Singularity extraction in kernel functions in closed region problems

Abstract

A general method of obtaining the free space particular solution and the required homogeneous solution decomposition in closed region problems in electromagnetics is described. This allows the singular nature of the kernel function to be handled analytically. The remaining homogeneous solution which is expressed in an eigenfunction series is rapidly convergent. The method should be of particular value in vector integral equation formulations where the dyadic kernel is highly singular. The method is applied to the rectangular cavity dyad.

Technical memorandum. Rapidly converging expressions of dyadic green's functions for parallel-plate transmission line

“…With respect to the usual fullmode expansion of the Green's functions for resonators, these hybrid expressions exhibit a much faster convergence when the observation point is near to the source point. As is well known, in these cases, the full modal expansions converge very slowly, due to the singularity of the Green's functions [4]. The hybrid expressions are obtained by extracting from the original full modal expansions their low-frequency approximations and by transforming the extracted series into different forms.…”

Full-wave analysis and design of passive microwave and millimetre-wave devices based on dielectric-loaded cavity resonators

“…Nevertheless, these representations of G e have demonstrated to be inadequate for the kind of problems that we are trying to solve, since their eigenfunctions series have very poor convergence properties near the singularities even when they are avoided. In the work of Howard and Seidel [94] it was pointed out that this problem is due to the singularity associated to G e ; they improved the convergence of the series involved by extracting a singular irrotational term (of the order R −3 ) in closed form from the eigenfunctions series. However, the remaining series had still a singularity of the order R −1…”

“…• There is a weaker singularity contained in the solenoidal term The first singularity evidenced above was firstly extracted from the electric dyadic Green' function in [94], whereas the second one was extracted for the first time in the work of Bressan and Conciauro [82]. For this purpose the authors decomposed G e into: …”

“…They extracted from the electric dyadic Green's function not only the irrotational singularity like in [94], but also a solenoidal weaker one (of the order R…”

Επιλυση Του Προβληματος Σκεδασης Απο Σκεδαστη Τυχαιας Γεωμετριας Μεσα Σε Στρωματοποιημενο Μεσο Με Την Βοηθεια Των Δυαδικων Συναρτησεων Green

“…Με το ίδιο πρόβλημα ασχολείται και ο Howard (1974), που εξάγει πάλι ένα διορθωτικό όρο για τη δυαδική συνάρτησηΰΓββη του κενού χώρου από τα ολοκλη ρωτικά υπόλοιπα των διανυσματικών κυματικών συναρτήσεων Η. Η μορφή, όμως, του όρου αυτού είναι αρκετά πολύπλοκη, ενώ αγνοεί τα ολοκληρωτικά υπόλοιπα των διανυσματικών κυματικών συναρτήσεων Ε. Το ίδιο πρόβλημα για τη περίπτωση των κοιλοτήτων τον απασχολεί και αργότερα (Howard and Seidel, 1978).…”