Method of Boundary Integral Equations in the Problem of Diffraction of a Monochromatic Electromagnetic Wave by a System of Perfectly Conducting and Piecewise Homogeneous Dielectric Objects

Abstract

We consider the three-dimensional problem of diffraction of a monochromatic electromagnetic wave by a system of objects of various physical nature, including dielectric bodies (domains), perfectly conducting bodies, and perfectly conducting screens. The perfectly conducting bodies may be placed in an exterior medium or immersed into the dielectric domains. In addition, the perfectly conducting screens may reside at the interface of the dielectric domains, being part of each of those. We give a boundary value problem for the Maxwell equations that describes the electromagnetic field under consideration. Integral representations are derived for the electromagnetic field in terms of surface integrals, and the boundary value problem is reduced to a system of boundary integral equations containing weakly and strongly singular surface integrals. The integral equations are written on the dielectric and perfectly conducting parts of the interface between the dielectric domains, on the surfaces of the perfectly conducting bodies, and on the perfectly conducting screens.