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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/11397

Title: 移動式Trefftz 法在聲場問題之研究
A Study on the Moving Trefftz Method in the Acoustic Field 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: 2002
Issue Date: 2011-06-28T08:19:37Z
Publisher: 行政院國家科學委員會
Abstract: 本研究成功推導出移動式 Trefftz 法求解聲場問題的 Helmholtz 方程式之特徵值問題。移動式 Trefftz 法不像傳統的 Trefftz 法僅能有一個源點,可容許許多源點存在於所關切的領域中,因此較傳統之方法更具彈性,特別是多連通領域且域內孔洞超過一個時的情況。由於基底函數係採用零階 Bessel 或 Neumann 函數,為使在移動式 Trefftz 法中有足夠數的基底,吾人因此須移動原點來建構出足夠的束限方程式。雖然原點的位置是可移動的,本研究證明出每個基底是彼此相互獨立的,且等效於傳統之 Trefftz 法。此外本研究也證明出:間接式移動 Trefftz 法是等效於直接式移動 Trefftz 法,因此一大特性是不論直接式或間接式 Trefftz 法都沒有假跟的問題存在。而天生即有的數值不穩定現象,本研究提出 Tikhonov’ s 正規化法與奇異直分解法來克服之。數值算例驗證出本研究所提方法之準確與可行性。
In this research, the moving Trefftz methods are derived to deal with the eigenproblems of the Helmholtz equation. Unlike the conventional Trefftz method having only one origin, the moving Trefftz method allows many origins in the configuration. Due to this property, the moving Trefftz method is more flexible than the conventional one especially when a multiply connected domain with holes more than one is considered. Since only zeroth order Bessel and/or Neumann functions are adopted as the bases functions, in order to have enough bases in the moving Trefftz method one should move the origins to construct enough constraint equations. Although the locatiuon of origins are movable, it is proved that every bases of this configuration is independent of others, and the current approach is equivalent to the conventional Trefftz method by equivalency of bases. Furthermore, it is proved that the indirect moving Trefftz method proposed here is equivalent to the direct one. There exists therefore no spurious eigensolution in both direct and indirect moving Trefftz methods. To overcome the inherent numerical instability existing in both of the direct and indirect moving Trefftz methods, the generalized singular-value decomposition(GSVD) and Tikhonov's regularization method are suggested to cope with. Several examples are provided to show its validity.
Relation: NSC91-2611-E019-016
URI: http://ntour.ntou.edu.tw/ir/handle/987654321/11397
Appears in Collections:[系統工程暨造船學系] 研究計畫

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