An advanced computational method for radiation and scattering of acoustic waves in three dimensions

The method proposed in this paper provides a computational method for implementing the Helmholtz integral formula for acoustic radiation and scattering problems associated with arbitrary shaped three-dimensional bodies. In particular an isoparametric element formulation is used in which both the surface geometry and the acoustic variables on the surface of the body are represented by second-order shape functions within the local coordinate system. A general formula for the surface velocity potential and the exterior field is derived. This result is applicable to nonsmooth bodies, i.e., it includes the case where the surface may have a nonunique normal (e.g., at the edge of a cube). Test cases are shown involving spherical, cylindrical, and cubical geometry.