Computation of acoustic acattering from objects in Shallow waters by conventional and fast multipole BEM

The Shallow-water environment has significant influences on the acoustic scattering from objects, but the characteristics are quite different from those of free-space problems. A high-performance numerical model of conventional and fast multipole BEM based on Burton-Miller formulation for acoustic scattering from objects in shallow-water waveguides is established for the first time. The numerical model is also combined with the well-developed sound propagation theory for ocean acoustics; the mirror image method is adopted for the near-field problem; and, the normal mode method (i.e. the famous open-source code kraken) is chosen for the far-field problem. The time and space complexities of conventional and fast multipole BEM are compared and analyzed by the computation of different-scale problems. The algorithms are validated by comparison with the scattering results of a rigid sphere situated in a shallow-water waveguide, computed by each method. The horizontal directivity and the frequency responses of scattering from different objects in shallow-water waveguides are computed, and the shallow-water target echoes are obtained by inverse FFT. The results show that, the complexity of conventional BEM is at least O(N
²
), and the fast multipole BEM is O(N log N). Combined with these two methods, various-scale problems can be computed efficiently. The multipath effects of shallow-water waveguides bring in obvious interferences in the space domain; a `comb filter' effect in the frequency domain; and, also large extension of the target echoes in the time domain. Such characteristics are rather like that of sound propagation problems in the ocean waveguide. Further, it can be found that, at least for simple objects, the frequency characteristics of the scattering are controlled by the shallow-water waveguide, and different objects only take on modulation effects on the amplitude of the frequency response, which are completely different from those of free-space problems.