Investigation of Electromagnetic Diffraction by a Dielectric Body in a Waveguide using the Method of Volume Singular Integral Equation

The problem of diffraction of an electromagnetic field by a locally nonhomogeneous body in a perfectly conducting waveguide of rectangular cross section is considered. This problem is reduced to solving a volume singular integral equation (VSIE). The examination of this equation is based on the analysis of the corresponding boundary value problem (BVP) for the system of Maxwell's equations and the equivalence of this BVP and VSIE. The existence and uniqueness for VSIE in the space of square-integrable functions are proved. A numerical Galerkin method for the solution of VSIE is proposed, and its convergence is proved.