I. Introduction
Methods for studying high-frequency resonant scattering phenomena, such as the analysis of near-zero-index (NZI) materials made of dielectric rods [1], rely on the accelerated full-wave solvers of boundary integral equations aiming at the rigorous determination of electromagnetic fields that satisfy Maxwell's equations. The outputs of such solvers are optimized using genetic algorithms (GA), and reliability of these solvers is well-tested with experiments [2]. The components of the developed simulation and optimization environment are as given in [3], where the duration of the optimizations performed by the GA shortens mainly due to the electromagnetic solver. The studies conducted for NZI structures point to the electric-magnetic current combined-field integral equation (JMCFIE) formulation as the most appropriate for such a solver [4]. This formulation is accelerated by preconditioning with two layers of approximate multilevel fast multipole algorithm (MLFMA) application and is used in the study here for 3D simulations [5]. These choices led to reception of the desired accuracy at small iteration numbers, i.e., for a relative residual error of 10−3 in Fig. 1, from 8 to 35 iterations for the cases in Fig. 2.
Observation line on the center cut plane of rods (left). Cross section maps of two rod-array configurations (right).
Durations of 3D simulations when MLFMA accelerated JMCFIE is used to solve the cross sections in fig. 1 for different rod-lengths.