iso | zh-TW | |
| dc.subject | 有限元素 | zh_TW |
| dc.subject | 寬頻元素 | zh_TW |
| dc.subject | 非結構性元素 | zh_TW |
| dc.subject | Helmholtz方程式 | zh_TW |
| dc.subject | spectral element | en |
| dc.subject | Helmholtz equation | en |
| dc.subject | unstructured element | en |
| dc.subject | finite element | en |
| dc.subject | hp method | en |
| dc.title | 寬頻元素法應用於解非結構性元素Helmholtz方程式 | zh_TW |
| dc.title | Helmholtz Solver in unstructured mesh with Spectral Element Method | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 93-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃美嬌,王安邦 | |
| dc.subject.keyword | 寬頻元素,有限元素,非結構性元素,Helmholtz方程式, | zh_TW |
| dc.subject.keyword | spectral element,hp method,finite element,unstructured element,Helmholtz equation, | en |
| dc.relation.page | 75 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-07-19 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 機械工程學研究所 | zh_TW |
| 顯示於系所單位： | 機械工程學系 | |
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