Reconstruction of the corrosion boundary for the Laplace equation by using a boundary collocation method

Fenglian Yang, Liang Yan and Ting Wei

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 79, issue 7, 2148-2156

Abstract: In this paper, we consider the identification of a corrosion boundary for the two-dimensional Laplace equation. A boundary collocation method is proposed for determining the unknown portion of the boundary from the Cauchy data 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 is provided by the generalized cross-validation criterion. Numerical examples show that the proposed method is reasonable and feasible.

Keywords: Laplace equation; Boundary collocation method; Inverse boundary problem (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2009:i:7:p:2148-2156

DOI: 10.1016/j.matcom.2008.11.019

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