Windowed Green function method for the Helmholtz equation in the presence of multiply layered media
Windowed Green function method for the Helmholtz equation in the presence of multiply layered media
复制标题
存在多层介质时亥姆霍兹方程的加窗格林函数法
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Carlos P'erez
中科院分区：
文献类型：
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作者：
Oscar P. Bruno;Carlos P'erez
本文提出了一种新的方法来解决问题的二维和三维声散射（特别是二维电磁散射）的障碍物和缺陷中存在的任意数量的可穿透层。依赖于使用某些缓慢上升的窗口函数，所提出的窗口绿色函数的方法有效地评估振荡积分在无界域，具有高精度，而不求助于非常昂贵的索末菲积分，通常被用来占底层平面多层结构的效果。所提出的方法，其理论基础在最近的贡献中提出（Bruno et al. 2016 SIAM J. Appl. Math. 76，1871-1898. (doi：10.1137/15 M1033782）），快速、准确、灵活且易于实施。我们的数值实验表明，从所提出的方法产生的数值误差减少速度比任何负功率的窗口大小。在本文中考虑的一些例子中，所提出的方法是上千倍的速度，对于给定的精度，比相应的方法的基础上使用索末菲积分。
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 the presence of an arbitrary number of penetrable layers. Relying on the use of certain slow-rise windowing functions, the proposed windowed Green function approach 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 multilayer structures. The proposed methodology, whose theoretical basis was presented in the recent contribution (Bruno et al. 2016 SIAM J. Appl. Math. 76, 1871–1898. (doi:10.1137/15M1033782)), 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 the use of Sommerfeld integrals.