Application of singular integral equations for solving problems of wave diffraction on an array composed of irregular planar strips

Abstract

While studying the diffraction of electromagnetic waves on ideally conducting arrays, the solution to electrodynamic boundary value problems is traditionally reduced to that of the first or second boundary value problem of mathematical physics. However, variation in the geometry of the structure that we deal with and allowance for its physical parameters (e.g., the impedance) that were not previously taken into account result in the complication of the mathematical model under consideration. Solving electrodynamic boundary value problems for superconductors and superconducting coatings suggests introducing impedance boundary conditions [1]. This corresponds to solving the third and fourth boundary value problems for such structures (with allowance for connection of the normal and tangential derivatives). In this paper, an approach is proposed based on employing the Kontorovich–Lebedev integral transformation and singular integral equations. This approach is used for solving problems of wave diffraction on a three-dimensional array consisting of irregular planar impedance strips on which the third and fourth boundary conditions are given.