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論文名稱 Title |
Trefftz方法使用一般解求解3維Laplace方程 The method of fundamental solution for Laplace's equation in 3D |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
35 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2009-06-04 |
繳交日期 Date of Submission |
2009-07-09 |
關鍵字 Keywords |
柱、球、source點、collocation點、一般解法、Laplace方程、3維問題 Laplace's equation, method of fundamental solutions, sources points, collocation points, cylinder, spheres, 3D problems |
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統計 Statistics |
本論文已被瀏覽 5736 次,被下載 2857 次 The thesis/dissertation has been browsed 5736 times, has been downloaded 2857 times. |
中文摘要 |
在目前,大部份的文獻都僅討論使用一般解法(MFS)處理2維問題,為了使一般解法(MFS)有更好的效力,本篇將拓展至處理3維問題。 當3維的一般解基底 Φ(x,y)=1/(4π||x-y||), x,y∈R^3 已知,source點的位置在實際計算中便顯得十分重要。在本篇論文中,我們選定柱形的解域,source點佈於比解域大的柱或球體上。最後將有些數值結果與總結一些有用的結論,而理論分析在將來完成。 |
Abstract |
For the method of fundamental solutions(MFS), many reports deal with 2D problems. Since the MFS is more advantageous for 3D problems, this thesis is devoted to Laplace's equation in 3D problems. Since the fundamental solutions(FS) Φ(x,y)=1/(4π||x-y||), x,y∈R^3 are known, the location of source points is important in real computation. In this thesis, we choose a cylinder as the solution domain, and the source points on larger cylinders and spheres. Numerical results are reported, to draw some useful conclusions. The theoretical analysis will be explored in the future. |
目次 Table of Contents |
Contents 1 Introduction 4 2 Algorithms of Method of Fundamental Solutions 6 3 Particular Solutions of Laplace’s Equation in Cylindrical Coordinates 9 4 Numerical Results 13 5 Conclusions 19 |
參考文獻 References |
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