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

Authors: DIVAKOV D.V.¹^,2, TYUTYUNNIK A.A.¹^,2
Affiliations:
1. Peoples' Friendship University of Russia (RUDN University)
2. Joint Institute for Nuclear Research
Issue: No 2 (2023)
Pages: 46-53
Section: КОМПЬЮТЕРНАЯ АЛГЕБРА
URL: https://rjmseer.com/0132-3474/article/view/675756
DOI: https://doi.org/10.31857/S0132347423020097
EDN: https://elibrary.ru/MFUGDU
ID: 675756

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Abstract

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.

About the authors

D. V. 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. A. TYUTYUNNIK

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

Author for correspondence.
Email: tyutyunnik-aa@rudn.ru
Moscow, Russia; Dubna, Moscow oblast, Russia

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