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

Authors:
Fenglian Yang;Liang Yan;Ting Wei
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China;School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China;School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China
Venue:
Mathematics and Computers in Simulation
Year:
2009

Citing 2
Cited 1

Finite difference schemes and partial differential equations

Finite difference schemes and partial differential equations
Stable determination of boundaries from Cauchy data

SIAM Journal on Mathematical Analysis

Original article: A new investigation into regularization techniques for the method of fundamental solutions

Mathematics and Computers in Simulation

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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.