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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 楊德良 | |
| dc.contributor.author | Cheng-Wei Lee | en |
| dc.contributor.author | 李晟煒 | zh_TW |
| dc.date.accessioned | 2021-06-13T06:55:57Z | - |
| dc.date.available | 2007-07-30 | |
| dc.date.copyright | 2005-07-30 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-07-27 | |
| dc.identifier.citation | [1] V.D. Kupradze and M. A. Aleksidze (1964), The method of functional equations for the approximate solution of certain boundary value problems, U.S.S.R. Computational mathematics and mathematical physics, Vol. 4, pp.82-126.
[2] R. L. Johnston and G. Fairweather (1984), The method of fundamental solutions for problems in potential flow, Appl. Math. Modeling, Vol.8, pp. 265-270. [3] M. A. Golberg (1995), The method of fundamental solutions for Poisson’s equation, Eng. Anal. Bound. Elem., Vol.16, pp. 205-213. [4] A. Karagoerghis and G. Fairweather (1987), The method of fundamental solutions for the numerical solution of the biharmonic equation, J. Comput. Phys., Vol.69, pp.434-459. [5] D. L. Young, C. C. Tsai, K. Murugesan, C. M. Fan and C. W. Chen (2004), Time-dependent fundamental solutions for homogeneous diffusion problems, Eng. Anal. Bound. Elem., Vol.28, pp.1463-1473. [6] G. Fairweather and A. Karageorghis (2003), The method of fundamental solutions for scattering and radiation problems, Eng. Anal. Bound. Elem., Vol.27, pp.759-769. [7] G. Fairweather, A. Karageorghis, The method of fundamental solutions for elliptic boundary value problems, Adv. Comput. Math. 9 1998 69-95. [8] G. Fairweather, A. Karageorghis and P. A. Martin (2003), The method of fundamental solutions for scattering and radiation problems, Engineering Analysis with Boundary Elements, Vol. 27, pp. 759-769. [9] W. S. Hwang, L. P. Hung, C. H. Ko, Non-singular boundary integral formulations for plane interior potential problems, Int. J. Numer. Meth. Eng. 53 2002 1751-1762. [10] M. A. Tournour, N. Atalla, Efficient evaluation of the acoustic radiation using multipole expansion, Int. J. Numer. Meth. Eng. 46 1999 825-837. [11] C. C. Tsai, Meshless numerical methods and their engineering applications. Ph.D. Dissertation of Institute of Civil Engineering, National Taiwan University, Taiwan, 2002. [12] W. C. Tang, M. G. Lim, and R. T. Howe, Electrostatic comb drive levitation and control method, J. Microelectromech. Syst., vol.1, no.4, pp. 170-178, 1992. [13] YS Liao, S,W. Chyuan and JT Chen, Computational study of the effect of finger width and aspect ratios for the electrostatic levitating force of MEMS combdrive, J. Microelectromech. Syst., vol 14, no.2, pp 305-312, 2005. [14] P. P. Silvester and F. L. Ferrari, finite elements for electrical engineers, Cambridge: Cambridge University Press, 1983. [15] C. A. Brebbia, The boundary element method for engineers, New York : Wiley, 1978. [16] R. A.Gingold, J. J. Maraghan, Smoothed particle hydrodynamics: theory and applications to non-spherical stars, Man. Not. Astro. Soc., Vol. 181 1977 375-389. [17] T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, P. Krysl, Meshless methods: An overview and recent developments, comput. meth. appl. Mech. Engrg., 139 1996 pp.3-47. [18] W. Chen, Tanaka M, A meshless, integration-free, and boundary-only RBF technique, comput. math. appl. Vol.43 2002, 379-391. [19] J.T. Chen, S.R. Lin, K. H. Chen, I.L. Chen, S. W. Chyuan, Eigenanalysis for membranes with stringers using conventional BEM in conjunction with SVD technique, Comput. Methods Appl. Mech. Engrg., 192 (2003) 1299-1322. [20] Y. S. Liao, S.-W. Chyuan and J. T. Chen, An alternatively efficient method (DBEM) for simulating the electrostatic field and levitating force of a MEMS combdrive, J. Micromech. Microeng. 14 (2004) 1258–1269. [21] David K. Cheng, field and wave electromagnetics, Addison-Wesley Pub., 1989. [22] Balanis, Constantine A., Advanced engineering electromagnetics, New York : Wiley, 1989. [23] J. T. Chen, M. H. Chang, K. H. Chen and I. L. Chen (2002), Boundary collocation method for acoustic eigenalysis of three-dimensional cavities using radial basis function, Computational Mechanics, Vol.29, pp.392-408. [24] J. T. Chen, M. H. Chang, K. H. Chen and S. R. Lin (2002), The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function, J. Sound and Vibration, Vol.257, pp.667-711. [25] N. Engheta, W. D. Murphy, V. Rokhlin and M.S. Vassiliou (1992), The fast multipole method for electromagnetic scattering problems, IEEE Trans. Antennas and propagation, Vol. 40, pp. 634-641. [26] M. Di Vico, F. Frezza, L. Pajewski and G. Schettini (2005), Scattering by a finite set of perfectly conducting cylinders buried in a dielectric half-space: a spectral-domain solution, IEEE Trans. Antennas and Propagation, Vol 53, pp. 719-727. [27] A. K. Hamid and M. I. Hussein (2003), Iterative solution to the electromagnetic plane wave scattering by two parallel conducting elliptic cylinders, J. Electromagn. Waves and Appl., Vol. 17, pp. 813-828. [28] T. Roy, T. K. Sarkar, A. R. Djordjevic