Schwinger variational principle calculations of wave scattering from conducting cylinders using physically motivated trial functions

The Schwinger variational principle for the scattering amplitude is applied to two related test problems: an infinitely long perfectly conducting circular cylinder and a hemicylindrically embossed plane illuminated by a normally incident plane wave whose magnetic field is perpendicular to the cylinder axis (TM polarization). It is demonstrated that the variational principle yields very good results with trial functions containing only a few variational parameters, provided the trial functions mimic not only the correct boundary conditions on the scatterer surface but also the expected shadowing effects of the obstacle. A variety of analytical variational limits for both low and high frequencies are derived, which, together with the numerical results for intermediate frequencies, compare very favorably with the available exact solutions.