Fast iterative solution of acoustic multiple scattering problems

Abstract

Multiple scattering (MS) of waves by a system of scatterers is of great theoretical and practical importance. It is required in a wide variety of physical contexts such as the implementation of “invisibility” cloaks, the effective parameter characterization, etc. An iteratively computable Neumann series (NS) expansion technique is employed to expedite the MS solution. The method works if the spectral radius of the interaction matrix is less than one. The spectral properties of this matrix are investigated for different configurations of cylinders; the validity of solution is shown by modifying the number of scatterers M and their separation distance, d. The iterative solution works well for two rigid cylinders at any considered values of frequency,ω and d. The results show that the iterative algorithm is fast. The convergence rate analysis shows that the effectiveness of technique depends on the M, ω and d. Shrinking d, and rising M and ω weaken the convergence. We improve the algorithm by accelerating the overall convergence characteristics of NS. We use matrix manipulation and renormalization techniques provided for MS of fast atomic nuclei to improve NS convergence, and employ Padé approximants to expand the validity range of NS solutions. The iterative approach can be extended for a band of frequencies, and applied for multi-frequency wave propagation problems.