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

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 manipula...

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Veröffentlicht in:Programming and computer software Jg. 49; H. 2; S. 100 - 107
Hauptverfasser: Divakov, D. V., Tyutyunnik, A. A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Moscow Pleiades Publishing 01.04.2023
Springer Nature B.V
Schlagworte:
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
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:0361-7688
1608-3261
DOI:10.1134/S0361768823020081