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An efficient and highly accurate solver for multi-body acoustic scattering problems involving rotationally symmetric scatterers

机译:一个高效,高精度的求解器,用于解决涉及旋转对称散射体的多体声散射问题

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摘要

A numerical method for solving the equations modeling acoustic scattering in three dimensions is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries involving cavities, solutions accurate to seven digits or better were obtained. The method relies on a Boundary Integral Equation formulation of the scattering problem, discretized using a high-order accurate Nystroem method. A hybrid iterative/direct solver is used in which a local scattering matrix for each body is computed, and then GMRES, accelerated by the Fast Multipole Method, is used to handle reflections between the scatterers. The main limitation of the method described is that it currently applies only to scattering bodies that are rotationally symmetric.
机译:提出了一种求解三维三维声散射方程的数值方法。该方法能够在个人工作站上处理几十个散射体,每个散射体的波长长。即使对于涉及空腔的几何形状,也可以获得精确到7位数或更佳的解。该方法依赖于散射问题的边界积分方程公式,该公式使用高阶精确Nystroem方法离散化。使用混合迭代/直接求解器,其中计算每个物体的局部散射矩阵,然后使用通过快速多极方法加速的GMRES处理散射体之间的反射。所描述的方法的主要局限性在于,它目前仅适用于旋转对称的散射体。

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