A numerically stable algorithm for scattering from several circular cylinders including metamaterials with different boundary conditions

The analytically obtained algebraic equation systems for the TM/TE-z polarized monochromatic waves scattering from eccentrically layered circular cylinders are ill-conditioned for numerical calculations. Therefore, such ill conditioned systems must be regularized for reliable numerical results. Here, the steps of the regularization of the ill conditioned system obtained for the scattered field from a circular metamaterial cylinder includes three parallel circular cylinders: a dielectric, an impedance and a perfect electric conductor is explained. In the regularization procedure used here each circular boundary brings block(s) correspond to its electromagnetic property and the regularization procedure is done according to this block(s). For this end a system that consists of perfect electric conductor (PEC), impedance, dielectric, and metamaterial cylinders is discussed and thus the steps of a regularization procedure for a general system that has all the type of boundaries in terms of electromagnetics will be explained here. As a result, if a new boundary is included to the system then it is sufficient to locate the blocks related to this boundary suitably.