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This paper presents a semi-analytical approach to solve the three-dimensional acoustic scattering problems with multiple spheroids subjected to a plane sound wave. The results can provide benchmark solutions that are useful for evaluating the accuracy of various numerical methods. To satisfy the Helmholtz equation in the spheroidal coordinate system, the scattered acoustic field is formulated in terms of radial and angular prolate spheroidal wave functions which also satisfy the radiation condition at infinity. The multipole method, the directional derivative and the collocation technique are combined to propose a collocation multipole method in which the acoustic field and its normal derivative with respect to the non-local spheroidal coordinate system can be calculated without any truncated error, frequently induced by using the addition theorem for a multiply-connected domain problem. The boundary conditions are satisfied by collocating points on the surface of each spheroid. By truncating the higher order terms of the multipole expansion, a finite linear algebraic system is acquired. The scattered field can then be determined according to the given incident sound wave. The convergence analyses considering the specified error, the separation of spheroids and the wave number of an incident wave are first carried out to provide guide lines for the proposed method. Then the proposed results for acoustic scattering by one, two and three spheroids are validated by using the available analytical method and numerical methods such as boundary element method. Finally, the effects of the convexity and orientation of spheroid, the separation between spheroids and the incident wave number and angle on the near-field acoustic pressure and the far-field scattering pattern are investigated.

computation