具有多重分层介质的亥姆霍兹方程的窗口绿色函数方法
Windowed Green Function method for the Helmholtz equation in presence of multiply layered media
AI总结：
本文提出了一种新的方法，用于解决二维和三维声学散射（特别是二维电磁散射）问题，该方法在存在任意数量穿透层的情况下高效计算振荡积分，无需使用昂贵的 Sommerfeld 积分。
摘要：
本文提出了一种新的方法，用于解决二维和三维声学散射（特别是二维电磁散射）问题，该方法在存在任意数量穿透层的情况下高效计算振荡积分，无需使用昂贵的 Sommerfeld 积分。所提出的方法（其理论基础在最近的 SIAM J. Appl. Math. 76(5), p. 1871, 2016 中已给出）速度快、准确、灵活且易于实现。数值实验表明，所提出方法的数值误差随着窗口大小的负幂减少得更快。在本文讨论的多个例子中，所提出的方法在给定精度下比基于 Sommerfeld 积分的方法快多达数千倍。
英文摘要：
This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in presence an arbitrary number of penetrable layers. Relying on use of certain slow-rise windowing functions, the proposed Windowed Green Function approach (WGF) efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to the highly expensive Sommerfeld integrals that have typically been used to account for the effect of underlying planar multi-layer structures. The proposed methodology, whose theoretical basis was presented in the recent contribution (SIAM J. Appl. Math. 76(5), p. 1871, 2016), is fast, accurate, flexible, and easy to implement. Our numerical experiments demonstrate that the numerical errors resulting from the proposed approach decrease faster than any negative power of the window size. In a number of examples considered in this paper the proposed method is up to thousands of times faster, for a given accuracy, than corresponding methods based on use of Sommerfeld integrals.
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