  A numerical method for solving the equations modeling acoustic scattering is
presented. The method is capable of handling several dozen scatterers, each of
which is several wave-lengths long, on a personal work station. Even for
geometries involving cavities, solutions accurate to seven digits or better
were obtained. The method relies on a Boundary Integral Equation formulation of
the scattering problem, discretized using a high-order accurate Nystr\"om
method. A hybrid iterative/direct solver is used in which a local scattering
matrix for each body is computed, and then GMRES, accelerated by the Fast
Multipole Method, is used to handle reflections between the scatterers. The
main limitation of the method described is that it currently applies only to
scattering bodies that are rotationally symmetric.
