The regularization B-spline wavelet method for the inverse boundary problem of the Laplace equation from noisy data in an irregular domain

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.