and M. Salazar-Palma (1998), Time-domain analysis of TM scattering from conducting cylinders using a hybrid method, IEEE Trans. Microwave theory and techniques, Vol. 46, pp. 1471-1477. [29] D. L. Young and J. W. Ruan (2005), Method of fundamental solutions for scattering problem of electromagnetic waves, Computer Modeling in Engineering and Science, Vol. 7, pp. 223-232. [30] L. Marin and D. Lesnic (2005), The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations, Computers & Structures, Vol.83, pp. 267-278. [31] M. Abramowitz, I. A. Stegun, Handbook of mathematical functions with formulation graphs and mathematical tables, New York, Dover, 1972. [32] K. K. Mei and J. G van Bladel (1963), Scattering by perfectly-conducting rectangular cylinders, IEEE Transactions on antennas and propagation, Vol. 11, pp. 185-193. [33] M. Golberg, Boundary integral methods: numerical and mathematical aspects, WIT press, 1999. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/35507 | - |
| dc.description.abstract | 本論文提出一個含超強奇異性無網格法求解靜電及電磁波散射問題。藉由所提出的去除奇異性技術將含奇異與超強奇異的核函數正規化，本方法因此改善基本解法的缺點，同時將傳統基本解法的無網格的優良的性質被保留下來，而且不用遭遇奇異與數值積分的問題。因為核函數奇異與超奇異性被消除了，源點因此可被放置在真實邊界上且與邊界點重合，具爭議性的虛擬邊界也就可以不用管它了。再則，使用本法並配合領域分割法解決退化邊界的秩不足問題。最後在求解靜電與電磁波散射問題的數值結果例子中與解析解和對偶邊界元素法比較後，證明本法確實可行且精確的。 | zh_TW |
| dc.description.abstract | In this thesis, a hypersingular meshless method (HMM) is proposed to solve electrostatic and electromagnetic wave scattering problems. This method modifies the method of fundamental solutions (MFS) by using the desingularized technique to regularize the singularity and hypersingularity of the proposed kernel functions. In the meantime the meshless features of conventional MFS are preserved without singularity and numerical integration. The source points can be located on the real boundary coincident with boundary points since the diagonal terms of influence matrices are determined after the singularity and hypersingularity having being eliminated. So that testing to the controversial off-boundary distance can be avoided. Furthermore, by using the HMM in conjunction with domain decomposition technique, we also solve for the rank-deficiency problem with degenerate boundary. The numerical results are demonstrated it valid and accuracy in solving a number of testing cases for electrostatic and electromagnetic wave scattering problems after comparing with exact solutions and the results made by dual boundary element method. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T06:55:57Z (GMT). No. of bitstreams: 1 ntu-94-R92521324-1.pdf: 2651171 bytes, checksum: 979c3e64aea5bc7a8ba615511e25232c (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | 誌謝…………………………………………………………………………………………………….. I
中文摘要...……………………………………………………………………………………………. II Abstract……………………………………………………………………………………………......III Table List…………………………………………………………………..………………………… VI Figure List………………………………………………………………………………..…………..VII Chapter 1. Introduction................................................................................................................. 1 1-1. Motivation........................................................................................................................................... 1 1-2. Contents of the thesis .......................................................................................................................... 3 Chapter 2. HMM for solving electrostatic problems.................................................................... 5 2-1. Introduction........................................................................................................................................ 5 2-2. Formulation ........................................................................................................................................ 6 2-2.1. Electrostatic preliminary.............................................................................................................................. 6 2-2.2. Conventional method of fundamental solutions.......................................................................................... 7 2-2.3. Formulation of HMM................................................................................................................................... 8 2-2.4. HMM for interior electrostatic problem ...................................................................................................... 9 2-2.6. Treatment of degenerate boundary problems ............................................................................ 12 2-3. Numerical simulation with HMM for interior electrostatic problems ......................................... 13 2-3.1. Case 1-Circular domain with discontinuous Dirichlet BCs...................................................................... 13 2-3.2. Case 2-Rectangular domain with discontinuous Dirichlet BCs ............................................................... 14 2-3.3. Case 3-Rectangular domain with mixed-type problem (discontinuous BC)........................................... 