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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     title = {Solution of integral equations of linear antenna theory by finite element method},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
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     url = {http://geodesic.mathdoc.fr/item/SVMO_2023_25_1_a3/}
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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/