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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/11421

Title: 移動式Trefftz法在拉普拉斯問題之應用
Applications of the Moving Trefftz Method on Laplace Problems
Authors: 張建仁
Contributors: NTOU:Department of Systems Engineering and Naval Architecture
國立臺灣海洋大學:系統工程暨造船學系
Date: 2003
Issue Date: 2011-06-28T08:19:41Z
Publisher: 行政院國家科學委員會
Abstract: 本研究成功地推導出移動式 Trefftz 直接法與間接 法求解有限域 Laplace 場數值不穩定的現象。這是以 往學者所未曾指出的問題,而面對該問題本研究以 Tikhonov 正規化法和 L 曲線的概念來解決。此外本 研究並以移動式 Trefftz 法來處理一個孔洞以上的多 連通問題,因為該法可以容許在它的架構中有許多 原點存在,這與傳統式 Trefftz 法只能有一個原點是 相異的。最後本研究並證明出移動式 Trefftz 直接法 和間接法的前導係數矩陣具有相同的數學架構。數 值算例驗證出本研究所提方法之準確與可行性。
In this report, the direct and indirect moving Trefftz methods are derived to deal with the numerical instability problem encountered in the Laplace field of a finite domain, in which such a phenomenon has never been pointed out. To resolve this problem, the Tikhonov's regularization method and the L curve concept are developed. Since the moving Trefftz method allows many origins in its configuration which unties one origin constraint in the formulation, this method can be used to deal with a multiply-connected domain having holes more than one. By placing origins inside every hole, it is verified that the moving Trefftz method can successfully overcome such a difficulty. Moreover, it is found that the leading matrix of the direct method and that of the indirect one are transposed to each other. Finally, a numerical example is provided to show the validity of the proposed methods.
Relation: NSC92-2611-E019-010
URI: http://ntour.ntou.edu.tw/ir/handle/987654321/11421
Appears in Collections:[系統工程暨造船學系] 研究計畫

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