Multiple scattering from many bounded obstacles: An improved matrix formulation

Abstract

The acoustic scattering from many interacting, bounded, three-dimensional obstacles has been treated by several authors [see for example, V. Twersky, J. Math. Phys. 8, 589 (1967) or B. Peterson and S. Ström, J. Acoust. Soc. Am. 56, 771 (1974)]. In particular, Peterson and Ström exended the single-scatterer transition (T) matrix formalism to several obstacles (including all orders of multiple scattering) by using the translation properties of the spherical basis functions to translate the multiple scattered fields of each scatterer. However, for numerically exact results, the present state of development is cumbersome to apply to more than two scatterers, and convergence of the rescattering matrices is sensitive to scatterer separation. in this paper, an improved matrix formalism, which also incorporates the single-scatterer T matrix and sums the multiple-scattering series exactly, is given by using the transformation between the cylindrical and spherical basis sets to perform the translations among the origins of the various scatterers in the cylindrical basis set. A formalism that is both simpler and less numerically sensitive to the separation of the various obstacles results. Exact numerical calculations of the scattering from a linear array of as many as ten spherical scatterers are presented.