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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 | Yu-Fei Wang | en |
dc.contributor.author | 王雨非 | zh_TW |
dc.date.accessioned | 2021-06-13T03:13:24Z | - |
dc.date.available | 2006-08-29 | |
dc.date.copyright | 2006-08-29 | |
dc.date.issued | 2006 | |
dc.date.submitted | 2006-08-21 | |
dc.identifier.citation | [1] D.L. Young, K.H. Chen, C.W. Lee, Novel meshless method for solving the potential problems with arbitrary domains, J. Comput. Phys., 209, Page 290-321, 2005.
[2] D. L. Young, K.H. Chen, C.W. Lee, Singular meshless method using double layer potentials for exterior acoustics, J. Acoust. Soc. Am., 119(1), Page 96-107, 2006. [3] T. Belytschko, L. Gu, Y. Lu, Fracture and crack growth by element-free Galerkin methods, Model. Simul. Mater. Sci. Engrg. 2, Page 519-534, 1994. [4] D.L. Young, S.C. Jane, C.Y. Lin, C.L. Chiu, K.C. Chen, Solutions of 2D and 3D Stokes laws using multiquadrics method, Engineering Analysis with Boundary Elements, 28, Page 1233-1243, 2004. [5] G..N. Borzdov, Plane-wave superpositions defined by orthonormal scalar functions on two and three dimensional manifolds, Phys. Rev. E., 61, Page 4462-4478, 1999. [6] C. Shu, H. Ding, K.S. Yeo, Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier–Stokes equations, Comput. Methods Appl. Mech. Engrg., 192, Page 941-954, 2003. [7] V.D. Kupradze and M.A. Aleksidze, The method of functional equations for the approximate solution of certain boundary value problems, Z. Vycho. Mat., 4, Page 633-715, 1964 [8] M.A. Golberg, The method of fundamental solutions for Poisson’s equation, Engng. Anal. Bound. Elem., 16, Page 205-213, 1995. [9] C.S. Chen, The method of fundamental solutions for nonlinear thermal explosions, Commun. numer. methods eng., 11, Page 675-681, 1995. [10] D.L. Young, S.P. Hu, C.W. Chen, C.M. Fan and K. Murugesan, Analysis of elliptical waveguides by the method of fundamental solutions, Microw. opt. technol. lett, 44(6), Page 552-558, 2005. [11] G. Fairweather, A. Karageorghis, The method of fundamental solutions for elliptic boundary value problems, Adv. Comput. Math., 9, Page 69-95, 1998. [12] J.T. Chen, S.R. Kuo, K.H. Chen, Y.C. Cheng, Comments on vibration analysis of arbitrary shaped membranes using non-dimensional dynamic influence function, J. Sound Vib., 235 (1), Page 156-171, 2000. [13] J.T. Chen, M.H. Chang, K.H. Chen, S.R. Lin, The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function, J. Sound Vib., 257(4), Page 667-711, 2002. [14] J.T. Chen, M.H. Chang, K.H. Chen, Boundary collocation method for acoustic eigenanalysis of three-dimensional cavities using radial basis function, Comput. Mech., 29, Page 392-408, 2002. [15] J.T. Chen, I.L. Chen, C.S. Wu, On the equivalence of MFS and Trefftz method for Laplace problems, Proceeding of Global Chinese workshop on boundary element and meshless method, China, Hebei, 2003. [16] J.T. Chen, I.L. Chen, K.H. Chen, Y.T. Yeh, Y.T. Lee, A meshless method for free vibration of arbitrarily shaped plates with clamped boundaries using radial basis function, Engng. Anal. Bound. Elem., 28, Page 535-545, 2004. [17] S.W. Kang, J.M. Lee, Y.J. Kang, Vibration analysis of arbitrary shaped membranes using non-dimensional dynamic influence function, J. Sound Vib., 221(1), Page 117-132, 1999. [18] S.W. Kang, J.M. Lee, Application of free vibration analysis of membranes using the non-dimensional dynamic influence function, J. Sound Vib., 234 (3), Page 455-470, 2000. [19] W. Chen, M. Tanaka, A meshfree, integration-free and boundary-only RBF technique, Comput. Math. Appl., 43, Page 379-391, 2002. [20] W. Chen, Y.C. Hon, Numerical investigation on convergence of boundary knot method in the analysis of homogeneous Helmholtz, modified Helmholtz and convection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 192, Page 1859-1875, 2003. [21] J. D. Jackson, Classical Electrodynamics, third edition, John Wiley & Sons, 1999. [22] D. J. Griffiths, Introduction to Electrodynamics, third edition, Prentice Hall, 1999. [23] D. K. Cheng, Field and wave electromagnetics, second edition, Addison Wesley, 1989. [24] J. C. Slater