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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 楊德良 | |
dc.contributor.author | Yao-Chi Kuo | en |
dc.contributor.author | 郭曜琪 | zh_TW |
dc.date.accessioned | 2021-06-13T06:15:40Z | - |
dc.date.available | 2011-02-08 | |
dc.date.copyright | 2006-02-08 | |
dc.date.issued | 2006 | |
dc.date.submitted | 2006-02-03 | |
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[2] Chiu, C.L., Non-singular boundary integral equation for the analysis of the electromagnetic problems. M.S. Dissertation of Institute of Civil Engineering, National Taiwan University, Taiwan, (2002). [3] Chang, I.T., Multiquadric method analysis for some flow field problems. M.S. Dissertation of Institute of Engineering Science and Ocean, National Taiwan University, Taiwan, (2003). [4] Chen, J.T., Lin, J. H., Kuo, S.R., Chyuan, S.W., Boundary element analysis for the Helmholtz eigen value problems with a multiply connected domain. Proceedings of the Royal Society of London Series A; 457: 2521-2546, (2001). [5] Chen, J.T., Lin, S.R., Chen, K.H., Chen, I.L., Chyuan, S.W., Eigenanalysis for membranes with stringers using conventional BEM in conjunction with SVD technique. Computer Methods in Applied Mechanics and Engineering; 192: 1299-1322, (2003). [6] Chang, M.H., Analysis of acoustic eigenfrequencies and eigenmodes by using the meshless method, M.S. Thesis, National Taiwan Ocean University, Taiwan, (2001). [7] Fan, C.M., The non-singular boundary integral equations analysis to some engineering problems, M.S. Dissertation of Institute of Civil Engineering, National Taiwan University, Taiwan, (2001). [8] Kansa, E.J., Hon, Y.C., Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Computers and Mathematics with Applications; 39:123-137, (2000). [9] Kansa, E.J., Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-I. Surface approximations and partial derivative estimates. Computers and Mathematics with Applications; 19(6-8):127-145, (1990). [10] Lo, D.C., Numerical study of free surface flow and convective heat transfer for 2D and 3D problems. Ph.D. Dissertation of Institute of Civil Engineering, National Taiwan University, Taiwan, (2004). [11] Lo, D.C., Young, D.L., Arbitrary Lagrangian-Eulerian finite element analysis of free surface flow using a velocity-vorticity formulation. Journal of Computational Physics; 195: 175-201, (2004). [12] Lo, D.C., Young, D.L., Two-dimensional incompressible flows by velocity-vorticity formulation and finite element method, Journal of Mechanics; 17(1):13-20, (2001). [13] Lo, D.C. Two dimensional velocity-vorticity formulation for incompressible flows with free surfaces by the finite element method. M.S. Thesis, National Taiwan University, (2000). [14] Lin, Y.C., Method of fundamental solutions for the bi-harmonic equations and vibration problems of thin plate. M.S. Dissertation of Institute of Civil Engineering, National Taiwan University, Taiwan, (2003). [15] Omid Z. Mehdizadeh, Marius Paraschivoiu. Investigation of a two-dimensional spectral element method for Helmholtz’s equation. Journal of Computational Physics; 189: 111-129, (2003) [16] Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P. Numerical recipes in FORTRAN, 2nd ed; Cambridge, Ch. 2, 51-62. (1992) [17] Quan, J.R., Chang, C.T., New insights in solving distributed system equations by the quadrature methods. Computers and Chemistry Engineering; vol. 13, 779-778, (1989) [18] Shu, C., Analysis of elliptical waveguides by differential quadrature method. IEEE transaction on microwave theory and techniques; vol. 48, No. 2, 319-322, (2000). [19] Shu, C., Xue, H., Solution of Helmholtz equation by differential quadrature method. Computer Methods in Applied Mechanics and Engineering; Vol 175, No 1-2: 203-212, (1999). [20] Shu, C., Ding, H., Yeo, K.S., Local radial basis function differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering ; 192:941-954 (2003). [21] Shu, C., Ding, H., Chen, H.Q., Wang, T.G., An upwind local RBF-DQ method for simulation of inviscid compressible flows. Computer Methods in Applied Mechanics and Engineering; 194: 2001-2017, (2005). [22] Shu, C., Ding, H., Yeo, K.S., Computation of Incompressible Navier-Stokes Equations by Local RBF-based Differential Quadrature Method. Computer Modeling in Engineering and Science; vol.7, no.2: 