The fast multipole method (FMM) is an efficient algorithm for calculating electrostatic interactions in molecular simulations and a promising alternative to Ewald summation methods. Translation of multipole expansion in spherical harmonics is the most important operation of the fast multipole method and the fast Fourier transform (FFT) acceleration of this operation is among the fastest methods of improving its performance. The technique relies on highly optimized implementation of fast Fourier transform routines for the desired expansion sizes, which need to incorporate the knowledge of symmetries and zero elements in the input arrays. Here a method is presented for automatic generation of such, highly optimized, routines.

中文翻译：

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用于球谐函数中多极展开变换的 FFT 的自动生成

快速多极法 (FMM) 是计算分子模拟中静电相互作用的有效算法，也是 Ewald 求和方法的有前途的替代方法。球谐函数中多极展开的转换是快速多极方法最重要的运算，而该运算的快速傅立叶变换 (FFT) 加速是提高其性能的最快方法之一。该技术依赖于针对所需扩展大小的快速傅立叶变换例程的高度优化实现，这需要在输入数组中结合对称性和零元素的知识。这里提出了一种自动生成这种高度优化的例程的方法。