Scalar wave diffraction by axially symmetrical flat system of infinitely thin perfectly conducting circular rings

A new strong mathematically rigorous and numerically efficient method for solving the boundary value problem of scalar wave diffraction by a flat system of infinitely thin circular ring shaped screens is proposed. The method is based on the combination of the Orthogonal Polynomials Approach and on the ideas of the methods of analytical regularization. The solution is generalization of the investigation done for one ring. As a result of the suggested regularization procedure, the initial boundary value problem was equivalently reduced to the infinite system of the linear algebraic equations of the second kind, i.e. to an equation of the type (I+H)x=b, x,b∈l₂-in the space l₂ of square summable sequences. This equation can be solved numerically by means of truncation method with, in principle, any required accuracy.