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Mathematical and numerical analysis of dielectric waveguides by the integral equation method
Russia.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.ORCID iD: 0000-0002-2691-2820
2013 (English)In: Progress in Electromagnetics Research Symposium, ISSN 1559-9450, 388-393 p.Article in journal (Refereed) PublishedText
Abstract [en]

The eigenvalue problems for generalized natural modes of an inhomogeneous dielectric waveguide without a sharp boundary and a step-index dielectric waveguide with a smooth boundary of cross-section are formulated as problems for the set of time-harmonic Maxwell equations with partial radiation conditions at infinity in the cross-sectional plane. The original problems are reduced by the integral equation method to nonlinear spectral problems with Fredholm integral operators. Properties of the spectrum are investigated. The Galerkin and collocation methods for the calculations of generalized natural modes are proposed and convergence of the methods is proved. Some results of numerical experiments are discussed.

Place, publisher, year, edition, pages
Cambridge, USA: Electromagnetics Academy , 2013. 388-393 p.
Keyword [en]
Collocation method; Eigenvalue problem; Fredholm integral; Inhomogeneous dielectrics; Integral equation methods; Numerical experiments; Partial radiation conditions; Time-harmonic maxwell equations, Eigenvalues and eigenfunctions; Integral equations, Dielectric waveguides
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-43866ScopusID: 2-s2.0-84884766642OAI: oai:DiVA.org:kau-43866DiVA: diva2:945142
Conference
PIERS 2013 - Conference of Progress in Electromagnetics Research Symposium, Stockholm, 12-15 August 2013
Available from: 2016-06-30 Created: 2016-06-30 Last updated: 2016-07-01Bibliographically approved

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Shestopalov, Yuri
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