Reconstruction of part of a boundary for the Laplace equation by using a regularized method of fundamental solutions
Abstract: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.
Document Type: Research Article
Affiliations: School of Mathematics and Statistics, Lanzhou University, P. R. China
Publication date: 2009-12-01