随机障碍散射中远场统计的快速计算
Rapid computation of far-field statistics for random obstacle scattering
AI总结：
本文研究了随机障碍散射问题中远场统计的数值近似，提出通过引入人工界面直接计算Cauchy数据的二阶统计量，从而快速评估散射波的远场统计特性，并利用低秩近似减少计算成本。
摘要：
本文考虑了在随机障碍散射问题中远场统计的数值近似。特别是，我们考虑了远场模式和远离散射体的散射波的期望值以及相应的方差的计算。为此，我们引入一个人工界面，几乎必然包含所有随机散射体的实现。在该界面处，我们通过边界积分方程直接近似Cauchy数据的二阶统计量，即期望值和方差。从这些量中，我们能够快速评估外部域内散射波的统计特性，包括远场的期望值和方差。通过利用Cauchy数据的两点相关函数的低秩近似，我们大大降低了计算散射波方差的成本。数值结果被提供以证明所提出方法的可行性。
英文摘要：
In this article, we consider the numerical approximation of far-field statistics for acoustic scattering problems in the case of random obstacles. In particular, we consider the computation of the expected far-field pattern and the expected scattered wave away from the scatterer as well as the computation of the corresponding variances. To that end, we introduce an artificial interface, which almost surely contains all realizations of the random scatterer. At this interface, we directly approximate the second order statistics, i.e., the expectation and the variance, of the Cauchy data by means of boundary integral equations. From these quantities, we are able to rapidly evaluate statistics of the scattered wave everywhere in the exterior domain, including the expectation and the variance of the far-field. By employing a low-rank approximation of the Cauchy data's two-point correlation function, we drastically reduce the cost of the computation of the scattered wave's variance. Numerical results are provided in order to demonstrate the feasibility of the proposed approach.
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