Abstract:
The application of a hybrid asymptotic/finite-element method to the problem of scattering from prismatically shaped objects is considered. The hybrid method is based on patching a short wavelength asymptotic expansion of the scattered field to a finite-element interpolation 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. An asymptotic DtN (Dirichlet-to-Neumann) map on this artificial boundary represents the effect of the outer domain on the solution within this new boundary. 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. The method is applied to diffraction by a blunted wedge, which in this context represents a degenerate prism. The hybrid scattering solution shall be compared to a complete analytic field representation found using matched asymptotic expansions. [Work supported by ONR.]