Geodesic
The numerical solution of the inverse problem for Maxwell's equations based on the Laguerre functions
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 4, pp. 325-335 
A. F. Mastryukov. The numerical solution of the inverse problem for Maxwell's equations based on the Laguerre functions. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 4, pp. 325-335. http://geodesic.mathdoc.fr/item/SJVM_2013_16_4_a2/
@article{SJVM_2013_16_4_a2,
     author = {A. F. Mastryukov},
     title = {The numerical solution of the inverse problem for {Maxwell's} equations based on the {Laguerre} functions},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {325--335},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_2013_16_4_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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

[1] Fedorenko R. P., Priblizhennoe reshenie zadach optimalnogo upravleniya, Nauka, M., 1978 | MR | Zbl

[2] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1980 | MR

[3] Newman G. A., Alumbaugh D. L., “Three-dimensional magnetotelluric inversion using non-linear conjugate gradients”, Geophysical J. International, 140:3 (2000), 410–424 | DOI

[4] Mastryukov A. F., “Reshenie obratnoi zadachi dlya uravneniya diffuzii na osnove spektralnogo preobrazovaniya Lagerra”, Matematicheskoe modelirovanie, 19:9 (2007), 15–26 | MR | Zbl

[5] Mastryukov A. F., Mikhailenko B. G., “Reshenie obratnoi zadachi dlya volnovogo uravneniya na osnove spektralnogo preobrazovaniya Lagerra”, Geologiya i geofizika, 44:7 (2007), 747–754

[6] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979 | MR

[7] Landau L. D., Lifshits E. M., Elektrodinamika sploshnykh sred, Nauka, M., 1982 | MR

[8] A. G. Tarkhov (red.), Elektrorazvedka, Spravochnik geofizika, Nedra, M., 1980

[9] Epov M. I., Mironov V. L., Komarov S. A., Muzalevskii K. V., “Rasprostranenie sverkhshirokopolosnogo elektromagnitnogo impulsa v neftenasyschennoi srede”, Geologiya i geofizika, 50:1 (2009), 58–66

[10] Fornberg B., Ghrist M., “Spatial finite difference approximation for wave-type equations”, SIAM J. Numer. Anal., 37 (1999), 105–130 | DOI | MR | Zbl