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

Abstract

The new regularization of the well-known analytical formulation of the monochromatic electromagnetic wave scattering by a few eccentrically multilayered homogenous circular cylinders is presented. It is found out that a regularization of this formulation is absolutely necessary. The two-sided regularization that we made is based on the integral formulation of the mentioned problem. The polarization of the fields are parallel to the longitudinal axes of the cylinders; thus, a two dimensional problem for each both polarizations are under consideration. The condition number of the resulting algebraic system is uniformly bounded while its truncation number increases. The numerical results are validated by existing results such as near and far fields obtained under various geometrical and electrical parameters of the scattering problem. Numerical results including the condition numbers of the regularized and nonregularized systems show that only regularized system gives numerically stable results with any desired accuracy in a wide range of frequencies from quasistatic to rather high-frequency range, limited only by the capabilities of the computer with the guarantee of the physical reliability of the solution.

Superalgebraically Converging Galerkin Method for Electromagnetic Scattering by Dielectric Cylinders

“…Therefore, obtaining the Fourier coefficients of the tangential fields via SoV (Figures 1a and 1b) and (À2λ 0 , 0), (2λ 0 , 0) (Figures 1a and 1b) and radii ρ i : 3λ 0 /2, λ 0 /2 (Figures 1a and 1b) and λ 0 /2, λ 0 /2 (Figures 1a and 1b), respectively. Dikmen et al (2015) is numerically stable unlike its unregularized versions, it provides any Fourier coefficient in a stable numerical-analytical fashion with exponential convergence. We can observe the same kind of convergence of the Fourier coefficients achieved with the proposed approach here for EFIE and MFIE until the machine precision is reached.…”

“…We will provide a comparison of the achieved results with a numerically stable canonical solution based on separation of variables (SoV) representation of the fields, designed for a multitude of circularly cylindrical interfaces separating the dielectric domains (Dikmen et al, ). This is the perfect tool for the purpose since it provides the analytical formulation for two dielectric circular cylinders whose numerical implementation is well conditioned.…”

“…Therefore, the 2‐D solvers are sifted out among all, to obtain express results. For example, the simplest representation of the boundaries can be used in a model widely useful from remote sensing to power transmission (Dikmen et al, ). It was shown there that the risks and mastery required to solve even such problem of a simple model are big, to achieve an accurate solution.…”

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

“…This formulation corresponds to the integral formulation in [1] and will be expressed as an infinite linear algebraic system of the first kind (LAES1). As stated in [3] and exemplified in [8], the verifications of the numerical solutions to a certain * Correspondence: dikmen@gyte.edu.tr boundary value problem reduced to such a LAES1, being held with physical requirements such as reciprocity of the fields or boundary conditions, are circumstantial. This fact was taken into account in [2,3] and [8], in the first for two perfectly conducting circular cylinders and in the third for two layered eccentric circular cylinders.…”

“…As stated in [3] and exemplified in [8], the verifications of the numerical solutions to a certain * Correspondence: dikmen@gyte.edu.tr boundary value problem reduced to such a LAES1, being held with physical requirements such as reciprocity of the fields or boundary conditions, are circumstantial. This fact was taken into account in [2,3] and [8], in the first for two perfectly conducting circular cylinders and in the third for two layered eccentric circular cylinders. It is well known [9] that the only practical way to obtain a reliable and stable solution avoiding round-off errors is to make sure that the condition number of the truncated algebraic system does not reach (preferably) or exceed (meaning no significant digits are obtained) the word length (i.e.…”