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Methods of singular and hypersingular integral equations in antenna modeling

TitleMethods of singular and hypersingular integral equations in antenna modeling
AuthorsI. V. Boykov1, P. V. Aykashev1
1Penza State University
AnnotationThe work is devoted to a review of modern mathematical methods for studying electric vibrators and antennas. It is noted that the main mathematical apparatus for modeling antennas are integral equations - Pocklington’s integro-differential equation, Gallen’s integral equation, singular and hypersingular integral equations. It is shown that singular and hypersingular integral equations are physically and mathematically correct apparatus for modeling electromagnetic processes in a vibrator and studying electromagnetic fields of antennas. The literature is presented, which describes the methods of singular and hypersingular integral equations used in modeling electromagnetic processes in antennas of various topologies. A brief review of fractal antennas is given and the connection between classical fractals and antennas constructed according to the topology of these fractals is noted.
Keywordssingular and hypersingular integral equations, wire antennas, mirror antennas, fractal antennas
CitationBoykov I. V., Aykashev P. V. ''Methods of singular and hypersingular integral equations in antenna modeling'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, October 8-11, 2020). Saransk: SVMO Publ, 2020. - pp. 179-190. Available at: http://conf.svmo.ru/files/2020/papers/article06.pdf. - Date of access: 18.10.2021.