S.P. Kulikov, N.Yu. Sotnikova
The estimation of electromagnetic diffraction field on a locally inhomogeneous dielectic, based on the use of the first term of the optimal series of simple iteration for the solution of two-and three-dimensional vector singular integral equation of electromagnetic scattering was proposed and tested. The estimation is effective owing to the established analytically and numerically properties of quasi-static and resonance spectrum of an integral operator. Based on the established algorithms for optimal parameter of convergence of the optimal simple iteration for evaluation of the scattered field a formula of the first approximation which greatly expands the range of applicability of the ordinary Born approximation was proposed and allows in this area to effectively measure the scattered field insulator without solving the integral equation. The specific problems of diffraction of quasi-static, near-resonant, and also mixed in different coordinate ranges wavelengths, including those with the existing of exact solution were studied numerically. A comparative analysis of conventional and optimized approximations was done, the area of the effective use of the optimized approximations was shown. The numerical studies have shown good relative accuracy of the optimized Born approximation for enough large values of permittivity, for both a medium with losses and without them.