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Method for computing waveguide scattering matrices in the vicinity of thresholds. / Plamenevski, B.A.; Poretski, A.S.; Sarafanov, O.V.

In: St. Petersburg Mathematical Journal, Vol. 26, No. 1, 2015, p. 91-116.

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@article{aead7e38dbed48ad86b904d4a7f87d75,
title = "Method for computing waveguide scattering matrices in the vicinity of thresholds",
abstract = "{\textcopyright} 2014 American Mathematical Society. A waveguide occupies a domain G in Rn+1, n ≥ 1, having several cylindrical outlets to infinity. The waveguide is described by the Dirichlet problem for the Helmholtz equation. The scattering matrix S(μ) with spectral parameter μ changes its size when μ crosses a threshold. To calculate S(μ) in a neighborhood of a threshold, an {"}augmented{"} scattering matrix S(μ) is introduced, which keeps its size near the threshold and is analytic in μ there. A minimizer of a quadratic functional JR(·, μ) serves as an approximation to a row of the matrix S(μ). To construct such a functional, an auxiliary boundary-value problem is solved in the bounded domain obtained by cutting off the waveguide outlets to infinity at a distance R. As R→∞, the minimizer a(R, μ) tends exponentially to the corresponding row of S(μ) uniformly with respect to μ in a neighborhood of the threshold. The neighborhood may contain some waveguide eigenvalues corresponding to eigenfunctions exponentially decaying at",
author = "B.A. Plamenevski and A.S. Poretski and O.V. Sarafanov",
year = "2015",
language = "English",
volume = "26",
pages = "91--116",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "1",

}

RIS

TY - JOUR

T1 - Method for computing waveguide scattering matrices in the vicinity of thresholds

AU - Plamenevski, B.A.

AU - Poretski, A.S.

AU - Sarafanov, O.V.

PY - 2015

Y1 - 2015

N2 - © 2014 American Mathematical Society. A waveguide occupies a domain G in Rn+1, n ≥ 1, having several cylindrical outlets to infinity. The waveguide is described by the Dirichlet problem for the Helmholtz equation. The scattering matrix S(μ) with spectral parameter μ changes its size when μ crosses a threshold. To calculate S(μ) in a neighborhood of a threshold, an "augmented" scattering matrix S(μ) is introduced, which keeps its size near the threshold and is analytic in μ there. A minimizer of a quadratic functional JR(·, μ) serves as an approximation to a row of the matrix S(μ). To construct such a functional, an auxiliary boundary-value problem is solved in the bounded domain obtained by cutting off the waveguide outlets to infinity at a distance R. As R→∞, the minimizer a(R, μ) tends exponentially to the corresponding row of S(μ) uniformly with respect to μ in a neighborhood of the threshold. The neighborhood may contain some waveguide eigenvalues corresponding to eigenfunctions exponentially decaying at

AB - © 2014 American Mathematical Society. A waveguide occupies a domain G in Rn+1, n ≥ 1, having several cylindrical outlets to infinity. The waveguide is described by the Dirichlet problem for the Helmholtz equation. The scattering matrix S(μ) with spectral parameter μ changes its size when μ crosses a threshold. To calculate S(μ) in a neighborhood of a threshold, an "augmented" scattering matrix S(μ) is introduced, which keeps its size near the threshold and is analytic in μ there. A minimizer of a quadratic functional JR(·, μ) serves as an approximation to a row of the matrix S(μ). To construct such a functional, an auxiliary boundary-value problem is solved in the bounded domain obtained by cutting off the waveguide outlets to infinity at a distance R. As R→∞, the minimizer a(R, μ) tends exponentially to the corresponding row of S(μ) uniformly with respect to μ in a neighborhood of the threshold. The neighborhood may contain some waveguide eigenvalues corresponding to eigenfunctions exponentially decaying at

M3 - Article

VL - 26

SP - 91

EP - 116

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 1

ER -

ID: 3929907