### A far field based T-matrix method for three dimensional acoustic scattering

#### Abstract

The acoustic scattering properties of an obstacle are completely described by its infinite acoustic T-matrix. The T-matrix is particularly useful when one is interested in analysing changes in sound wave propagation with respect to various changes in orientation or configuration of single or multiple scatterers. This is because the T-matrix is independent of the incoming wave directions and hence can be used to easily simulate the scattered sound waves, without the need to fully set up and solve each reconfigured system. However, in practice one must use the truncated finite dimensional T-matrix, which is usually computed using the null field method. For acoustically large obstacles or highly non-spherical particles the null field method is numerically unstable. In this work we describe an efficient and stable method for computing the truncated T-matrix using a surface integral equation reformulation and a high order acoustic surface scattering algorithm.

**References**- D. Colton and R. Kress.
*Inverse Acoustic and Electromagnetic Scattering Theory*. Springer, 1998. - A. Doicu, T. Wriedt, and Y. Eremin.
*Light Scattering by Systems of Particles. Null-Field Method with Discrete Sources---Theory and Programs*. Springer Verlag, 2006. - M. Ganesh and I. G. Graham. A high-order algorithm for obstacle scattering in three dimensions.
*J. Comput. Phys.*, 198:211--242, 2004. doi:10.1016/j.jcp.2004.01.007. - F. M. Kahnert. Numerical methods in electromagnetic scattering theory.
*J. Quant. Spectrosc. Radiat. Transfer*, 79--80:775--824, 2003. doi:10.1016/S0022-4073(02)00321-7. - P. A. Martin.
*Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles*. Cambridge University Press, 2006. - M. I. Mishchenko, L. D. Travis, and A. A. Lacis.
*Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering*. Cambridge University Press, 2006. - M. I. Mishchenko, L. D. Travis, and D. W. Mackowski. T-matrix computations of light scattering by nonspherical particles: a review.
*J. Quant. Spectrosc. Radiat. Transfer*, 55:535--575, 1996. doi:10.1016/0022-4073(96)00002-7. - B. Peterson and S. Strom. T matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of {E}(3).
*Physical Review D*, 8:3661--3678, 1973. doi:10.1103/PhysRevD.8.3661. - P.C. Waterman. Matrix formulation of electromagnetic scattering.
*Proc. IEEE*, 53:805--812, 1965. - W. J. Wiscombe. Improved Mie scattering algorithms.
*Applied Optics*, 19, 1980. http://www.opticsinfobase.org/abstract.cfm?URI=ao-19-9-1505.

DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1441

**Remember,**for most actions you have to record/upload into this online system

**and then**inform the editor/author via clicking on an email icon or Completion button.

ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.