Geodesic
Solution of integral equations of linear antenna theory by finite element method
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 25 (2023) no. 1, pp. 554-564.

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The aim of the work is to construct a computational scheme of the finite element method in relation to integral equations describing current distributions in thin wire antennas. In particular, for linear antennas of small thickness, the problem can be reduced to the integral Gallen equation. As a research method, preference is given to the finite element method, since it has quite a lot of flexibility in terms of choosing basis functions and selecting a grid of nodes. In addition, this method is a powerful and effective means of solving mathematical physics’ problems, which makes it possible to accurately describe complex curved boundaries of the solution domain and boundary conditions. The paper builds a numerical method for solving the integral Gallen equation using the finite element approach. According to the proposed computational scheme, a software implementation was built and a comparative analysis of the results was carried out. This approach as a whole showed low accuracy, which is probably due to the fact that this problem belongs to the class of incorrect ones and, in general, is due to the issue of determining the limits of applicability of the Gallen equation.
Keywords: Gallen equation, integral equation, basis function, Galerkin method, finite element method. 
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D. V. Tarasov. Solution of integral equations of linear antenna theory by finite element method. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 25 (2023) no. 1, pp. 554-564. http://geodesic.mathdoc.fr/item/SVMO_2023_25_1_a3/

[1] Yu. T. Zyryanov, P. A. Fedyunin, O. A. Belousov [i dr.], Antenny : ucheb. posobie, Izd-vo FGBOU VPO «TGTU»., Tambov, 2014, 128 pp.

[2] R. Mitra, Vychislitelnye metody v elektrodinamike, Mir., M., 1977, 487 pp. | MR

[3] A. V. Manzhirov, A. D. Polyanin, Spravochnik po integralnym uravneniyam: metody resheniya, Faktorial Press, M., 2000, 384 pp.

[4] I. V. Boikov, P. V. Aikashev, “Primenenie nepreryvnogo operatornogo metoda k resheniyu uravnenii Poklingtona i Gallena dlya tonkikh provolochnykh antenn”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 3 (55) (2020), 127–146 | DOI

[5] N. V. Rogova, Metody veivlet-analiza chislennogo resheniya odnomernykh zadach elektrodinamiki, avtoref. diss. ... kand. fiz.-mat. nauk, Voronezh, 2008, 16 pp.

[6] D. V. Tarasov, G. A. Konnov, “Primenenie metoda konechnykh elementov dlya resheniya integralnykh uravnenii teorii lineinykh antenn”, Analiticheskie i chislennye metody modelirovaniya estestvenno-nauchnykh i sotsialnykh problem, materialy XV Mezhdunar. nauch.-tekhn. konf., ed. I. V. Boikova, Izd-vo PGU, Penza, 2020, 66–74

[7] I. V. Boikov, Priblizhennye metody resheniya singulyarnykh integralnykh uravnenii, Izd-vo Penz. gos. un-ta, Penza, 2004., 316 pp.

[8] V. A. Neganov, I. V. Matveev, S. V. Medvedev, “Metod svedeniya uravneniya Poklingtona dlya elektricheskogo vibratora k singulyarnomu integralnomu uravneniyu”, Pisma v ZhETF, 26:12 (2000), 86–94.

[9] I. V. Boikov, D. V. Tarasov, “Primenenie gipersingulyarnykh integralnykh uravnenii k chislennomu modelirovaniyu elektricheskogo vibratora”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Tekhnicheskie nauki, 4 (2008), 94–106

[10] P. Silvester, R. Ferrari, Metod konechnykh elementov dlya radioinzhenerov i inzhenerov-elektrikov, per.s angl., Mir, M., 1986, 229 pp.

[11] L. Segerlind, Primenenie metoda konechnykh elementov, per. s angl., Mir, M., 1979, 392 pp.