195-205, (2005). [23] Young, D.L., Hu, S.P., Chen, C.W., Fan, C.M., Murugesan, K. Analysis of elliptical wave guides by the method of fundamental solutions, Microwave and Optical Technology Letters; vol.21, no.1 : 25-31, (2005) [24] Young, D.L., Chen, C.W., Fan, C.M., Tsai, C.C., The method of fundamental solutions with eigenfunctions expansion method for nonhomogeneous diffusion equation. Numerical Methods for Partial Differential Equations. (In press), (2005) [25] Tsai, C.C., Meshless numerical methods and their engineering applications. Ph.D. Dissertation of Institute of Civil Engineering, National Taiwan University, Taiwan, (2002). | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34568 | - |
dc.description.abstract | 在這篇論文中,我們應用區域多元二次微分積分法求解卜易松、赫姆霍茲特徵值與穴室流場問題。無網格數值方法有許多種類﹐本方法是基於區域分解技術並結合多元二次法與微分積分法,也是無網格數值方法的一種。因此,本方法仍保有無網格法不需要建立網格組織的特性。在本論文中,我們使用此方法與傳統多元二次法、理論解析解、以及其他數值方法結果作比較。本論文主要貢獻在於應用此方法在不規則區域以及方法的行為分析。由比較結果可以看出此方法與其他方法的結果相當吻合。因此﹐我們認為此數值方法是一可信賴且有效率的方法。 | zh_TW |
dc.description.abstract | In this thesis, we employ the meshless local Multiquadric Differential Quadrature method (LMQDQ method) to deal with the Poisson, Helmholtz eigenvalue and cavity flow problems. Meshless methods can be classified as lots of categories. The numerical method in this thesis combines the Multiquadric method (MQ method) and the domain decomposition technique in Differential Quadrature (DQ) form. Thus, this method keeps the mesh-free property. We will discuss this method in the thesis and compare the results with those obtained by the conventional MQ method, analytic solutions or numerical solutions made by other methods. The main contribution of the thesis is to employ LMQDQ method to solve irregular domain problem and the behavior analysis of this method. These results indicate that this method is reliable and efficient. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T06:15:40Z (GMT). No. of bitstreams: 1 ntu-95-R92521319-1.pdf: 7761331 bytes, checksum: c8876fd399020db60b1883d6dc05747d (MD5) Previous issue date: 2006 | en |
dc.description.tableofcontents | Table of contents
摘要 I Abstract II Table of contents III Table caption V Figure caption VI Chapter 1 Introduction 1 1.1 Objective 1 1.2 Outline of the thesis 2 Chapter 2 Literature review and formulation of LMQDQ method 4 2.1 DQ method 4 2.1.1 Advantages and weaknesses of DQ method 9 2.2 Meshless methods, RBFs and MQ method 14 2.2.1 RBFs 14 2.2.2 MQ RBF 16 2.2.3 Weaknesses of RBFs interpolation 17 2.3 Formulation of LMQDQ method 18 Chapter 3 Numerical solutions of Poisson equation using LMQDQ method 21 3.1 Results of Dirichlet boundary condition 21 3.2 Results of Neumann boundary condition 31 Chapter 4 Helmholtz eigenvalue problem 42 4.1 Governing equations and SVD technique 42 4.1.1 Governing equations 42 4.1.2 Singular value decomposition 45 4.2 Square eigenvalue problem 47 4.2.1 Results and comparisons for square TM case 48 4.2.2 Results and comparisons for square TE case 50 4.3 Circular eigenvalue problem 53 4.3.1 Results and comparisons for circular TM case 54 4.3.2 Results and comparisons for circular TE case 57 4.4 Multi-connected domain eigenvalue problem 60 4.5 Peanut-shaped eigenvalue problem 67 Chapter 5 Cavity flow problem 72 5.1 The velocity-vorticity formulation 72 5.2 Steady Stokes cavity problem 74 5.3 Steady Navier-Stokes cavity problem 78 Chapter 6 Conclusion, recommendations and further works 85 6.1 Conclusions 85 6.2 Recommendations and further works 86 References 87 | |
dc.language.iso | en | |
dc.title | 以區域多元二次微分積分法求解卜易松、赫姆霍茲特徵值與穴室流場問題 | zh_TW |
dc.title | The Local Multiquadric Differential Quadrature Method for Poisson, Helmholtz Eigenvalue and Cavity Flow Problems | en |
dc.type | Thesis | |
dc.date.schoolyear | 94-1 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 廖清標,范佳銘,卡艾瑋 | |
dc.subject.keyword | 多元二次法,微分積分法,區域多元二次微分積分法,區域分解技術,卜易松方程式,赫姆霍茲特徵值問題,穴室流場問題, | zh_TW |
dc.subject.keyword | Multiquadric method,Differential Quadrature method,local Multiquadric Differential Quadrature method,domain decomposition technique,Poisson equation,Helmholtz eigenvalue problem,cavity flow problem, | en |
dc.relation.page | 90 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2006-02-04 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
顯示於系所單位: | 土木工程學系 |
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