Diffraction of waves by a rectangular cylinder

A rigorous method for solving problems of the diffraction of waves by an ideally conducting rectangular cylinder, regarded as a composite body formed by ″gluing together″ flat ribbons, is proposed. The method is based on the idea of the method of partial inversion of an operator and the method of moments. As a result the problem is reduced to the solution of infinite systems of linear algebraic equations (SLAE). It is shown that the method of reduction is applicable to the solution of these systems. The unknowns are the coefficients in the expansion of the density functions of the surface currents on the faces of the cylinder in a complete system of Gegenbauer polynomials with a weighting factor taking into account the form of the behavior of the currents at the edges. The proposed method incorporates, as a special case, a new rigorous solution of the problem of diffraction of waves by a collection of flat ribbons with parallel generatrices. The characteristics of the distribution of the currents on the faces of a rectangular cylinder, the total scattering cross section, and the radiation pattern of the scattered field are studied based on a numerical calculations.