一种用于振荡晶格和的快速求和方法。
A Fast Summation Method for Oscillatory Lattice Sums.
作者信息
Denlinger Ryan, Gimbutas Zydrunas, Greengard Leslie, Rokhlin Vladimir
机构信息
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1110.
National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305.
出版信息
J Math Phys. 2017;58(2). doi: https://doi.org/10.1063/1.4976499.
We present a fast summation method for lattice sums of the type which arise when solving wave scattering problems with periodic boundary conditions. While there are a variety of effective algorithms in the literature for such calculations, the approach presented here is new and leads to a rigorous analysis of Wood's anomalies. These arise when illuminating a grating at specific combinations of the angle of incidence and the frequency of the wave, for which the lattice sums diverge. They were discovered by Wood in 1902 as singularities in the spectral response. The primary tools in our approach are the Euler-Maclaurin formula and a steepest descent argument. The resulting algorithm has super-algebraic convergence and requires only milliseconds of CPU time.
我们提出了一种快速求和方法，用于求解具有周期性边界条件的波散射问题时出现的那种晶格和。虽然文献中有多种用于此类计算的有效算法，但这里提出的方法是新的，并且能对伍德异常进行严格分析。当以特定的入射角和波频率组合照射光栅时会出现伍德异常，此时晶格和发散。它们在1902年由伍德发现，是光谱响应中的奇点。我们方法的主要工具是欧拉 - 麦克劳林公式和最速下降论证。所得算法具有超代数收敛性，并且只需要几毫秒的CPU时间。
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