A fast algorithm for the two-dimensional Helmholtz transmission problem with large multiple scattering configurations

We develop an efficient three-stage algorithm for simulating multiple acoustic scattering by two-dimensional configurations comprising large numbers of penetrable scatterers. Our approach is based on a boundary integral equation reformulation of the Helmholtz transmission partial differential equation, and a reduction of the boundary integral system for computationally efficient evaluation of wave interactions between scatterers. A key ingredient of our algorithm is to represent the interactions between scatterers using expansions of cylindrical wavefunctions. For large numbers of scatterers, this approach facilitates the application of the fast multipole method, leading to linear complexity of the algorithm with respect to the number of scatterers. Numerical results demonstrate the efficiency of our algorithm for configurations containing a few hundred to hundreds of thousands of individual scatterers.