A method for computing waveguide scattering matrices in the presence of point spectrum

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференции

1 цитирование (Scopus)

Выдержка

A waveguide G lies in ℝ n+1 , n > 1, and outside a large ball coincides with the union of finitely many non-overlapping semi-cylinders ("cylindrical ends"). The waveguide is described by the operator {L(x,D x ) - μ, B(x,D x )} of an elliptic boundary value problem in G, where L is a matrix differential operator, B is a boundary operator, and μ is a spectral parameter. The operator {L, B} is self-adjoint with respect to a Green formula. The role of L can be played, e.g., by the Helmholtz operator, by the operators in elasticity theory and hydrodynamics. As approximation for a row of the scattering matrix S(μ), we take the minimizer of a quadratic functional J R ( ,μ). To construct the functional, we solve an auxiliary boundary value problem in the bounded domain obtained by truncating the cylindrical ends of the waveguide at distance R. As R → ∞, the minimizer a(R, μ) tends with exponential rate to the corresponding row of the scattering matrix uniformly on every finite closed interval of the continuous spectrum not containing the thresholds. Such an interval may contain eigenvalues of the waveguide with eigenfunctions exponentially decaying at infinity ("trapped modes"). Eigenvalues of this sort, as a rule, occur in waveguides of complicated geometry. Therefore, in applications, the possibility to avoid worrying about (probably not detected) trapped modes turns out to be an important advantage of the method. For the reader convenience we first formulate the method for the Helmholtz operator and then present the method for the general elliptic problem.

Язык оригиналаанглийский
Название основной публикацииECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
Страницы588-596
Число страниц9
СостояниеОпубликовано - 1 дек 2012
Событие6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 - Vienna, Австрия
Продолжительность: 10 сен 201214 сен 2012

Серия публикаций

НазваниеECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

Конференция

Конференция6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
СтранаАвстрия
ГородVienna
Период10/09/1214/09/12

Отпечаток

Point Spectrum
Scattering Matrix
Waveguide
Waveguides
Scattering
Computing
Operator
Boundary value problems
Hermann Von Helmholtz
Minimizer
Eigenvalue
Green's Formula
Quadratic Functional
Closed interval
Eigenvalues and eigenfunctions
Continuous Spectrum
Elasticity Theory
Elliptic Boundary Value Problems
Elasticity
Elliptic Problems

Предметные области Scopus

  • Математика и теория расчета
  • Прикладная математика

Цитировать

Plamenevskii, B., & Sarafanov, O. (2012). A method for computing waveguide scattering matrices in the presence of point spectrum. В ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (стр. 588-596). (ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers).
Plamenevskii, Boris ; Sarafanov, Oleg. / A method for computing waveguide scattering matrices in the presence of point spectrum. ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers. 2012. стр. 588-596 (ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers).
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Plamenevskii, B & Sarafanov, O 2012, A method for computing waveguide scattering matrices in the presence of point spectrum. в ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers. ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers, стр. 588-596, Vienna, Австрия, 10/09/12.

A method for computing waveguide scattering matrices in the presence of point spectrum. / Plamenevskii, Boris; Sarafanov, Oleg.

ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers. 2012. стр. 588-596 (ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers).

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференции

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N2 - A waveguide G lies in ℝ n+1 , n > 1, and outside a large ball coincides with the union of finitely many non-overlapping semi-cylinders ("cylindrical ends"). The waveguide is described by the operator {L(x,D x ) - μ, B(x,D x )} of an elliptic boundary value problem in G, where L is a matrix differential operator, B is a boundary operator, and μ is a spectral parameter. The operator {L, B} is self-adjoint with respect to a Green formula. The role of L can be played, e.g., by the Helmholtz operator, by the operators in elasticity theory and hydrodynamics. As approximation for a row of the scattering matrix S(μ), we take the minimizer of a quadratic functional J R ( ,μ). To construct the functional, we solve an auxiliary boundary value problem in the bounded domain obtained by truncating the cylindrical ends of the waveguide at distance R. As R → ∞, the minimizer a(R, μ) tends with exponential rate to the corresponding row of the scattering matrix uniformly on every finite closed interval of the continuous spectrum not containing the thresholds. Such an interval may contain eigenvalues of the waveguide with eigenfunctions exponentially decaying at infinity ("trapped modes"). Eigenvalues of this sort, as a rule, occur in waveguides of complicated geometry. Therefore, in applications, the possibility to avoid worrying about (probably not detected) trapped modes turns out to be an important advantage of the method. For the reader convenience we first formulate the method for the Helmholtz operator and then present the method for the general elliptic problem.

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Plamenevskii B, Sarafanov O. A method for computing waveguide scattering matrices in the presence of point spectrum. В ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers. 2012. стр. 588-596. (ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers).