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Solving an inverse problem for Maxwell’s equations numerically with Laguerre functions

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Abstract

An inverse problem is solved by an optimization method using Laguerre functions. Numerical simulations are carried out for one-dimensional Maxwell’s equations in the wave and diffusion approximations. The spatial distributions of permittivity and conductivity in a medium are determined from a known solution at a certain point. A Laguerre harmonics function is minimized. The minimization is performed by the conjugate gradient method. The results of determining permittivity and conductivity are presented. The influence of the shape and spectrum of a source of electromagnetic waves on the solution accuracy of the inverse problem is investigated. The solutions with broadband and harmonic sources of electromagnetic waves are compared in accuracy.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    A. F. Mastryukov

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  1. A. F. Mastryukov
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Correspondence to A. F. Mastryukov.

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Original Russian Text © A.F. Mastryukov, 2013, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2013, Vol. 16, No. 4, pp. 325–335.

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Mastryukov, A.F. Solving an inverse problem for Maxwell’s equations numerically with Laguerre functions. Numer. Analys. Appl. 6, 279–288 (2013). https://doi.org/10.1134/S1995423913040034

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  • DOI: https://doi.org/10.1134/S1995423913040034

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