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We consider a two-part method for computing the acoustic scattering T-matrix of a three dimensional particle. The first part involves accurately computing the far fields by solving a number of particular scattering problems. The second part calculates the T-matrix from these far fields using the Fourier transform over the sphere. The two-part method was first introduced in Ganesh and Hawkins [J. Comput. Appl. Math. 234, 1702–1709]. The focus of this work is to demonstrate the numerical stability and physical correctness of the two-part method for scattering by nonspherical particles with large aspect ratios and size parameters that are at the upper limit of numerical stability for the current state-of-the-art algorithm. The numerical stability of the method is attributed to elimination of the Hankel functions by working with the far field. The numerical experiments use our recently developed open-source software package (TMATROM3) that implements the two-part method. [ABSTRACT FROM AUTHOR]

Regarding wave scattering on a three-dimensional nonspherical obstacle, the Rayleigh hypothesis states that the scattered field can be expanded everywhere outside the obstacle using only outgoing eigensolutions of the underlying Helmholtz equation. However, the correctness of this assumption has not yet been finally clarified, although it is important for the near-field analysis of scattering processes and for multiple scattering. To circumvent this uncertainty, Waterman introduced the extended boundary condition to develop his T-matrix method. This approach leads to the restriction that, when modeling multiple scattering processes using this T-matrix, the smallest circumscribing spheres of the individual obstacles must not overlap. The purpose of this paper is to provide a justification of the correctness of Rayleigh's hypothesis and clarify its implications for modeling multiple scattering. We show that Waterman's T-matrix can in fact be used inside the critical region between the surface of the obstacle and its smallest circumscribing sphere to represent the near-field and that one does not necessarily have to exclude an overlap of these spheres in the multiple scattering modeling. The theoretical considerations in the first part of this paper are supplemented by a numerical study of a benchmark configuration for multiple scattering in the last part. [ABSTRACT FROM AUTHOR]

Recently Janus particles have become important in several technological fields because they have interesting properties compared with homogeneous particles. The interaction of Janus particles with sound waves is of particular interest for diagnostic purposes, and also in applications in micro- and nanotechnology. In this paper the authors demonstrate that a method of fundamental solution combined with a T-matrix that is computed from far-field information can be applied with benefit to analyse the scattering of sound waves by a particular type of Janus sphere. Moreover, it is shown that this method converges faster than the conventional T-matrix method introduced by Waterman [(1969). J. Acoust. Soc. Am. 45, 1417–1429]. This is of special importance if orientation averaged scattering quantities are required, or if multiple scattering processes on Janus spheres are considered. This method is used to demonstrate the interesting phenomenon of an enhanced side scattering intensity that is larger than the forward scattering intensity, and that this effect can be strengthened using a particular configuration of two identical Janus spheres. Finally, the authors discuss a useful approximation that can be readily applied for two or more Janus spheres. [ABSTRACT FROM AUTHOR]

The impedance matrix method is applied to study the scattering of flexural waves propagating in an infinite thin plate containing an N-beam resonator. The resonator consists of a circular hole containing a smaller plate connected to the background plate by a number N of rectangular beams. After representing the boundary conditions in a modal multipole expansion form, a compact expression is obtained for the T-matrix, which relates the incident and the scattered transverse (out-of-plane) waves. The analysis of the scattering cross-section reveals interesting scattering features, like resonances and anisotropy, associated to this type of resonators. Numerical experiments performed within the framework of the finite element method support the accuracy of the model here developed. [ABSTRACT FROM AUTHOR]

The transition (T) matrix of Waterman has been very useful for computing fast, accurate acoustic scattering predictions for axisymmetric elastic objects, but this technique is usually limited to fairly smooth objects that are not too aspherical unless complex basis functions or stabilization schemes are used. To ease this limitation, a spherical-basis formulation adapted from approaches proposed recently by Waterman [J. Acoust. Soc. Am. 125(1), 42-51 (2009)] and Doicu, Eremin, and Wriedt [Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources (Academic, London, 2000)] is suggested. This is implemented by simply transforming the high-order outgoing spherical basis functions within standard T-matrix formulations to low-order functions distributed along the object's symmetry axis. A free-field T matrix is produced in a nonstandard form, but computations with it become much more stable for elongated aspherical elastic shapes. Some advantages of this approach over the approaches of Waterman and Doicu, Eremin, and Wriedt are noted, and sample calculations for a 10:1 Al prolate spheroid and a 10:1 Al super-spheroid of order 10 are given to demonstrate the enhanced stability. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Multiple scattering of acoustic waves in a planar horizontal waveguide by finite-length cylinders is considered. Cylinder height equals the waveguide depth, and both are vertically constrained by the pressure-release boundaries. An analytically exact solution is obtained via normal mode expansion method in conjunction with the concept of the T matrix. The problem is decomposed into an infinite number of two-dimensional multiple scattering problems, modulated by waveguide mode shapes. Examples are presented for an isovelocity waveguide in which the medium is uniform and the waveguide depth is constant. It is found that, in numerical computations, including one or two evanescent modes captures the essence of the evanescent modes. Multiple scattering in the waveguide is compared with the corresponding two-dimensional case. It is concluded that, in low frequencies, the wave patterns in the two cases are very similar, with a shift in the frequency. The similarity diminishes when there are multiple propagating modes. Despite the mode mixing, some key features in the scattering as observed in the two-dimensional problem remain observable in the waveguide case. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]