An iterative numerical method for time-harmonic acoustic multiple scattering from complexly shaped obstacles is devised. The classical formulation of multiple scattering problem is transformed into a set of single scattering boundary value problems (BVPs) coupled at their scatterer boundaries. By introducing iterative procedures, the single scattering BVPs are decoupled and a convenient domain truncation technique, employing artificial boundaries, reduces the unbounded domain of the original BVPs to relatively small bounded domain around each scatterer. Then, high order Karp’s farfield expansions absorbing boundary conditions (KFE) are imposed at the artificial boundaries of each scatterer. An overall high order numerical method is constructed by combining these absorbing boundary conditions (ABC) with a high order isogeometric finite element method (IGA) in the interior of the computational domains. We performed ample numerical experiments for complex configuration of scatterers, using the isogeometric finite elements and also finite differences techniques combined with the high order KFE. They show accuracies close to machine precision and high order rate of convergence at relatively low computational costs.

中文翻译：

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高阶局部ABC多重散射的高效迭代方法


设计了一种用于复杂形状障碍物的时谐声多次散射的迭代数值方法。多重散射问题的经典公式被转换为一组在其散射体边界耦合的单散射边界值问题 (BVP)。通过引入迭代过程，单散射 BVP 被解耦，并且一种方便的域截断技术，采用人工边界，将原始 BVP 的无界域减少到每个散射体周围相对较小的有界域。然后，在每个散射体的人工边界处施加高阶卡普远场扩展吸收边界条件 (KFE)。通过将这些吸收边界条件 (ABC) 与计算域内部的高阶等几何有限元方法 (IGA) 相结合，构建了整体高阶数值方法。我们使用等几何有限元以及有限差分技术与高阶 KFE 相结合，对散射体的复杂配置进行了大量的数值实验。它们以相对较低的计算成本显示出接近机器精度的精度和高阶收敛率。