An FMM for periodic boundary value problems for cracks for Helmholtz' equation in 2D
An FMM for periodic boundary value problems for cracks for Helmholtz' equation in 2D
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DOI：
10.1002/nme.2077
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发表时间：
2008-01
影响因子：
2.9
通讯作者：
Y. Otani;N. Nishimura
中科院分区：
文献类型：
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作者：
Y. Otani;N. Nishimura
本文提出了一种用于解决二维亥姆霍兹方程周期性边值问题的 FMM（快速多极子方法）。周期性格林函数是我们公式中的重要组成部分，它可以在傅里叶分析的帮助下有效计算。我们通过将获得的数值结果与传统方法计算的结果进行比较来验证所提出的方法。然后，我们将所提出的方法应用于分析周期性裂纹阵列的散射问题，并绘制能量透射率与波数的关系图。阻带和相关现象可以清晰地观察到。版权所有 © 2007 约翰·威利父子有限公司
This paper presents an FMM (fast multipole method) for periodic boundary value problems for Helmholtz' equation in 2D. The periodic Green function is an important ingredient in our formulation, which is computed efficiently with the help of the Fourier analysis. We validate the proposed method by comparing the obtained numerical results with those computed with the conventional approach. We then apply the proposed method to the analysis of scattering problems for periodic array of cracks and plot the energy transmittance vs wave numbers. The stopband and related phenomena are observed clearly. Copyright © 2007 John Wiley & Sons, Ltd.