Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)2369710.22363/2658-4670-2020-28-1-62-76Modeling and SimulationМатематическое моделированиеResearch ArticleCalculation of the normal modes of closed waveguidesВычисление нормальных мод закрытых волноводовMalykhMikhail D.МалыхМихаил Дмитриевич

Doctor of Physical and Mathematical Sciences, Assistant Professor of Department of Applied Probability and Informatics

доктор физико-математических наук, доцент кафедры прикладной информатики и теории вероятностей

malykh-md@rudn.ruDivakovDmitriy V.ДиваковДмитрий Валентинович

Candidate of Physical and Mathematical Sciences, Assistant of Department of Applied Probability and Informatics

кандидат физико-математических наук, ассистент кафедры прикладной информатики и теории вероятностей

divakov-dv@rudn.ruEgorovAlexandre A.ЕгоровАлександр Алексеевич

Doctor of Physical and Mathematical Sciences, Chief Researcher of Department of Oscillations

доктор физико-математических наук, главный научный сотрудник отдела колебаний

yegorov@kapella.gpi.ruKuzivYaroslav Yu.КузивЯрослав Юрьевич

PhD student of Department of Applied Probability and Informatics

аспирант кафедры прикладной информатики и теории вероятностей

yaroslav.kuziw@yandex.ruPeoples’ Friendship University of Russia (RUDN University)Российский университет дружбы народовA. M. Prokhorov General Physics Institute Russian Academy of SciencesИнститут общей физики имени А. М. Прохорова РАН15122020281VOL 28, NO1 (2020)ТОМ 28, №1 (2020)627609052020Copyright ©; 2020, Malykh M.D., Divakov D.V., Egorov A.A., Kuziv Y.Y.Copyright ©; 2020, Малых М.Д., Диваков Д.В., Егоров А.А., Кузив Я.Ю.2020Malykh M.D., Divakov D.V., Egorov A.A., Kuziv Y.Y.Малых М.Д., Диваков Д.В., Егоров А.А., Кузив Я.Ю.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/23697

The aim of the work is the development of numerical methods for solving waveguiding problems of the theory of waveguides, as well as their implementation in the form of software packages focused on a wide range of practical problems from the classical issues of microwave transmission to the design of optical waveguides and sensors. At the same time, we strive for ease of implementation of the developed methods in computer algebra systems (Maple, Sage) or in software oriented to the finite element method (FreeFem++). The work uses the representation of electromagnetic fields in a waveguide using four potentials. These potentials do not reduce the number of sought functions, but even in the case when the dielectric permittivity and magnetic permeability are described by discontinuous functions, they turn out to be quite smooth functions. A simple check of the operability of programs by calculating the normal modes of a hollow waveguide is made. It is shown that the relative error in the calculation of the first 10 normal modes does not exceed 4%. These results indicate the efficiency of the method proposed in this article.

Целью работы является разработка и создание численных методов решения некоторых задач теории волноводов, а также их реализация в виде комплексов программ, ориентированных на широкий круг практических проблем от классических вопросов передачи СВЧ излучения до проектирования оптических волноводов и датчиков. При этом мы стремимся к простоте реализации разрабатываемых методов в системах компьютерной алгебры (Maple, Sage) или в программном обеспечении, ориентированном на метод конечных элементов (FreeFem++). В работе использовано представление электромагнитных полей в волноводе при помощи четырёх потенциалов. Эти потенциалы не уменьшают число искомых функций, но даже в том случае, когда диэлектрическая и магнитная проницаемости описываются разрывными функциями, они оказываются достаточно гладкими функциями. Сделана простейшая проверка работоспособности программ путём вычисления нормальных мод полого волновода. Показано, что относительная ошибка в вычислении первых 10 нормальных мод не превышает 4%. Эти результаты свидетельствуют о работоспособности предложенного в настоящей статье метода.

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