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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 1, Pages 93–96 (Mi faa3175)  

This article is cited in 5 scientific papers (total in 5 papers)

Brief communications

On Computation of Waveguide Scattering Matrices for the Maxwell System

B. A. Plamenevskiia, A. S. Poretskiiab, O. V. Sarafanova

a St. Petersburg State University, Faculty of Physics
b University of Jyväskylä

Abstract: The Maxwell system is considered in a waveguide with perfectly conducting boundary having several cylindrical outlets to infinity. A minimizer of a quadratic functional serves as an approximation to a row of the scattering matrix. To construct such a functional, we solve an auxiliary boundary value problem in the bounded domain obtained by cutting off, at a distance $R$, the waveguide outlets to infinity. As $R$ tends to infinity, the minimizer $a(R, k)$ tends at exponential rate to the corresponding row of the scattering matrix.

Keywords: truncated waveguide, quadratic functional, minimizer, exponential convergence

Funding Agency Grant Number
Saint Petersburg State University 11.38.666.2013
Russian Foundation for Basic Research 12-01-00247а


DOI: https://doi.org/10.4213/faa3175

Full text: PDF file (154 kB)
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English version:
Functional Analysis and Its Applications, 2015, 49:1, 77–80

Bibliographic databases:

UDC: 517.958+621.372.8
Received: 10.10.2014

Citation: B. A. Plamenevskii, A. S. Poretskii, O. V. Sarafanov, “On Computation of Waveguide Scattering Matrices for the Maxwell System”, Funktsional. Anal. i Prilozhen., 49:1 (2015), 93–96; Funct. Anal. Appl., 49:1 (2015), 77–80

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Korolkov A.I. Nazarov S.A. Shanin A.V., “Stabilizing solutions at thresholds of the continuous spectrum and anomalous transmission of waves”, ZAMM-Z. Angew. Math. Mech., 96:10 (2016), 1245–1260  crossref  mathscinet  isi  scopus
    2. S. A. Nazarov, “The asymptotic behaviour of the scattering matrix in a neighbourhood of the endpoints of a spectral gap”, Sb. Math., 208:1 (2017), 103–156  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. B. A. Plamenevskii, A. S. Poretskii, O. V. Sarafanov, “A method for approximate computation of waveguide scattering matrices”, Russian Math. Surveys, 75:3 (2020), 509–568  mathnet  crossref  crossref  isi
    4. B. A. Plamenevskii, A. S. Poretskii, “Izluchenie i rasseyanie v elektromagnitnykh volnovodakh vblizi porogov”, Algebra i analiz, 32:4 (2020), 234–270  mathnet
    5. S. A. Nazarov, “Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides”, Izv. Math., 84:6 (2020), 1105–1160  mathnet  crossref  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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