Inverse Boundary Value Problem for Determination of Permittivity of Dielectric Body in a Waveguide using the Method of Volume Singular Integral Equation

Abstract

The problem of diffraction of an external electromagnetic field by a locally nonhomogeneous body in a perfectly conducting waveguide is examined. 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 L₂ are proved. A numerical Galerkin method for the solution of VSIE is proposed and its convergence is proved.
Inverse boundary value problem for determination of permittivity of dielectric body in a waveguide is reduced to the nonlinear volume singular integral equation.