Abstract:

We consider the application of a hybrid asymptotic/boundary integral equation (BIE) method to the problem of scattering from prismatically shaped objects. The hybrid method is based on patching a short wavelength asymptotic expansion of the scattered field to a BIE evaluation of the near field. In patching, the diffracted field shape functions with unknown amplitude are forced to agree smoothly with the solution in the near field along a curve at a prescribed distance from the diffraction points. This allows us to replace the original boundary value problem with an asymptotically equivalent boundary value problem, the domain of which is small and efficiently discretized. Since the domain of the numerical problem is small and may be chosen at will, we completely circumvent non-uniqueness problems associated with ``forbidden frequencies.'' Thus very high-frequency calculations can be performed using single layer potential equations with no problems of ill conditioning. The hybrid scattering solution shall be compared to a complete analytic field representation found using matched asymptotic expansions. [Work supported by ONR.]