Scattering by a hybrid asymptotic/finite element method Original Research Article

We describe a hybrid asymptotic/finite element method with application to the solution of the Helmholtz equation for large wavenumber. Thus, this method is suitable to compute the acoustic field radiated or scattered by acoustically large objects. The method is based on patching a short wavelength asymptotic expansion of the ‘outer’ field to an FEM interpolation of the ‘inner’ field. The patching takes place on an artificial boundary. Continuity of the field and its normal derivative across the artificial boundary is enforced weakly in a variational setting. The variational principle is described, as is an element-like implementation strategy. Two example applications are included: diffraction by a truncated wedge and radiation by a source on a wave bearing surface.