Efficient computation of 3-D acoustical scattering from multiple arbitrarily shaped objects using the boundary element method/fast multipole method (BEM/FMM)

Abstract

Many applications require computation of acoustic fields in systems consisting of a large number of scatterers, which may have complex shape. Despite the boundary element method being a well-known technique for solution of the boundary value problems for the Helmholtz equation, its capabilities are usually limited by the memory and speed of computers, and conventional methods can be applicable to relatively small (up to order of 10<th>000 boundary elements) problems. We developed and implemented an efficient computational technique, based on an iterative solver employing generalized minimal residual method in combination with matrix-vector multiplication speeded up with the fast multipole method. We demonstrate that this technique has O(N) memory and computational complexity and enables solution of problems with thousands of scatterers (millions of boundary elements) on a desktop PC. The test problems solved are of moderate frequency (up to kD≤150, where k is the wavenumber and D is the size of the computational domain). Solution of large scale scattering problems was tested by comparison with the FMM-based T-matrix method applicable for simple shape objects reported earlier [Gumerov and Duraiswami, J. Acoust. Soc. Am., 117(4), 1744–1761 (2005)], visualization, and physical interpretation of the results.