Felsen, Leopold B.; Mongiardo, Mauro; Russer, Peter
Electromagnetic Field Representations and Computations in Complex Structures Ii: Alternative Green's Functions
In this second paper of the three-part sequence, we deal with alternative Green's function (GF) representations for the subdomain (SD) problem in the complexity architecture of Part I . The relevant GFs for systematic analytic modelling are those associated with at least partially vector and co-ordinate separable boundary conditions. Such lsquocanonicalrsquo GFs, when lsquomatchedrsquo to a real problem, can form background kernels which simplify the numerical complexity of real-problem exact integral equations. The analytic machinery involves Sturm-Liouville (SL) theory for the reduced one-dimensional (1D) spectral GF problems resulting from separation of variables in various co-ordinates, set in its most general form in the complex spectral wavenumber domain. Spectral synthesis in the complex spectral wavenumber planes for 2D and 3D co-ordinate-separable full GFs lays the foundation for direct construction (via contour deformations, branch point, and pole residue evaluations) of alternative field representations, and their correspondingly different wave-physical phenomenologies. Illustrative examples show the connection between the canonical GFs and their network representations. Copyright ï¿œ 2002 John Wiley & Sons, Ltd.
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields