Multiple Scattering from $N$ Spheres Using Multipole Reexpansion

Abstract. A semi-analytical technique for the solution of problems of wave scattering from multiple spheres is developed. This technique extensively uses the theory for the translation and rotation of Helmholtz multipoles that was developed in our earlier work (Gumerov & Duraiswami, 2001). Results are verified by comparison with commercial boundary element software. The method developed is likely to be very useful in developing fast algorithms for many important problems, including those arising in simulations of composite media and multiphase flow.

[1]  Larry S. Davis,et al.  Efficient evaluation of reverberant sound fields , 2001, Proceedings of the 2001 IEEE Workshop on the Applications of Signal Processing to Audio and Acoustics (Cat. No.01TH8575).

[2]  Ramani Duraiswami,et al.  Fast, Exact, and Stable Computation of Multipole Translation and Rotation Coefficients for the 3-D Helmholtz Equation , 2001 .

[3]  Ramani Duraiswami,et al.  Modeling the effect of a nearby boundary on the HRTF , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[4]  R. Duda,et al.  Modeling the effect of torso on the head‐related transfer function via the boundary‐element method , 2001 .

[5]  V. Ralph Algazi,et al.  Individualized HRTFs using computer vision and computational acoustics , 2000 .

[6]  Jiming Song,et al.  Error Analysis for the Numerical Evaluation of the Diagonal Forms of the Scalar Spherical Addition Theorem , 1999 .

[7]  R. Duda,et al.  Range dependence of the response of a spherical head model , 1998 .

[8]  R. Duraiswami,et al.  Linear pressure waves in fogs , 1995, Journal of Fluid Mechanics.

[9]  Michael A. Epton,et al.  Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations , 1995, SIAM J. Sci. Comput..

[10]  S. Hanish A treatise on acoustic radiation , 1989 .

[11]  Robert I. Nigmatulin,et al.  Sound waves in monodisperse gas-particle or vapour-droplet mixtures , 1988, Journal of Fluid Mechanics.

[12]  P. Morse,et al.  Methods of theoretical physics , 1955 .