SYMBOLIC-NUMERICAL IMPLEMENTATION OF THE GALERKIN METHOD FOR APPROXIMATE SOLUTION OF THE WAVEGUIDE DIFFRACTION PROBLEM

D. V. DIVAKOV; Диваков Д. В.; A. A. TYUTYUNNIK; Тютюнник А. А.

doi:10.31857/S0132347423020097

SYMBOLIC-NUMERICAL IMPLEMENTATION OF THE GALERKIN METHOD FOR APPROXIMATE SOLUTION OF THE WAVEGUIDE DIFFRACTION PROBLEM

Autores: DIVAKOV D.¹^,2, TYUTYUNNIK A.¹^,2
Afiliações:
1. Peoples' Friendship University of Russia (RUDN University)
2. Joint Institute for Nuclear Research
Edição: Nº 2 (2023)
Páginas: 46-53
Seção: КОМПЬЮТЕРНАЯ АЛГЕБРА
URL: https://journals.rcsi.science/0132-3474/article/view/137619
DOI: https://doi.org/10.31857/S0132347423020097
EDN: https://elibrary.ru/MFUGDU
ID: 137619

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Resumo

In this paper, we construct a symbolic-numerical implementation of the Galerkin method for approximate solution of the waveguide diffraction problem at the junction of two open planar three-layer waveguides. The Gelerkin method is implemented in the Maple computer algebra system by symbolic manipulations; its software implementation is based on the scprod symbolic-numerical procedure, which enables the numerical calculation of scalar products for the Galerkin method based on symbolic expressions. The use of symbolic manipulations makes it possible to speed up the calculation of integrals in the Galerkin method owing to single-run symbolic calculation of integrals typical for the problem, rather than multiple numerical integration.

Sobre autores

D. DIVAKOV

Peoples' Friendship University of Russia (RUDN University); Joint Institute for Nuclear Research

Email: divakov-dv@rudn.ru
Moscow, Russia; Dubna, Moscow oblast, Russia

A. TYUTYUNNIK

Peoples' Friendship University of Russia (RUDN University); Joint Institute for Nuclear Research

Autor responsável pela correspondência
Email: tyutyunnik-aa@rudn.ru
Moscow, Russia; Dubna, Moscow oblast, Russia

Bibliografia

Tolstikhin O.I., Ostrovsky V.N., Nakamura H. Siegert Pseudo-States as a Universal Tool: Resonances, S Matrix, Green Function // Physical Review Letters. 1997. V. 79. № 11. P. 2026–2029.
Sveshnikov A.G. The basis for a method of calculating irregular waveguides // USSR Computational Mathematics and Mathematical Physics. 1963. V. 3. № 1. P. 219–232.
Eremin Y.A., Sveshnikov A.G. Study of scalar diffraction at a locally inhomogeneous body by a projection method // USSR Computational Mathematics and Mathematical Physics. 1976. V. 16. № 3. P. 255–260.
Delitsyn A.L. On the completeness of the system of eigenvectors of electromagnetic waveguies // Computational Mathematics and Mathematical Physics. 2011. V. 51. № 10. P. 1771–1776.
Sveshnikov A.G. A substantiation of a method for computing the propagation of electromagnetic oscillations in irregular waveguides // USSR Computational Mathematics and Mathematical Physics. 1963. V. 3. № 2. P. 413–429.
Mathematics-based software and services for education, engineering, and research https://www.maplesoft.com/
Свешников А.Г. Неполный метод Галеркина // ДАН СССР. 1977. Т. 236. № 5. С. 1076–1079.
Диваков Д.В., Тютюнник А.А. Символьное исследование спектральных характеристик направляемых мод плавно-нерегулярных волноводов // Программирование. 2022. № 2. С. 23–32.
Tiutiunnik A.A., Divakov D.V., Malykh M.D., Sevastianov L.A. Symbolic-Numeric Implementation of the Four Potential Method for Calculating Normal Modes: An Example of Square Electromagnetic Waveguide with Rectangular Insert // Lecture Notes in Computer Science. 2019. V. 11661. P. 412–429.
Виницкий C.И., Гердт В.П., Гусев А.А., Касчиев М.С., Ростовцев B.А., Самойлов В.Н., Тюпикова Т.В., Чулуунбаатар О. Символьночисленный алгоритм вычисления матричных элементов параметрической задачи на собственные значения // Программирование. 2007. Т. 33. № 2. С. 63–76.
Зорин A.В., Севастьянов Л.А., Третьяков Н.П. Компьютерное моделирование водородоподобных атомов в квантовой механике с неотрицательной функцией распределения // Программирование. 2007. Т. 33. № 2. С. 50–62.
Диваков Д.В., Тютюнник А.А. Символьное исследование собственных векторов для построения общего решения системы ОДУ с символьной матрицей коэффициентов // Программирование. 2021. 1. С. 11–24.
Shevchenko V.V. Spectral decomposition in eigen- and associated functions of a nonselfadjoint problem of Sturm–Liouville type on the entire axis // Differ. Uravn. 1979. V. 15. № 11. P. 2004–2020.
Gevorkyan M.N., Kulyabov D.S., Lovetskiy K.P., Sevastyanov A.L., Sevastyanov L.A. Waveguide modes of a planar optical waveguide // Mathematical Modelling and Geometry. 2015. V. 3. № 1. P. 43–63.
Sevastianov L.A., Egorov A.A., Sevastyanov A.L. Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures // Physics of Atomic Nuclei. 2013. V. 76. № 2. P. 224–239.