Vector problem of electromagnetic wave diffraction by a system of inhomogeneous volume bodies, thin screens, and wire antennas

The vector problem of time-harmonic electromagnetic wave diffraction by a system of non-intersecting solid inhomogeneous bodies, infinitely thin perfectly conducting screens and wire antennas in the semi-classical formulation is considered. The original boundary value problem for Maxwell’s equations is reduced to a new system of singular integral equations over the volume domains, the screen surfaces and antennas, that is, over compact domains of dimension 3, 2, and 1. To obtain the equations, the fields scattererd by the bodies and the screens were represented via volume and surface potentials, respectively. To solve the integral equations approximately, the Galerkin method is applied; basis functions on the body, the screens and antennas are introduced as well as formulas for matrix elements in Galerkin method. Combining potential theory and pseudodifferential calculus allowed to obtain results on solvability of new system of integro-differential equations, as well as to theoretically justify the Galerkin method. To solve the problem of diffraction by obstacles of complex shape, novel subhierarchical approach is applied.