The development of a fast multipole method (FMM) accelerated iterative solution of the
boundary element method (BEM) for the Helmholtz equations in three dimensions is
described. The FMM for the Helmholtz equation is significantly different for problems with
low and high k D (where k is the wavenumber and D the domain size), and for large
problems the method must be switched between levels of the hierarchy. The BEM requires
several approximate computations (numerical quadrature, approximations of the boundary …