Bj. Stoyanov et Ra. Farrell, SCHWINGER VARIATIONAL PRINCIPLE CALCULATIONS OF WAVE SCATTERING FROM CONDUCTING CYLINDERS USING PHYSICALLY MOTIVATED TRIAL FUNCTIONS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(2), 1996, pp. 1907-1916
The Schwinger variational principle for the scattering amplitude is ap
plied to two related test problems: an infinitely long perfectly condu
cting circular cylinder and a hemicylindrically embossed plane illumin
ated by a normally incident plane wave whose magnetic field is perpend
icular to the cylinder axis (TM polarization). It is demonstrated that
the variational principle yields very good results with trial functio
ns containing only a few variational parameters, provided the trial fu
nctions mimic not only the correct boundary conditions on the scattere
r surface but also the expected shadowing effects of the obstacle. A v
ariety of analytical variational limits for both low and high frequenc
ies are derived, which, together with the numerical results for interm
ediate frequencies, compare very favorably with the available exact so
lutions.