Computation of scattering from clusters of spheres using the fast multipole method

TitleComputation of scattering from clusters of spheres using the fast multipole method
Publication TypeJournal Articles
Year of Publication2005
AuthorsGumerov NA, Duraiswami R
JournalThe Journal of the Acoustical Society of America
Pagination1744 - 1761
Date Published2005///
Keywordsacoustic wave scattering, convergence of numerical methods, iterative methods, matrix multiplication

A T-matrix based method of solution of the multiple scattering problem was presented by the authors [J. Acoust Soc. Am. 112, 2688–2701 (2002)]. This method can be applied to the computation of relatively small problems, since the number of operations required grows with the number of spheres N as O(N3), and with the sixth power of the wave number. The use of iterative techniques accelerated using the fast multipole method (FMM) can accelerate this solution, as presented by Koc and Chew [J. Acoust. Soc. Am. 103, 721–734 (1998)] originally. In this study we present a method that combines preconditioned Krylov subspace iterative techniques, FMM accelerated matrix vector products, a novel FMM-based preconditioner, and fast translation techniques that enable us to achieve an overall algorithm in which the cost of the matrix-vector multiplication grows with N as O(N log N) and with the third power of the wave number. We discuss the convergence of the iterative techniques, selection of the truncation number, errors in the solution, and other issues. The results of the solution of test problems obtained with the method for N ∼ 102–104 for different wave numbers are presented. © 2005 Acoustical Society of America.