TY - JOUR
T1 - On the Green's function for the Helmholtz operator in an impedance circular cylindrical waveguide
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
UR - http://www.scopus.com/inward/record.url?scp=77955430273&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2010.05.053
DO - 10.1016/j.cam.2010.05.053
M3 - Article
SN - 0377-0427
VL - 235
SP - 244
EP - 262
JO - Journal of computational and applied mathematics
JF - Journal of computational and applied mathematics
IS - 1
ER -