On the Green's function for the Helmholtz operator in an impedance circular cylindrical waveguide

Carlos Pérez-Arancibia; Mario Durán

doi:10.1016/j.cam.2010.05.053

On the Green's function for the Helmholtz operator in an impedance circular cylindrical waveguide

Carlos Pérez-Arancibia^*, Mario Durán

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

11 Citations (Scopus)

Abstract

This paper addresses the problem of finding a series representation for the Green's function of the Helmholtz operator in an infinite circular cylindrical waveguide with impedance boundary condition. Resorting to the Fourier transform, complex analysis techniques and the limiting absorption principle (when the undamped case is analyzed), a detailed deduction of the Green's function is performed, generalizing the results available in the literature for the case of a complex impedance parameter. Procedures to obtain numerical values of the Green's function are also developed in this article.

Original language	English
Pages (from-to)	244-262
Number of pages	19
Journal	Journal of computational and applied mathematics
Volume	235
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2010.05.053
Publication status	Published - 1 Nov 2010
Externally published	Yes

Keywords

Cylindrical waveguide
Green's function
Helmholtz equation
Impedance boundary condition

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10.1016/j.cam.2010.05.053

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title = "On the Green's function for the Helmholtz operator in an impedance circular cylindrical waveguide",

abstract = "This paper addresses the problem of finding a series representation for the Green's function of the Helmholtz operator in an infinite circular cylindrical waveguide with impedance boundary condition. Resorting to the Fourier transform, complex analysis techniques and the limiting absorption principle (when the undamped case is analyzed), a detailed deduction of the Green's function is performed, generalizing the results available in the literature for the case of a complex impedance parameter. Procedures to obtain numerical values of the Green's function are also developed in this article.",

keywords = "Cylindrical waveguide, Green's function, Helmholtz equation, Impedance boundary condition",

author = "Carlos P{\'e}rez-Arancibia and Mario Dur{\'a}n",

note = "Funding Information: This work was supported by CONICYT/PBCT project ADI#30/2006 (Chile) and by the CONICYT Fellowship for Master Students. The authors are grateful to Dr. Jean-Claude N{\'e}d{\'e}lec from CMAP, Ecole Polytecnique, Palaiseau, France, for his helpful comments on the manuscript.",

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AU - Pérez-Arancibia, Carlos

AU - Durán, Mario

N1 - Funding Information: This work was supported by CONICYT/PBCT project ADI#30/2006 (Chile) and by the CONICYT Fellowship for Master Students. The authors are grateful to Dr. Jean-Claude Nédélec from CMAP, Ecole Polytecnique, Palaiseau, France, for his helpful comments on the manuscript.

PY - 2010/11/1

Y1 - 2010/11/1

N2 - This paper addresses the problem of finding a series representation for the Green's function of the Helmholtz operator in an infinite circular cylindrical waveguide with impedance boundary condition. Resorting to the Fourier transform, complex analysis techniques and the limiting absorption principle (when the undamped case is analyzed), a detailed deduction of the Green's function is performed, generalizing the results available in the literature for the case of a complex impedance parameter. Procedures to obtain numerical values of the Green's function are also developed in this article.

AB - This paper addresses the problem of finding a series representation for the Green's function of the Helmholtz operator in an infinite circular cylindrical waveguide with impedance boundary condition. Resorting to the Fourier transform, complex analysis techniques and the limiting absorption principle (when the undamped case is analyzed), a detailed deduction of the Green's function is performed, generalizing the results available in the literature for the case of a complex impedance parameter. Procedures to obtain numerical values of the Green's function are also developed in this article.

KW - Cylindrical waveguide

KW - Green's function

KW - Helmholtz equation

KW - Impedance boundary condition

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DO - 10.1016/j.cam.2010.05.053

M3 - Article

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VL - 235

SP - 244

EP - 262

JO - Journal of computational and applied mathematics

JF - Journal of computational and applied mathematics

IS - 1

ER -

On the Green's function for the Helmholtz operator in an impedance circular cylindrical waveguide

Abstract

Keywords

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