S. P. Kulikov, I. Yu. Shumov

Proposed and tested scheme for solving the integral equation (IE) of the electromagnetic scattering by a locally inhomogeneous dielectric media which significantly reduces the error of the numerical solution. The scheme was tested in one-dimensional case. Typically, the solution IE with a feature of the kernel used the method of finite sums, together with the quadrature formula of rectangles, because the more accurate quadrature formula in this case lead to greater error. This effect is illustrated well in this work, with a one-dimensional IE of electromagnetic scattering with a singularity in the derivative of the kernel. It is shown that the use of equivalent transformation of the original equation with the removal of singularity on the diagonal of the kernel leads to the possibility of using quadrature formulas of higher order accuracy. The behavior of the error in the numerical solution of IE is similar to the behavior of the error corresponding to the numerical integration without kernel features. Error in the equation decision in schemes with different quadrature formulas analyzed by comparing with a strong solution of the scattering of a plane wave on a homogeneous layer and a layer of a special type non-uniform structure. The values of the physical accuracy of the approximation in the form of number of grid cells per wavelength in the medium required to achievement a graphical accuracy of the solution for this scheme. In view of these laws, solutions of specific problems of electromagnetic scattering by a nonuniform resonant dielectric layer of biological origin, with high values of permittivity and conductivity was got. The solution of large com-plex near-singular SLAE, which is obtained in the numerical scheme, effectively solved by the iterative method of Biconjugate Gradient.