An efficient algorithm for simulating scattering by a large number of two dimensional particles

Simulation of waves scattered by a large number of particles is important for several applications---for example, to investigate interactions between particles in an ensemble---and hence to design efficient configurations. Substantial computer memory is required for the direct treatment of an ensemble with hundreds of particles as a single scattering configuration. This memory bottleneck is avoided by using multiple scattering iterative methods, which allow treatment of one particle at a time, but require substantial computing time at each step of the iteration to take into account reflections from the rest of the particles, and require a large number of iterations for convergence. We develop a novel fast, high order, memory efficient algorithm to simulate multiple acoustic scattering induced by an ensemble with hundreds of particles in two space dimensions. References S. Acosta and V. Villamizar. Coupling of Dirichlet-to-Neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering. J. Comput. Phys. , 229:5498--5517, 2010. doi:10.1016/j.jcp.2010.04.011 . A. Anand, Y. Boubendir, F. Ecevit, and F. Reitich. Analysis of multiple scattering iterations for high-frequency scattering problems II: The three-dimensional scalar case. Numer. Math. , 114:373--427, 2010. doi:10.1007/s00211-009-0263-1 . M. Balabane. Boundary decomposition for Helmholtz and Maxwell equations 1: disjoint sub-scatterers. Asymp. Anal. , 38:1--10, 2004. http://iospress.metapress.com/content/vu2bd0w9mkem8966/ . D. Colton and R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory . Springer, 1998. F. Ecevit and F. Reitich. Analysis of multiple scattering iterations for high-frequency scattering problems. I: The two-dimensional case. Numer. Math. , 114:271--354, 2009. doi:10.1007/s00211-009-0249-z . M. Ganesh and S. C. Hawkins. A high-order algorithm for multiple electromagnetic scattering in three dimensions. Numer. Algorithms , 50:469--510, 2009. doi:10.1007/s11075-008-9238-z . M. Ganesh and S. C. Hawkins. Three dimensional electromagnetic scattering T-matrix computations. J. Comp. Appl. Math. , 234:1702--1709, 2010. doi:10.1016/j.cam.2009.08.018 . P. A. Martin. Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles . Cambridge University Press, 2006. M. I. Mishchenko, L. D. Travis, and A. A. Lacis. Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering . Cambridge University Press, 2006.