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Identification of a Corroded Boundary and its Robin Coefficient

Published online by Cambridge University Press:  28 May 2015

B. Bin-Mohsin  and
D. Lesnic
B. Bin-Mohsin*
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK Department of Mathematics, King Saud University, P.O. Box 4341, Riyadh 11491, Saudi Arabia
D. Lesnic*
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
Corresponding author. Email: mmbbm@maths.leeds.ac.uk
Corresponding author. Email: amt5ld@maths.leeds.ac.uk
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Abstract

An inverse geometric problem for two-dimensional Helmholtz-type equations arising in corrosion detection is considered. This problem involves determining an unknown corroded portion of the boundary of a two-dimensional domain and possibly its surface heat transfer (impedance) Robin coefficient from one or two pairs of boundary Cauchy data (boundary temperature and heat flux), and is solved numerically using the meshless method of fundamental solutions. A nonlinear unconstrained minimisation of the objective function is regularised when noise is added into the input boundary data. The stability of the numerical results is investigated for several test examples, with respect to noise in the input data and various values of the regularisation parameters.

Keywords

65N2065N2165N80Helmholtz-type equationsinverse problemmethod of fundamental solutionsregularisation
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 2 , May 2012 , pp. 126 - 149
Copyright
Copyright © Global-Science Press 2012

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