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題 名 | A Green's Function Numerical Method for Some Inverse Boundary Value Problems=格林函數數值方法解邊界反算問題 |
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作 者 | Melnikov,Yuri A.; Powell,Jeffrey O.; | 書刊名 | 中國工程學刊 |
卷 期 | 22:6 1999.11[民88.11] |
頁 次 | 頁813-820 |
分類號 | 440.11 |
關鍵詞 | 孔洞形狀確認問題; 過定資料; 格林函數; 邊界元素法; 最佳化最小平方法與反算問題; Boundary elements; Inverse problems; |
語 文 | 英文(English) |
中文摘要 | 本文求解傳導板上勢能、靜電或穩態熱傳等物理現象的孔洞形狀確認問題。一個 含孔洞之簡單形狀的板子,一則大小、形狀、孔洞位置已知,一則邊界上的熱通量已知,邊 界條件一端給定一次邊界量(如電壓,溫度)另一端給定二次邊界量(如熱適量),在量得 邊界的另一邊界量後構成過定邊界問題。從這種過定資料,本文所提供的方法可決定(1)板 子的孔洞位置(孔洞邊界上給定熱通量)、(2)孔洞邊界上熱通量(孔洞位置給定)。本文將 邊界元素法、最佳化最小平方法與格林函數在邊界值上特有的性質,應用在孔洞形狀確認問 題的數值處理上。一個有效率建構格林函數的技巧也被簡短的回顧。 |
英文摘要 | We solve identification problems in potential theory, electrostatics, steady state heat conduction, etc, in conductive plates. A plate with simple shape contains a hole. Either the size, shape, and location of the hole, or the flux across its boundary, is unknown, Boundary conditions are prescribed on part of the plate edge, and voltage or heat is applied to the remainder. An additional measurement is taken on part of the plate edge. From this overspecified data, we determine (1) the structure of the hole, given the flux across its boundary, or (2) the flux across the hole boundary, given the hole. Boundary elements, least squares optimization, and special boundary value properties of Green's functions are exploited in this numerical treatment of the identification problem. |
本系統中英文摘要資訊取自各篇刊載內容。