The boundary-element method for the determination of a heat source dependent on one variable
The boundary-element method for the determination of a heat source dependent on one variable
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DOI：
10.1007/s10665-005-9023-0
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发表时间：
2006-01
影响因子：
1.3
通讯作者：
A. Farcas;D. Lesnic
中科院分区：
文献类型：
--
作者：
A. Farcas;D. Lesnic
本文利用正问题的一般条件和一个称为超定的补充条件，研究了抛物型热方程中确定热源的反问题。在这个问题中，如果热源仅与空间相关，则超定是在给定的单个时刻的温度测量，而如果热源仅与时间相关，则超定是由安装在热导体内部的单个热电偶记录的瞬态温度测量。这些测量确保了反问题有唯一的解，但这个解是不稳定的，因此问题是不适定的。这种不稳定性是克服使用吉洪诺夫正则化方法与差异的原则或L-曲线标准的正则化参数的选择。发展了边界元法数值求解反问题，并对一些基准算例进行了数值计算和讨论
This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions of the direct problem and a supplementary condition, called an overdetermination. In this problem, if the heat source is taken to be space-dependent only, then the overdetermination is the temperature measurement at a given single instant, whilst if the heat source is time-dependent only, then the overdetermination is the transient temperature measurement recorded by a single thermocouple installed in the interior of the heat conductor. These measurements ensure that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method with the discrepancy principle or theL-curve criterion for the choice of the regularization parameter. The boundary-element method (BEM) is developed for solving numerically the inverse problem and numerical results for some benchmark test examples are obtained and discussed