An FMM for orthotropic periodic boundary value problems for Maxwell's equations
An FMM for orthotropic periodic boundary value problems for Maxwell's equations
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DOI：
10.1080/17455030802616863
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发表时间：
2009-02
影响因子：
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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
本文提出了一种求解三维正交各向异性麦克斯韦方程组周期问题的快速多极子方法。本文研究二维介质散射体阵列在两个正交方向上以不同的周期长度周期性排列的散射问题。利用周期绿色函数的多极展开和局部展开来加速积分方程的求解。我们推导出周期性的绿色函数及其衍生物的傅立叶积分表达式，这是我们制定的基本成分。所提出的FMM中使用的细胞不是立方的，因为我们确定的FMM树中的“0级细胞”的周期性结构的单位细胞。我们展示了FMM算法引入非立方细胞所需的修改。通过数值试验，我们得出结论，该方法是有效的和准确的。
This paper presents a Fast Multipole Method (FMM) for orthotropic periodic problems for Maxwell's equations in 3D. We consider scattering problems where two-dimensional arrays of dielectric scatterers are arranged periodically with different periodic lengths in two orthogonal directions. The multipole and local expansions of the periodic Green function are used for accelerating the solution of the integral equations. We derive Fourier integral expressions for the periodic Green function and its derivatives, which are essential ingredients in our formulation. The cells used in the proposed FMM are not cubic because we identify the unit cell of the periodic structure with the ‘level 0 cell’ in the FMM tree. We show modifications required to the FMM algorithm for introducing non-cubic cells. Through numerical tests we conclude that the proposed method is efficient and accurate.