Numerical Analysis and Applications

, Volume 6, Issue 4, pp 279–288 | Cite as

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



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.


numerical algorithm Maxwell’s equations electromagnetic wave conductivity inverse problem Laguerre method finite difference linear equations accuracy 


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© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics, Siberian BranchRussian Academy of SciencesNovosibirskRussia

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