| 一类热传导反问题中边界温度场的重建算法 |
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| 引用本文： | 何碧琴,张文.一类热传导反问题中边界温度场的重建算法[J].江西科学,2010,28(2):141-143,149. |
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| 作者姓名： | 何碧琴 张文 |
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| 作者单位： | 东华理工大学数学与信息科学学院,江西,抚州,344000 |
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| 基金项目： | 国家自然科学基金(10861001);;江西省自然科学基金(2009GZS0001) |
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| 摘 要： | 给出了一类二维热传导方程反问题中边界温度场的重建算法。首先将反问题归结为一泛函极小化问题;然后通过对未知边界的有限维逼近,将反问题分解成一系适定的热传导方程正问题;最后根据偏微分方程线性问题的叠加原理,将泛函极小化问题离散为线性代数方程组,再应用Tikhonov正则化方法求解线性代数方程组,从而获得边界温度场的数值解。数值算例表明了本文的算法是有效的,且具有较强的稳定性。
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| 关 键 词： | 反问题 边界温度场 热传导方程 算法 |
An Algorithm for Reconstructing the Boundary Temperature of an Inverse Heat Conduction Problem |
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| HE Bi-qin,ZHANG Wen.An Algorithm for Reconstructing the Boundary Temperature of an Inverse Heat Conduction Problem[J].Jiangxi Science,2010,28(2):141-143,149. |
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| Authors: | HE Bi-qin ZHANG Wen |
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| Institution: | School of Mathematics & Information Science/a>;East China Institute of Technology/a>;Jiangxi Fuzhou 344000 PRC |
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| Abstract: | An algorithm is presented for reconstructing the boundary temperature of a two-dimensional inverse heat conduction problem.The inverse problem is formulated to a functional minimization problem;and it is transformed into a series of direct problems of heat conduct equation that are well-posed by a finite approximation of the unknown boundary temperature.Finally,according to partial differential equations the superposition principle of linear problem,the functional minimization problem is discretized into li... |
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| Keywords: | Inverse problem Boundary temperature Heat conduct equation Algorithm |
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