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On the Green’s function for the Helmholtz operator in an impedance circular cylindrical waveguide. (English) Zbl 1201.78016

Summary: 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.

MSC:

78A50 Antennas, waveguides in optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations

Software:

RFSFNS; BRENT; ELF; GNOME
PDFBibTeX XMLCite
Full Text: DOI

References:

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