A Rigorous Algorithm for the Boundary Value Problem of Dielectric Bodies Based on the Analytical Regularization Method

Abstract

In this paper, the application of the Analytical Regularization Method (ARM) to a dielectric cylinder is presented. At first, the matrix of the algebraic system is constructed as a 2 × 2 block matrix where the off-diagonal blocks consist of the Fourier coefficients of non-singular operators and the entries of the diagonal blocks involve the associated singularities. Then the left- and right-hand side operators of the ARM built up on these singularities are applied to the algebraic system, transforming it to a second kind one in form of $(I + H)y=b$ where $I$ the identity operator and $H$ is a compact operator in space $l_{2}$. The algorithm is applied to a dielectric cylinder illuminated by a TM -z polarized plane wave. The formulation of TE-z polarization is almost the same except the field functions will be in terms of magnetic field and its normal derivative. The numerical results are validated by the solution of separation of variables for a circular dielectric cylinder and then the superiority of the second kind system to the first kind one is shown by means of the condition number with respect to the truncation number of the algebraic system.