Gleb Beliakov, Stephen Buckley
School of Information Technology
Deakin University
221 Burwood Hwy, Burwood, 3125, AUSTRALIA
e-mail: gleb@deakin.edu.au
School of Science and Technology
Charles Sturt University
Wagga Wagga, 2678, AUSTRALIA
e-mail: sbuckley@csu.edu.au

Abstract.We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental data.

Received: January 1, 2005

AMS Subject Classification: 65R20, 65R32, 78A05, 65K05, 90C26

Key Words and Phrases: inverse problems, global optimization, integral equations, geometrical optics

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 3