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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/12287

Title: 利用映像法與零場積分方程求解格林函數與邊界值問題
Study on Solving the Green$S Function and Boundary Value Problems by Using the Image Method and the Null-Field Integral Equation
Authors: 陳正宗
Contributors: NTOU:Department of Harbor and River Engineering
Date: 2009-08
Issue Date: 2011-06-29T01:38:56Z
Publisher: 行政院國家科學委員會
Abstract: 摘要:根據先前國科會計劃「零場積分方程解邊界值問題」的成功經驗,我們推廣到二維格林函數問題。我們利用零場積分方程搭配退化核以及加法定理、傅立葉級數與自適性觀察座標系統建立一線性代數系統。藉此線性代數系統可輕易地解出未知的傅立葉係數,進而求得域內點場量。接著將藉助疊加技巧後,則此問題可被拆解為兩部份。其中一部份為基本解問題與另一部份為無限域含特定邊界條件之圓形邊界值問題,而此特定邊界條件可由加法定理求得級數展開型式。將兩部分的解作疊加之後,則控制方程及邊界條件將會自動滿足。當使用映像法與加法定理來求解格林函數時,其映像點位置能簡單的計算出來。如此一來,滿足邊界條件的解析與數值解將可求得。最後,我們利用一些典型的例題來驗證方法的準確性及適用性。此外,透過使用映像法來尋找基本解法中最佳源點的位置。另外,以偏心圓環、半平面含一個孔洞及無限域含兩個圓洞問題的格林函數為例,經過連續的映射以後,最終得到凝固點與雙極座標中焦點間的關係,做進一步探討。
abstract:Following the success of using null-field BIEM to solve BVPs in the previous projects, we derived the Green’s functions of 2-D problems. By using the null-field integral equation approach, we introduce the degenerate kernel, namely the addition theorem, Fourier series and the adaptive observer system to construct the linear algebraic system. After obtaining the unknown Fourier coefficient, the interior potential can be calculated. By introducing the superposition technique, the problem is decomposed into two parts. One is the fundamental solution and the other is an infinite plane with circular boundaries subject to the specified boundary conditions derived from the addition theorem. After superimposing the two solutions, the governing equation and boundary condition are both satisfied automatically. By using the image method and addition theorem to derive the Green’s function, the location of the image point can be easily determined. Finally, several examples are given to demonstrate the accuracy and applicability. Besides, the optimal source location of MFS is studied by using the image method. For the Green’s functions of eccentric annulus, a half plane with a hole, an infinite plane with two holes, the relation between the focuses in the bipolar coordinate system and the frozen image points is discussed.
Relation: NSC98-2221-E019-017-MY3
URI: http://ntour.ntou.edu.tw/ir/handle/987654321/12287
Appears in Collections:[河海工程學系] 研究計畫

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