In this letter, the computation of the Green's function for one-dimensional (1-D) periodic structures is presented via a fast and accurate algorithm based on the philosophy of Kummer's decomposition (KD). The KD uses an optimal value for a quasi-periodicity parameter. An approximate optimal balance between direct summation and acceleration is constructed when necessary. The algorithm has been designed for easy extraction and analytical analysis of the irregular structure of the Green's function including logarithmic singularity. The shown numerical results for low- and quite high-frequency values demonstrate the high efficiency and accuracy of the algorithm in comparison with other known approaches. In particular, numerical comparisons to Ewald's and other methods are discussed.

中文翻译：

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一维周期结构格林函数的有效计算

在这封信中，一维 (1-D) 周期结构的格林函数的计算是通过基于库默分解 (KD) 原理的快速准确的算法呈现的。KD 使用准周期性参数的最佳值。必要时构建直接求和和加速之间的近似最佳平衡。该算法旨在轻松提取和分析分析格林函数的不规则结构，包括对数奇异性。所示的低频和相当高频值的数值结果证明了该算法与其他已知方法相比的高效率和准确性。特别是讨论了与 Ewald 和其他方法的数值比较。