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Symbolic derivation and numeric computation of dyadic Green's functions using Mathematica

Le-Wei Li
Organization: National University of Singapore
Mook-Seng Leong
Tat-Soon Yeo
Journal / Anthology

IEEE Antennas & Propagation Magazine
Year: 2001
Volume: 43
Issue: 1
Page range: 108-118

This paper presents a mathematical-software functional package that is capable of performing symbolic derivation and numeric computation of dyadic Green's functions for certain multilayered structures: a planar stratified multilayered medium, a spherical multilayered medium, a cylindrical multilayered medium, and a conducting rectangular waveguide with a multilayered dielectric load. The algorithms of this software package are based on the eigenfunction-expansion method. Using Mathematica, two packages were written to fulfill the aforementioned objectives. Upon completion of the software development, dyadic Green's functions for three-layered media were generated. A comparison of these outputs with published results showed good agreement. This demonstrated the applicability of the symbolic package. For the numeric package, the Green's dyadics for a particular three-layered spherical isotropic multilayered medium were generated as an illustration. These packages have been successfully implemented, and future derivation of dyadic Green's functions for these media may be performed.

*Mathematics > Calculus and Analysis > Differential Equations
*Science > Physics > Electromagnetism

dyadic green's function, Mathematica, nonhomogeneous media, rectangular waveguides, electromagnetic theory, planar stratified medium, spherical multilayered medium, cylindrical multilayered medium