Numerical comparison of the Green's function and the Waterman and Rayleigh theories of scattering from a cylinder with arbitrary cross-section

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Abstract
Until now much has been published of a theoretical nature concerning the validity or invalidity of the Rayleigh and Waterman methods for evaluating the field scattered from isolated perfectly conducting cylinders of arbitrary shape; however, little of conclusive, concrete nature has ensued. In the paper we propose to establish the conditions (if any) under which these methods may be employed with a reasonable degree of confidence in numerical applications. For this purpose, a description is given of one numerical technique appropriate to the Waterman theory, three numerical approaches to the Rayleigh theory and three numerical techniques for the now classical Green's function approach. The numerical results obtained from the latter are compared with those of the Rayleigh and Waterman methods in eighteen test cases covering a variety of cylinder shapes, incident angles and wavelengths. It is shown that the Rayleigh and Waterman methods yield accurate numerical results in all cases in which they lead to satisfactory verification of conservation of energy, and that all attempts fail to extract valid results from the Rayleigh theory in the case of oblique incidence on square and elliptical cylinders.

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