Method for computing waveguide scattering matrices in the vicinity of thresholds

Результат исследований: Научные публикации в периодических изданияхстатья

4 Цитирования (Scopus)

Выдержка

© 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
Язык оригиналаанглийский
Страницы (с-по)91-116
ЖурналSt. Petersburg Mathematical Journal
Том26
Номер выпуска1
СостояниеОпубликовано - 2015

Отпечаток

Scattering Matrix
Waveguide
Waveguides
Scattering
Computing
Minimizer
Augmented matrix
Infinity
Quadratic Functional
Helmholtz equation
Helmholtz Equation
Eigenvalues and eigenfunctions
Dirichlet Problem
Boundary value problems
Eigenfunctions
Bounded Domain
Boundary Value Problem
Tend
Eigenvalue
Calculate

Цитировать

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title = "Method for computing waveguide scattering matrices in the vicinity of thresholds",
abstract = "{\circledC} 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",
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Method for computing waveguide scattering matrices in the vicinity of thresholds. / Plamenevski, B.A.; Poretski, A.S.; Sarafanov, O.V.

В: St. Petersburg Mathematical Journal, Том 26, № 1, 2015, стр. 91-116.

Результат исследований: Научные публикации в периодических изданияхстатья

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

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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

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JO - St. Petersburg Mathematical Journal

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