Generalized Sommerfeld approach for the coated metallic bodies excitation

It is well known that the classical Fourier method is not applicable to the diffraction problems if an obstacle boundary is not a coordinate surface. Projection methods of the Galerkin´s type are the natural generalizations of the Fourier method, especially their non-complete variants using the Fourier expansions in terms of eigenfunctions of an angular operator. According to such a scheme, the unknown coefficient evaluation can be reduced to a boundary value problem for an infinite system of ordinary differential equations with variable matrix. One can solve the corresponding truncated system numerically to obtain an approximate solution to the problem. Nevertheless, the slow convergence of the approximate solution compared to the exact one makes this approach useless in the high-frequency case. Sommerfeld solution of diffraction problems for a sphere or circular cylinder using singular eigensolutions of the radial operator as an expansion basis is the single known example of a series that rapidly converges in the high-frequency region