A numerical method for solving a pseudodifferential equation in the diffraction problem in layers connected through a hole

The paper is devoted to the solvability of boundary value problem of diffraction for Maxwell equations in layers connected though a hole. The layers are formed by three infinitely thin and perfectly conducting parallel planes. Electromagnetic parameters can be different in the layers. Radiation conditions by Werner-Sveshnikov are used at the infinity. Method of Green functions is applied for reduction of boundary value problem to the pseudodifferential equation on a hole in Sobolev spaces. Fredholm property is established. The problem belongs to the class of problems of connection of volumes via a hole.