This study introduces a high accuracy and noise-robust numerical method, that is, the regularization B-spline wavelet method (RBSWM), for solving the inverse boundary problem of the Laplace equation with noisy data in an irregular domain. The problem that we consider is directly discretized by the B-spline wavelet scaling functions. To obtain a stable numerical solution of the problem for noisy data, the Tikhonov regularization technique augmented with the L-curve method is adopted. Numerical experiments demonstrate that the proposed method produces solutions with good stability and accuracy.

中文翻译：

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来自不规则域中有噪声数据的Laplace方程逆边界问题的正则化B样条小波方法

这项研究引入了一种高精度和鲁棒性强的数值方法，即正则化B样条小波方法（RBSWM），用于解决带噪数据在不规则域中的Laplace方程的逆边界问题。我们考虑的问题直接由B样条小波缩放函数离散化。为了获得噪声数据问题的稳定数值解，采用了L曲线法增强的Tikhonov正则化技术。数值实验表明，所提方法具有很好的稳定性和准确性。