A linear integral equation approach to the Robin inverse problem
A linear integral equation approach to the Robin inverse problem
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DOI：
10.1088/0266-5611/21/5/015
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发表时间：
2005-09
期刊：
影响因子：
2.1
通讯作者：
F. Lin;W. Fang
中科院分区：
文献类型：
--
作者：
F. Lin;W. Fang
我们考虑数值解的反问题的拉普拉斯方程的罗宾系数是从一个部分的边界测量恢复。首先，我们制定的问题的积分方程的边界。通过引入一个新的变量，所涉及的关键积分方程变成线性的，反问题的不适定性被清楚地揭示。在此线性的基础上，我们设计了基于线性最小二乘法的罗宾系数重建方法。一个适当的形式的正则化选择，直接（非迭代）和迭代方法进行了研究。数值算例表明，这些方法的有效性，在提供良好的估计罗宾系数的数据与无噪声。
We consider the numerical solution of an inverse problem for the Laplace equation where the Robin coefficient is to be recovered from a partial boundary measurement. We first formulate the problem by integral equations on the boundary. By introducing a new variable, the key integral equation involved becomes linear, and the ill-posedness of the inverse problem is clearly revealed. On the basis of this linearity, we then design linear least-squares-based methods for reconstruction of the Robin coefficient. A proper form of regularization is chosen, and both direct (non-iterative) and iterative methods are investigated. Numerical examples are presented to show the effectiveness of these methods in providing excellent estimates for the Robin coefficient from data with and without noise.