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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/13736

Title: 二維多連通區域的拉普拉斯內外域問題研究
Solving the interior and exterior Laplace problem in a two-dimensional multiply connected domain
Authors: Chung-Lun Kuo
Contributors: NTOU:Department of Mechanical and Mechatronic Engineering
Keywords: 配點法;特徵長度;單連通區域;多連通區域;內域;外域;線性方程
collocation method;characteristic length;simply connected domain;multiply connected domain;interior;exterior;linear equation
Date: 2006
Issue Date: 2011-06-30T07:26:40Z
Abstract: 對於二維拉普拉斯問題,本文利用分離變數法推導其級數解,再使用配點法來計算待定係數,並引入特徵長度的概念來提高求解的穩定性及精度。此方法在單連通、多連通區域均適用。邊界可以是任意形狀,並且對於內域、外域問題均可做計算。由數值計算的結果可以看出我們的方法有著很高的精度,對於邊界資料的擾動也有一定的穩定性。
In this paper we obtain the series solution by the separation of variables method for two-dimensional Laplace equation and calculate the coefficient of the series solution by the collocation method. We also introduce the characteristic length to improve the accuracy and the stability. This method can be used in both simply connected domain and multiply connected domain. The shape of boundary is arbitrary. This method can also be used in both interior problem and exterior problem. This method has high accuracy and stability even under the boundary data disturbance.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0M94720025
Appears in Collections:[機械與機電工程學系] 博碩士論文

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