Title
Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers
Abstract
We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Green's function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetic. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest.
Year
DOI
Venue
2016
10.1016/j.jcp.2016.08.019
J. Comput. Physics
Keywords
Field
DocType
Cylindrically stratified media,Anisotropic media,Green's function,Cylindrical coordinates,Electromagnetic radiation
Arithmetic underflow,Mathematical optimization,Cylindrical coordinate system,Green's function,Anisotropy,Eigenfunction,Tensor,Mathematical analysis,Numerical stability,Mathematics,Bessel function
Journal
Volume
Issue
ISSN
325
C
0021-9991
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Haksu Moon1152.46
Fernando L. Teixeira29716.97
Burkay Donderici351.61