Acoustic infinite elements for non-separable geometries

We present new infinite element formulations for solving acoustic scattering and radiation problems in the exterior of long, slender bodies. The new infinite elements are geometrically constructed from a prolate spheroid inscribed by the scatterer. These elements need not begin on a level surface of the prolate spheroidal coordinate system. Instead, they may be attached to any convex surface, including that of the scatterer itself. This scheme reduces, or even completely eliminates, finite element modeling of the exterior medium. The formulations may easily be extended to the cases of an interior oblate spheroid or ellipsoid. We present both conjugated and unconjugated formulations without any weighting factors, although it would be simple to include them. We describe a fast numerical scheme for computing the element integrals based on Chebychev approximation. We include numerical results for scattering from spheres and capped cylinders. These results demonstrate the accuracy and the dramatic reduction in computational expense of our new formulations compared to other coupled finite element/infinite element methods.