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

• Published in: Programming and computer software Vol. 49; no. 2; pp. 100 - 107
• Main Authors: Divakov, D. V., Tyutyunnik, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-04-2023; Springer Nature B.V
• Subjects: Algebra; Algorithms; Artificial Intelligence; Computer algebra; Computer Science; Diffraction; Eigenvalues; Galerkin method; Helmholtz equations; Integrals; Mathematical analysis; Numerical analysis; Numerical integration; Operating Systems; Ordinary differential equations; Software Engineering; Software Engineering/Programming and Operating Systems; Waveguides
• ISSN: 0361-7688; 1608-3261
• DOI: 10.1134/S0361768823020081

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.