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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24506

Title: 保群算法應用於求解待定邊界熱傳方程式問題
Applications of the Group-Preserving Scheme on Solving Problems of the Sideways Heat Equation
Authors: 張建仁;劉進賢
Contributors: NTOU:Department of Systems Engineering and Naval Architecture
Keywords: 反算熱傳導問題;保群算法;病態問題;半離散化
Date: 2007
Issue Date: 2011-10-20T08:12:32Z
Publisher: 行政院國家科學委員會
Abstract: 摘要:在本研究計畫中,吾人擬發展出一套數值方法求解由待定邊界熱傳方程式所統御的熱傳導反算問題。該問題係屬病態的,乃是因為其解若存在,而其解卻不連續。雖有其他學者提出許多做為改善此種病態問題之方式,卻未能有效改善。在本研究首先擬針對此病態問題考慮採用半離散化方法的穩定性來分析,然後再將常微分方程的時間部份以差分方式離散,並進一部應用保群算法做為空間方向的數值積分。由於這個新的計算法其數值邏輯,本身是建立在堅實的理論基礎之上,預期將可使吾人對此反算熱傳導問題有一更深入的瞭解。最後,吾人將設計出許多數值算例,特別是對於帶有噪訊值干擾的數值算例,我們將有深入之探討與解析,同時亦藉此來驗證我們所提出方法可有效解決上述諸多問題的廣度與效能。
Abstract:In this report, the inverse heat conduction problem governed by sideways heat equation has been investigated numerically. The problem is ill-posed because the solution, if it exists, does not depend continuously on the data. To begin with, this ill-posed problem is analyzed by considering the stability of the semi-discretization numerical schemes and then, the resulting ordinary differential equations at the discretized times are numerically integrated towards the spatial direction by using the group preserving scheme. Since this new computational algorithm is based on a concrete theoretical foundation, it can lead to a deeper understanding of inverse heat conduction problem. At last, several designed numerical examples especially with noisy data will be carefully discussed and validated the proposed method such that it can further verify the wideness and effectiveness of the present method in dealing with those mentioned problems.
Relation: NSC95-2221-E019-078
URI: http://ntour.ntou.edu.tw/handle/987654321/24506
Appears in Collections:[系統工程暨造船學系] 研究計畫

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