beliakov-mathematicalmodelling-2005.pdf (652.13 kB)
Mathematical modelling of the refractive index reconstruction through global optimization
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 da.ta..
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Journal
International journal of pure and applied mathematics : IJPAMVolume
18Issue
3Pagination
389 - 403Publisher
Academic PublicationsLocation
Sofia, BulgariaISSN
1311-8080Language
engNotes
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C1 Refereed article in a scholarly journalCopyright notice
2005, Academic PublicationsUsage metrics
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