Fast Hybrid Algorithms For High Frequency Scattering

This paper deals with numerical methods for high frequency wave scattering. It introduces a new hybrid technique that couples a directional fast multipole method for a subsection of it scattering surface to an asymptotic formulation over the rest of the scattering domain. The directional fast multipole method is new and highly efficient for the solution of the boundary integral formulation of a general scattering problem but it requires at least a few unknowns per wavelength on the boundary. The asymptotic method that was introduced by Bruno and collaborators requires much fewer unknowns. Oil the other hand the scattered field must have a simple structure. Hybridization of these two methods retains their best properties for the solution of the full problem, Numerical examples are given for the solution of the Helmholtz equation in two space dimensions.