14 2-3.4. Case 4-Arbitrary domain cases (cases 4-1 to 4-3)...................................................................................... 15 2-3.5. Case 5-Degenerate boundary interior problems ....................................................................................... 16 2-4. Numerical simulation with HMM for exterior electrostatic problems......................................... 16 2-5. Remark.............................................................................................................................................. 17 Chapter 3. HMM for solving electromagnetic wave scattering problems................................. 18 3-1. Introduction...................................................................................................................................... 18 3-2. Formulation ...................................................................................................................................... 19 3-2.1. Governing equation .................................................................................................................................... 19 3-2.1.1. Maxwell’s equations ........................................................................................................................... 19 3-2.1.2. Wave equations .................................................................................................................................. 21 3-2.1.3. Helmholtz equation ............................................................................................................................ 21 3-2.2. Analytical solution for a circular conducting cylinder.............................................................................. 24 3-2.3. Formulation of HMM for electromagnetic wave scattering problems .................................................... 26 3-2.3.1. Formulation of double layer potentials............................................................................................. 27 3-2.3.2. Derivation of diagonal coefficients of influence matrices for arbitrary domain using a HMM.. 29 3-3. Numerical results for homogeneous electromagnetic wave scattering problems........................ 31 3-3.1. Scattering through a circular cylinder ....................................................................................................... 32 3-3.2. Scattering through a rectangular cylinder................................................................................................. 33 3-3.3. Scattering through a peanut-shaped cylinder............................................................................................ 34 Chapter 4. Conclusions and further researches......................................................................... 35 4-1. Conclusions ....................................................................................................................................... 35 4-2. Further studying............................................................................................................................... 35 Appendix A. The detail derivations of equations for both Laplace’s equation and Helmholtz equation. ………………………………………………………………………………………37 Appendix B. Discretization process of MFS for single and double layer potentials.................... 38 References………………………………………………………………………………………......... 42 | |
| dc.language.iso | en | |
| dc.subject | 雙層勢能 | zh_TW |
| dc.subject | 領域分割法 | zh_TW |
| dc.subject | 靜電問題 | zh_TW |
| dc.subject | 完全導體柱 | zh_TW |
| dc.subject | 電磁波傳問題 | zh_TW |
| dc.subject | 靜電問題 | zh_TW |
| dc.subject | 去除奇異性技術 | zh_TW |
| dc.subject | 含超強奇異性無網格法 | zh_TW |
| dc.subject | 基本解法 | zh_TW |
| dc.subject | 徑向基底函數 | zh_TW |
| dc.subject | Hypersingular meshless method | en |
| dc.subject | multi-domain technique | en |
| dc.subject | method of fundamental solutions | en |
| dc.subject | desingularized technique | en |
| dc.subject | electrostatic problem | en |
| dc.subject | electromagnetic wave scattering problem | en |
| dc.subject | double layer potential | en |
| dc.subject | radial basis function | en |
| dc.subject | perfectly conducting cylinder | en |
| dc.title | 含超強奇異性無網格法於靜電學及電磁波散射問題之應用 | zh_TW |
| dc.title | The application of hypersingular meshless method for electrostatic and electromagnetic wave scattering problems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 93-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 盧衍祺,廖清標,卡艾偉,陳桂鴻 | |
| dc.subject.keyword | 含超強奇異性無網格法,基本解法,雙層勢能,徑向基底函數,去除奇異性技術,靜電問題,電磁波傳問題,完全導體柱,靜電問題,領域分割法, | zh_TW |
| dc.subject.keyword | Hypersingular meshless method,method of fundamental solutions,double layer potential,radial basis function,desingularized technique,electrostatic problem,electromagnetic wave scattering problem,perfectly conducting cylinder,multi-domain technique, | en |
| dc.relation.page | 80 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-07-28 | |
| 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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