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

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  • Yang, Fenglian
  • Yan, Liang
  • Wei, Ting

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.

Suggested Citation

  • Yang, Fenglian & Yan, Liang & Wei, Ting, 2009. "Reconstruction of the corrosion boundary for the Laplace equation by using a boundary collocation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2148-2156.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:7:p:2148-2156
    DOI: 10.1016/j.matcom.2008.11.019
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    Cited by:

    1. Lin, Ji & Chen, Wen & Wang, Fuzhang, 2011. "A new investigation into regularization techniques for the method of fundamental solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1144-1152.

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