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Symbolic-Numerical Implementation of the Galerkin Method for Approximate Solution of the Waveguide Diffraction Problem

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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.

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Funding

This work was supported by the Russian Science Foundation, project no. 20-11-20257.

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), ul. Miklukho-Maklaya 6, 117198, Moscow, Russia

    D. V. Divakov & A. A. Tyutyunnik

  2. Joint Institute for Nuclear Research, ul. Zholio-Kyuri 6, 141980, Dubna, Moscow oblast, Russia

    D. V. Divakov & A. A. Tyutyunnik

Authors
  1. D. V. Divakov
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  2. A. A. Tyutyunnik
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Correspondence to D. V. Divakov or A. A. Tyutyunnik.

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The authors declare that they have no conflicts of interest.

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Translated by Yu. Kornienko

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Divakov, D.V., Tyutyunnik, A.A. Symbolic-Numerical Implementation of the Galerkin Method for Approximate Solution of the Waveguide Diffraction Problem. Program Comput Soft 49, 100–107 (2023). https://doi.org/10.1134/S0361768823020081

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  • DOI: https://doi.org/10.1134/S0361768823020081

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