Identification of a Corroded Boundary and its Robin Coefficient
B. Bin-Mohsin 1, D. Lesnic 2*1 Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK and Department of Mathematics, King Saud University, P.O. Box 4341, Riyadh 11491, Saudi Arabia.
2 Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK.
Received 13 February 2012; Accepted (in revised version) 30 March 2012
Available online 27 April 2012
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.AMS subject classifications: 65N20, 65N21, 65N80
Key words: Helmholtz-type equations, inverse problem, method of fundamental solutions, regularisation.
Email: firstname.lastname@example.org (B. Bin-Mohsin), email@example.com (D. Lesnic)