and N. H. Frank, Electromagnetism, second edition, McGraw-Hill, 1947. [25] 陳正宗, 洪宏基, 邊界元素法, second edition, 新世界出版社, 1992. [26] A. Jeffrey, Advanced Engineering Mathematics, Academic press, p423-424, 2002 [27] C.S. Chen, Y.C. Hon, R.S. Schaback, Radial Basis Function with Scientific Computation (in preparation). [28] J.T. Chen, S.R. Kuo, K.H. Chen, Y.C. Cheng, Comments on vibration analysis of arbitrary shaped membranes using non-dimensional dynamic influence function, J. Sound Vib., 235 (1), Page 156-171, 2000. [29] J.T. Chen, M.H. Chang, K.H. Chen, S.R. Lin, The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function, J. Sound Vib., 257(4), Page 667-711, 2002. [30] J.T. Chen, M.H. Chang, K.H. Chen, Boundary collocation method for acoustic eigenanalysis of three-dimensional cavities using radial basis function, Comput. Mech., 29, Page 392-408, 2002. [31] J.T. Chen, I.L. Chen, C.S. Wu, On the equivalence of MFS and Trefftz method for Laplace problems, Proceeding of Global Chinese workshop on boundary element and meshless method, China, Hebei, 2003. [32] J.T. Chen, I.L. Chen, K.H. Chen, Y.T. Yeh, Y.T. Lee, A meshless method for free vibration of arbitrarily shaped plates with clamped boundaries using radial basis function, Engng. Anal. Bound. Elem., 28, Page 535-545, 2004. [33] S.W. Kang, J.M. Lee, Y.J. Kang, Vibration analysis of arbitrary shaped membranes using non-dimensional dynamic influence function, J. Sound Vib., 221(1), Page 117-132, 1999. [34] S.W. Kang, J.M. Lee, Application of free vibration analysis of membranes using the non-dimensional dynamic influence function, J. Sound Vib., 234 (3), Page 455-470, 2000. [35] W. Chen, M. Tanaka, A meshfree, integration-free and boundary-only RBF technique, Comput. Math. Appl., 43, Page 379-391, 2002. [36] W. Chen, Y.C. Hon, Numerical investigation on convergence of boundary knot method in the analysis of homogeneous Helmholtz, modified Helmholtz and convection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 192, Page 1859-1875, 2003. [37] M. Abramowitz, I.A. Stegun, Handbook of mathematical functions with formulation graphs and mathematical tables, New York, Dover, 1972. [38] D.L. Young, K.H. Chen, C.W. Lee, Novel meshless method for solving the potential problems with arbitrary domains, J. Comput. Phys., 209, Page 290-321, 2005. [39] C.W. Lee, The Application of Hypersingular Meshless Method for Electrostatic and Electromagnetic Wave Scattering Problems, MS Thesis, National Taiwan University, 2005. [40] Y. Niwa, S. Kobayashi and M. Kitahara, Determination of eigenvalues by boundary element methods, Development in boundary elements, Chap. 7, vol. 2, Applied Science Publishers, 1982. [41] W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical recipes in C++, 2nd edition, Cambridge University Press, 2002. [42] D.L. Young, S.P. Hu, C.W. Chen, C.M. Fan and K. Murugesan, Analysis of elliptical waveguides by the method of fundamental solutions, Microwave and Optical Technology Letters, 44(6), Page 552-558, 2005. [43] D.L. Young, C.W. Chen, C.M. Fan and C.C. Tsai, The Method of Fundamental Solutions with Eigenfunction Expansion Method for Nonhomogeneous Diffusion Equation, Numerical methods for partial differential equations, Wiley InterScience, online, 2006. [44] L.H. Shen, D.C. Lo, Y.C. Kuo, D.L. Young, Numerical Simulation of 2D Irregular Waveguide Problems by Local Multiquadrics Differential Quadrature method, 2006 (submitted for publication). [45] C.W. Lee, The Application of Hypersingular Meshless Method for Electrostatic and Electromagnetic Wave Scattering Problems, MS Thesis, National Taiwan University, 2005. [46] J.J. Bowman, T.B.A. Senior and P.L.E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, Hemisphere publishing Corp., 1987. [47] M. Ganesh and I.G. Graham, A high-order algorithm for obstacle scattering in three dimensions, Journal of Computational Physics, 198, Page 211-242, 2004. [48] K. Morgan, P. J. Brookes, O. Hassan and N. P. Weatherill, Parallel processing for the simulation of problems involving scattering of electromagnetic waves, Comput. Methods Appl. Mech. Engrg., 152, Page 157-174, 1998. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/31468 | - |
