A Boundary Element Regularization Method for the Boundary Determination in Potential Corrosion Damage

Authors: Berger J.R.¹; Martin P.A.²; Lesnic D.³

Source: Inverse Problems in Engineering, Volume 10, Number 2, 1 January 2002 , pp. 163-182(20)

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Abstract:

In this paper, we consider the inverse problem for the Laplace equation in two-dimensions which requires the determination of the location, size and shape of an unknown, or partially unknown, portion gamma

of the boundary part

of a solution domain Omega

R² from additional Cauchy data on the remaining portion of the boundary Gamma

. This problem arises in the study of quantitative non-destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused by corrosion. This inverse problem is approached using the boundary element method (BEM) in conjunction with the Tikhonov first-order regularization procedure. The choice of the regularization parameter is based on an L-curve type criterion although, alternatively one may use the discrepancy principle. Several examples which involve noisy Cauchy input data are thoroughly investigated showing that the numerical method produces a stable approximate solution which is also convergent to the exact solution as the data errors tend to zero.

Keywords: Boundary determination; Corrosion damage; Boundary element method; Regularization; L-curve

Document Type: Research article

Affiliations: 1: Division of Engineering, Colorado School of Mines, Golden, CO 80401-1887, USA 2: Department of Mathematical and Computer Sciences 3: Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK

Publication date: 2002-01-01