Volumetric integral equations for non-uniform impurities in the rectangular waveguide

Surface Integral Equations (SIEs) and Volumetric Integral Equations (VIEs) are widely used for solutions of electromagnetic boundary problems. The SIEs are convenient because they reduce the dimension of a problem (three-dimensional problems are reduced to two-dimensional SIEs) and allow all boundary and radiating conditions to be satisfied. Both the SIEs with the kernels as single- and double-layered potentials and the VIEs versus the electrical field distribution in the volume of an impurity, are known and have been used. In this paper the VIEs without surface integrals are developed for arbitrary dielectric and magnetic inclusions in the Rectangular Waveguide (RW). The goal of the paper is to elaborate the algorithms for solutions of boundary problems with arbitrary shaped inclusions and with arbitrary tensor permittivities and permeabilities (including bianisotropic ones). The method is based on piece-wise field approximations