Method of hypersingular integral equations in a three-dimensional problem of diffraction of electromagnetic waves on a piecewise homogeneous dielectric body

The problem of electromagnetic diffraction in a piecewise homogeneous medium that can consist of domains with different dielectric properties and can contain ideally conducting inclusions in the form of solid objects and screens is reduced to a system of integral equations with hypersingular integrals over surfaces separating the media with different dielectric properties. We prove the equivalence of the resulting system of integral equations and the original boundary value problem. We construct a numerical scheme for the solution of related integral equations based on methods of piecewise constant approximations and collocations; this scheme can be used on surfaces of fairly arbitrary form.