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In this paper, exact solutions to the problem of acoustic scattering by elastic spherical symmetric scatterers are developed. The scatterer may consist of an arbitrary number of fluid and solid layers, and scattering with single Neumann conditions (replacing Neumann-to-Neumann conditions) is added. The solution is obtained by separation of variables, resulting in an infinite series which must be truncated for numerical evaluation. The implemented numerical solution is exact in the sense that numerical error is solely due to round-off errors, which will be shown using the symbolic toolbox in MATLAB. A system of benchmark problems is proposed for future reference. Numerical examples are presented, including comparisons with reference solutions, far-field patterns and near-field plots of the benchmark problems, and time-dependent solutions obtained by Fourier transformation.

Isogeometric analysis (IGA) has proven to be an improvement on the classical finite element method (FEM) in several fields, including structural mechanics and fluid dynamics. In this paper, the performance of IGA coupled with the infinite element method (IEM) for some acoustic scattering problems is investigated. In particular, the simple problem of acoustic scattering by a rigid sphere, and the scattering of acoustic waves by an elastic spherical shell with fluid domains both inside and outside, representing a full acoustic-structure interaction (ASI) problem. Finally, a mock shell and a simplified submarine benchmark are investigated.The numerical examples include comparisons between IGA and the FEM. Our main finding is that the usage of IGA significantly increases the accuracy compared to the usage of C 0 FEM due to increased inter-element continuity of the spline basis functions.

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