An analytical formulation with ill-conditioned numerical scheme and its remedy: Scattering by two circular impedance cylinders

Abstract

The regularization of the well-known analytical formulation of the monochromatic electromagnetic wave scattering problem from a syvstem with two neighbor impedance circular cylinders is presented. It is the improvement and extension of the work done for scattering from two perfectly conducting circular cylinders. Numerical results show that it is numerically much safer to solve the obtained infinite algebraic system at a lower truncation number also by ensuring the reliability of the solution.

Well-conditioned algorithm for scattering by a few eccentrically multilayered dielectric circular cylinders

“…In a certain region, it is sufficient to represent the outgoing waves in the polar coordinates of the CB m that they start traveling [ Sever et al ., ; Toyama et al ., ; Ioannidou et al ., ]. Consequently, it becomes possible with the IF [ Bates , ] to represent uniquely for the eccentrically layered circular cylindrical regions with nonintersecting but arbitrarily placed multiple circular inclusions of the same kind as justified in the previous section.…”

“…Thus, alleviation of any difficulty along the implementation of an analytical model in a numerically stable fashion has utmost importance. The relevant concerns in the past five decades are issued in the context of implementation of the analytical formulations efficiently in computer [ Bates , ; Ivanov , ; Poyedinchuk et al ., ; Yiğit and Dikmen , ; Bruno and Lintner , ; Dikmen et al ., ; Sever et al ., ; Sandström and Akeab , ; Pan and Sheng , ].…”

“…[], and Sever et al . [], where m ≠ m` ) in the coupling region j = 1. The field representation of the configuration in Figure b is observed to assume outgoing waves out the CB 1,2 as m ≠ m` , each being expressed in local coordinates, and expression in the coupling region would only be valid if m = m` , since in this case, scattering field from either of the boundaries are incident for the other.…”

“…This problem was elaborated in Sever et al . [] for a pair of impedance circular cylinders; in Poyedinchuk et al . [], Sandström and Akeab [], and Pan and Sheng [] for a wider class of geometries; in [ Yiğit and Dikmen [] and Bruno and Lintner [] for open 2‐D geometries; and in Ivanov [] for pairs of canonic shapes.…”

“…This reduction is commonly referred to as the analytical regularization method [ Poyedinchuk et al ., ]. Because for such a LAES2, the condition number of the truncated system is uniformly bounded with the increasing dimension of the system [ Poyedinchuk et al ., ; Yiğit and Dikmen , ; Bruno and Lintner , ; Dikmen et al ., ; Sever et al ., ]. Therefore, the solution of y is available within the whole precision that the computer being used can provide, i.e., free from round‐off errors due to matrix inversion.…”