dc.description.abstract | 在本文中,提出並且實作了一個用來求解電磁波波導管、空腔共振器或電磁波散射問題的數值方法,其中牽涉到求解二維以及三維的赫姆霍茲方程式。在基本解法數值方法中,為避開奇異性將源點佈在離開邊界的虛擬邊界上是必要的。而在本文中提出的數值方法,使用了雙層勢能核函數替代傳統的基本解法中的單層勢能核函數,並且將源點直接佈在物理邊界上,使源點和邊界點重合,導致在矩陣中發生超強奇異性。這麼作的目的是在於藉由去除奇異性技術將含奇異性以及超強奇異性的格林函數正規化,以推導出係數矩陣中的對角線項。如此本數值方法保留了傳統基本解法的無網格特色,且應用本數值方法可以得到可靠的答案。本文中完成了包括電磁波波導管、空腔共振器以及三維的聲波散射問題的數值模擬,並且藉由跟解析解以及其他數值方法的結果比較來證明本方法是可行而且精確的。 | zh_TW |
dc.description.abstract | In this thesis, a numerical algorithm for solving the ElectroMagnetic (EM) waveguide, EM resonator and electromagnetic wave scattering problems, involving 2-D and 3-D Helmholtz equation, is described and implemented. In the Method of Fundamental Solutions (MFS), seeding location of the source points on a fictitious boundary off-setting from the real boundary is necessary. However, in the proposed method the double-layer potential kernel functions are employed as the alternative radial basis functions (RBFs) in the conventional MFS which uses the fundamental solutions, seeding the source points on the real boundary, and the source points coincide with the boundary points, causing hypersingularity occurs. The purpose of above-mentioned statements is to derive the diagonal terms of the influence matrices by using a desingularization technique to regularize the singularity and hypersingularity of the Green’s functions. Applying the proposed method in which the meshless features of the MFS are maintained yields a reliable solution. Numerical simulations consist of the solutions of electromagnetic waveguide, resonator and 3-D electromagnetic wave scattering problems. Numerical examples are performed, and compared the present numerical results with the analytical solutions, results of conventional MFS and other numerical methods. The validity and accuracy of the proposed method are well demonstrated. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T03:13:24Z (GMT). No. of bitstreams: 1 ntu-95-R93521330-1.pdf: 4246168 bytes, checksum: 63b1dc9cca015d4ca26c0d13aaee1c05 (MD5) Previous issue date: 2006 | en |
dc.description.tableofcontents | 中文摘要(I)
Abstract(II) Table Caption(V) Figure Caption(VI) Chapter 1. Introduction(1) 1.1 Motivation(1) 1.2 Literature Review(3) 1.3 Scope of the Thesis(4) References(5) Chapter 2. Electromagnetism Preliminaries(8) 2.1 Maxwell’s Equations(8) 2.2 Wave Equations and Helmholtz Equations(9) 2.3 Boundary Conditions(11) 2.4 Waveguide and Resonator(12) 2.5 Derivation of Analytical Solutions(15) References(21) Chapter 3. Hypersingular Meshless Method (HMM)(23) 3.1 Theory of the HMM(23) 3.2 Conventional Method of Fundamental Solutions(24) 3.3 Single and Double Layer potentials(25) 3.4 HMM for Helmholtz Equation(27) 3.5 Derivation of the Diagonal Coefficients of Influence Matrix(30) References(35) Chapter 4. HMM for Waveguide and Resonator Problems(37) 4.1 Frequency Analysis by the SVD Technique(37) 4.2 Waveguide Problems(40) 4.3 Resonator Problems(42) References(44) Chapter 5. HMM for Wave Scattering Problems(46) 5.1 Formulations(46) 5.2 Numerical Results(49) References(53) Chapter 6. Conclusions and Further Researches(54) 6.1 Conclusions(54) 6.2 Further Researches(55) Appendix A The Detail Derivations of Equations for both Laplace Equation and Helmholtz Equation(57) Appendix B The HMM for Interior Wave Scattering Problems(58) | |
dc.language.iso | en | |
dc.title | 含超強奇異性無網格法於波導管及電磁波問題之應用 | zh_TW |
dc.title | The Applications of Hypersingular Meshless Method for Waveguide and Electromagnetic Wave Problems | en |
dc.type | Thesis | |
dc.date.schoolyear | 94-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 盧衍祺,廖清標,卡艾瑋,陳桂鴻 | |
dc.subject.keyword | 無網格數值方法,徑向基底函數,基本解法,雙層勢能核函數,奇異性,超強奇異性,赫姆霍茲方程式,波導管,空腔共振器,散射, | zh_TW |
dc.subject.keyword | meshless method,radial basis functions,MFS,double layer potential,singularity,hypersingularity,Helmholtz equation,waveguide,scattering, | en |
dc.relation.page | 94 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2006-08-22 | |
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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