Methods for the accelerated computation of Green's functions with 2-D periodicity in layered media

A review of some recent methods for the efficient computation of two-dimensional (2-D) periodic Green's functions in layered dielectric media is presented in this contribution. 2-D periodic vector and scalar mixed-potential Green's functions for a multilayered environment are derived in the spectral domain first, and then the corresponding spatial-domain quantities are obtained through an efficient sum of spatial harmonics. Numerical acceleration techniques are performed by extracting slowly-converging and singular terms. Kummer-Poisson's formula and Ewald¿s transformations are applied when the sum of the extracted terms is added back and a comparison is performed, which shows the efficiency of the proposed methods for this kind of problems.

[1]  D. Shanks.  Non‐linear Transformations of Divergent and Slowly Convergent Sequences , 1955 .

[2]  K. E. Jordan,et al.  An efficient numerical evaluation of the Green's function for the Helmholtz operator on periodic structures , 1986 .

[3]  Raed M. Shubair,et al.  Efficient computation of the periodic Green's function in layered dielectric media , 1993 .

[4]  Guy A. E. Vandenbosch,et al.  The expansion wave concept. I. Efficient calculation of spatial Green's functions in a stratified dielectric medium , 1998 .

[5]  D. Wilton,et al.  Accelerating the convergence of series representing the free space periodic Green's function , 1990 .

[6]  G. Vandenbosch,et al.  Semantics of dyadic and mixed potential field representation for 3-D current distributions in planar stratified media , 2003 .

[7]  Roberto D. Graglia,et al.  On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle , 1993 .

[8]  John L. Volakis,et al.  Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation , 1999 .

[9]  P. P. Ewald.  Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[10]  K. Michalski,et al.  Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. I. Theory , 1990 .

[11]  M. I. Aksun,et al.  Comparative study of acceleration techniques for integrals and series in electromagnetic problems , 1995, IEEE Antennas and Propagation Society International Symposium. 1995 Digest.