## 1. Introduction

[2] The method of auxiliary sources (MAS) [*Popovidi-Zaridze et al.*, 1981; *Zaridze et al.*, 1998a, 1998b; *Leviatan and Boag*, 1987; *Leviatan et al.*, 1988; *Leviatan*, 1990; *Kaklamani and Anastassiu*, 2002; *Anastassiu et al.*, 2002, 2003, 2004] is generally considered as a promising alternative to standard integral equation techniques, such as the method of moments (MoM). Its inherent advantages include low computational cost [*Anastassiu et al.*, 2002], simple algorithmic structure (with respect to the matrix elements calculations) and substantial physical insight. Owing to its attractive features, it has successfully been applied to a very large variety of radiation and scattering problems [*Kaklamani and Anastassiu*, 2002]. Nevertheless, MAS is still not as popular as MoM, since the latter is still considered generally more reliable for the extraction of reference data. The main reason for this is the limited robustness of MAS, which is due to the ambiguity related to the location of the auxiliary sources (AS). In theory, there is no uniquely determinable location for the AS, although its choice affects the solution efficiency, indeed. It has been observed that, poor AS positioning often leads to an inexplicable, irregular behavior of the numerical solution. This behavior usually translates into slow convergence rates or unacceptably high boundary condition errors.

[3] Very recently, a rigorous assessment of the MAS accuracy for scattering from a perfectly conducting (PEC) circular cylinder has been carried out [*Anastassiu et al.*, 2003, 2004]. It was shown that for this particular geometry, the MAS matrix can be inverted analytically, via spectral analysis and matrix diagonalization. The eigenvalues and eigenvectors were evaluated using a technique [*Warnick and Chew*, 2000] based on the addition theorem of cylindrical functions [*Hochstadt*, 1986, p. 229]. The analysis resulted in the derivation of an exact expression for the boundary condition error, which is due to discretization (from now on merely called “error” for brevity), as well as for the system condition number. Comparisons showed that the theoretical, analytically evaluated error, and the actual, computational error (produced by numerical matrix inversion) were generally identical, except for some range of the auxiliary surface radius, where discrepancies occurred. These discrepancies revealed an irregular behavior of the computational error, and were fully explained on the grounds of noise smearing, introduced by poor matrix conditioning. It was also demonstrated that a few specific locations of the AS yielded particularly high boundary errors. It was shown that these locations were related to the zeros of Bessel functions of integer order, and were physically interpreted as resonance effects. Finally, optimization of the MAS solution was achieved, by choosing the AS location so that the boundary error was minimized.

[4] Although the results in the work of *Anastassiu et al.* [2003, 2004] explained the MAS behavior to a great extent for scattering from a PEC, cylindrical surface, they are not directly applicable to nonmetallic or arbitrarily shaped boundaries. However, it is well known that MAS capabilities can be exploited in many more cases [*Kaklamani and Anastassiu*, 2002], including dielectric circular [*Leviatan and Boag*, 1987], coated circular [*Leviatan et al.*, 1988] and impedance square cylinders [*Anastassiu et al.*, 2002]. In the references above it was shown that the far field results could be highly accurate, since the error was usually possible to reduce by moving the AS on the basis of experience and physical insight, but there was no investigation into the mathematics of the error-producing mechanisms. However, the error skyrocketed abruptly and unexpectedly, for special AS locations, just like in the PEC case. These locations were merely avoided in the solution process, but it remained unclear what exactly the cause of this phenomenon was.

[5] Given the potential of MAS to become a very useful and efficient technique for a wide range of electromagnetic problems in the near future, deep understanding of its accuracy characteristics is absolutely necessary, for the most generic scatterers possible. Since the MAS optimization issue has been largely unresolved so far, it is natural that relatively simple, canonical geometries must be investigated, as a first step toward this direction, setting the basis for future analysis of more complicated configurations. The purpose of this work is the MAS error estimation for scattering from dielectric circular cylinders. The method invoked is closely related to *Anastassiu et al.* [2003, 2004], involving eigenvalue analysis and matrix diagonalization, although significant modifications are necessary, since the boundary conditions are now different. Knowledge of an analytical expression for the error, as a function of the geometry parameters, allows MAS optimization with respect to the location of the AS, exactly like in the PEC case [*Anastassiu et al.*, 2003, 2004].

[6] The paper is organized as follows: Section 2 presents the analytical inversion of the MAS linear system, in addition to the derivation of the analytical error expressions for transverse magnetic (TM) polarization. Section 3 presents the derivation of the relevant matrix condition number. Section 4 presents numerical results whereas optimization issues are discussed. Finally, section 5 summarizes and concludes the article. An *e*^{jωt} time convention is assumed and suppressed throughout the paper.