ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

DOI 10.15507/2079-6900.25.202301.554-564

Original article

ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

MSC2020 65R20

Solution of integral equations of linear antenna theory by finite element method

D. V. Tarasov

Penza State University (Penza, Russian Federation)

Abstract. 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.

Key Words: Gallen equation, integral equation, basis function, Galerkin method, finite element method

For citation: D. V. Tarasov. Solution of integral equations of linear antenna theory by finite element method. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 25:1(2023), 554–564. DOI:

Submitted: 01.12.2022; Revised: 10.02.2023; Accepted: 24.02.2023

Information about the author:

Dmitriy V. Tarasov, Associate Professor, Department of Higher and Applied Mathematics, Penza State University (40 Krasnaya St., Penza 440026, Russia), Cand.Sci. (Technical Science), ORCID:,

The author have read and approved the final manuscript.

Conflict of interest: The author declare no conflict of interest.

Creative Commons Attribution 4.0 International License This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License.