Addition formulas and the Rayleigh identity for arrays of elliptical cylinders

Citation
Jg. Yardley et al., Addition formulas and the Rayleigh identity for arrays of elliptical cylinders, PHYS REV E, 60(5), 1999, pp. 6068-6080
Citations number
13
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW E
ISSN journal
1063651X → ACNP
Volume
60
Issue
5
Year of publication
1999
Part
B
Pages
6068 - 6080
Database
ISI
SICI code
1063-651X(199911)60:5<6068:AFATRI>2.0.ZU;2-C
Abstract
We apply the Rayleigh method to solve the problem where a uniform electrost atic held is imposed upon a rectangular array of elliptical cylinders embed ded in a matrix of unit dielectric constant. This new formulation overcomes geometric restrictions inherent in previous methods and is shown in princi ple and in various examples to converge far all possible geometries of the array and inclusion. Also presented are forms of both the interior and exte rior addition formulas for harmonic functions in elliptical coordinates tha t possess optimal regions of convergence. [S1063-651X(99)03609-0].