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博碩士論文 etd-0709109-015029 詳細資訊
Title page for etd-0709109-015029
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
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
35
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
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
統計
Statistics
本論文已被瀏覽 5736 次,被下載 2857
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
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