Geodesic
Diffraction of an electromagnetic wave in the gaps between plates
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 4, pp. 37-48 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the article, the problem of diffraction of a plane $TE$-polarized electromagnetic wave in the gaps between metal plates located in one plane is investigated. The diffraction problem is formulated in the form of a boundary-value problem for the Helmholtz equation with the “on metal” boundary conditions and a given asymptotic behavior on the edges of the screens. The solutions are searched for in the class of the waves propagating to infinity. The problem under consideration is reduced to an integral equation with a strong singularity of the kernel with respect to the trace of the electric field vector in the gap. The integral equation, in its turn, is reduced to an infinite system of linear algebraic equations with respect to the derived function expansion coefficients. Some singular integrals containing generalized Chebyshev polynoms are analytically calculated.
Mots-clés : diffraction
Keywords: $TE$-polarized electromagnetic wave, hypersingular integral equation, generalized Chebyshev polynoms. 
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D. N. Tumakov; A. R. Tukhvatova. Diffraction of an electromagnetic wave in the gaps between plates. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 4, pp. 37-48. http://geodesic.mathdoc.fr/item/UZKU_2011_153_4_a3/

[1] Repin V. M., “Difraktsiya elektromagnitnykh voln na pryamougolnom otverstii v ekrane”, Vychislitelnye metody i programmirovanie, 24, Izd-vo Mosk. un-ta, M., 1975, 50–68 | MR

[2] Butler M. C., Umanshankar K. R., “Electromagnetic Excitation of a Wire through an Aperture-Perforated Conducting Screen”, IEEE Trans. Antennas Propagat., AP-24:4 (1976), 456–462 | DOI

[3] Butler M. C., Rahmat-Samii Y., Mittra R., “Electromagnetic Penetration through Apertures in Conducting Surfaces”, IEEE Trans. Antennas Propagat., AP-26:1 (1978), 82–93 | DOI

[4] Shanin A. V., “K zadache o difraktsii na scheli. Nekotorye svoistva ryada Shvartsshilda”, Zap. nauch. seminarov POMI, 275, 2001, 258–285 | MR | Zbl

[5] Tumakov D. N., Tukhvatova A. R., “Difraktsiya elektromagnitnoi volny na scheli mezhdu polubeskonechnymi plastinami”, Trudy Ros. letnei shk. “Matematicheskoe modelirovanie fundamentalnykh ob'ektov i yavlenii v sistemakh kompyuternoi matematiki” i Ros. seminara "Nelineinye polya i relyativistskaya statistika v teorii gravitatsii i kosmologii, Foliant', Kazan, 2010, 95–104

[6] Ilinskii A. S., Smirnov Yu. G., Difraktsiya elektromagnitnykh voln na provodyaschikh tonkikh ekranakh (Psevdodifferentsialnye operatory v zadachakh difraktsii), IPRZhR, M., 1996, 176 pp.

[7] Pleschinskii I. N., Pleschinskii N. B., “Integralnye uravneniya zadachi sopryazheniya poluotkrytykh dielektricheskikh volnovodov”, Izv. vuzov. Matem., 2007, no. 5, 63–80 | MR | Zbl

[8] Pleschinskii N. B., Tumakov D. N., Metod chastichnykh oblastei dlya skalyarnykh koordinatnykh zadach difraktsii elektromagnitnykh voln v klassakh obobschennykh funktsii, Preprint PMF-2000-01, Izd-vo Kazan. matem. o-va, Kazan, 2000, 50 pp.

[9] Pleschinskii N. B., Uravnenie Gelmgoltsa v poluploskosti i skalyarnye zadachi difraktsii elektromagnitnykh voln na ploskikh metallicheskikh ekranakh, Preprint PMF-03-02, Izd-vo Kazan. matem. o-va, Kazan, 2003, 34 pp.

[10] Pleschinskii N. B., Modeli i metody volnovoi elektrodinamiki, Izd-vo Kazan. un-ta, Kazan, 2008, 105 pp.

[11] Boikov I. V., Dobrynina N. F., Priblizhennye metody vychisleniya integralov Adamara, Izd-vo Penz. gos. un-ta, Penza, 2007, 108 pp.

[12] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v 3 t., v. 3, FIZMATLIT, M., 2001, 662 pp.

[13] Abramovits M., Stigan I., Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979, 832 pp. | MR

[14] Lifanov I. K., Osobye integralnye uravneniya i metody ikh chislennogo resheniya, MAKS-Press, M., 2006, 68 pp.