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Computation of 3D Scattering from Clusters of Spheres using the Fast Multipole Method

Dr. Nail Gumerov

UMIACS at University of Maryland

Abstract:   A T-matrix based method of solution of the multiple scattering problem presented in our previous publication (JASA, 112, 2002, 2688-2701) in practice can be applied for computation of relatively small size problems (up to hundredes of scatterers), since the number of operations it requires grows with the number of scatterers N as O(N^3). In this study we present a method, which combines iterative techniques with the multilevel fast multipole method which employs fast translation algorithms. We show that in this case the number of operations grows with N as O(N) or O(NlogN) and the method is applicable to solution of problems with large amount of scatterers. We present results of solution of test problems obtained with the method where N can be substantially large (NĄ­10000; depends on the frequency of the acoustic field). We also discuss convergence of the iterative techniques, and investigate dependencies of the errors in solution for different wavenumbers, volume fractions of scatterers, boundary impedances, and other parameters. While the method was tested for spherical scatterers generalized consideration that enables extensions for scatterers of arbitrary shape is presented. [Joint work with Ramani Duraiswami. This study has been supported by the NSF awards 0086075 and 0219681].