Reconstruction of part of a boundary for the Laplace equation by using a regularized method of fundamental solutions
In this article, the identification of part of a boundary for the two-dimensional Laplace equation is investigated. One regularized method of fundamental solutions is used for determining an unknown portion of the boundary from the Cauchy data specified on a part of the boundary. Since the resulting matrix equation is badly ill-conditioned, a regularized solution is obtained by employing the Tikhonov regularization technique, while the regularization parameter for the regularization method is provided by the generalized cross-validation criterion. The numerical results show that the proposed method produces a convergent and stable solution.
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