Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres

Abstract

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two-and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.

The fast multipole method and Fourier convolution for the solution of acoustic scattering on regular volumetric grids

“…The collection of scattering spheres was chosen because it is easy to model and because efficient methods can be developed [29, 30] to compute solutions that may be used to validate the FMM. Because the FMM is designed to compute scattering from domains with arbitrarily variable medium characteristics, it can not exploit efficiencies associated with this particular geometry and is, therefore, not the optimum choice for these computations.…”

Estimation of scattering object characteristics for image reconstruction using a nonzero background

“…The calculation for a cylindrical object used an exact solution for a nonradial object consisting of multiple arbitrary-diameter nonconcentric cylinders with parallel axes [9]. The calculation for an elliptical object used a k -space method in which spatial derivatives are implemented in the spatial-frequency domain, the time history is obtained in steps using finite differences, and a perfectly matched boundary is included to avoid reflections from the edge of the spatial domain of the computation [10].…”

Scattering by single physically large and weak scatterers in the beam of a single-element transducer

“…Several works have also examined the effects of the beam shape when considering scattering. [25][26][27][28][29][30][31][32][33] These approaches require the use of simple beam models or simple geometric shapes for the scattering object.…”