A fast high order algorithm for multiple scattering from large sound-hard three dimensional configurations

Abstract

We describe an efficient fast high order algorithm for simulating acoustic scattering in an unbounded three dimensional medium exterior to a configuration with a large number of sound-hard particles. Surface integral representations of the scattered and far fields facilitate reformulation of the model for unknown fields on the closed bounded surface of each particle in the configuration. Our surface integral equation based algorithm uses a multiple scattering variant of complex dense system Krylov subspace techniques combined with an efficient matrix vector product scheme. In this article we develop a memory efficient fast algorithm in three steps using appropriate expansion methods (EM). The first step is based on a radiating basis EM (RadBEM) and the third step is based on a regular basis EM (RegBEM). The second step transforms RadBEM to RegBEM and is accelerated using the well known multilevel fast multipole method. The full algorithm has linear complexity with respect to the number of particles to evaluate quadratically large multiple scattering interactions exterior to the configuration. We present numerical results obtained with our fast algorithm for simulations with up to about twenty thousand sound-hard particles and for large dense complex systems with more than twelve million unknowns. We compare our results with a recent high-order accurate accelerated direct solver by Bremer et al. (2015) and demonstrate substantial computational advantages of our RadBEM–RegBEM algorithm.