The fast Fourier transform (FFT) has applications in almost every frequency related study, for example, in image and signal processing, and radio astronomy. It is also used as a Poisson operator inversion kernel in partial differential equations in fluid flows, in density functional theory, many-body theory, and others. The three-dimensional FFT has large time complexity . Hence, parallelization is used to compute such FFTs. Popular libraries perform slab division or pencil decomposition of data. None of the existing libraries achieve perfect inverse scaling of time with cores because FFT requires all-to-all communication and clusters hitherto do not have physical all-to-all connections. Dragonfly, one of the popular topologies for the interconnect, supports hierarchical connections among the components. We show that if we align the all-to-all communication of FFT with the physical connections of Dragonfly topology we will achieve a better scaling and reduce communication time.

中文翻译：

---

一种在并行快速傅里叶变换中节省 10% 通信时间的调度策略

快速傅里叶变换 (FFT) 几乎在所有与频率相关的研究中都有应用，例如图像和信号处理以及射电天文学。它还用作流体流动偏微分方程、密度泛函理论、多体理论等中的泊松算子反演核。三维FFT 具有较大的时间复杂度。因此，并行化用于计算此类 FFT。流行的图书馆对数据进行平板分割或铅笔分解。现有的库都没有实现完美的时间反向缩放核心，因为 FFT 需要全对全通信，而集群迄今没有物理全对全连接。Dragonfly 是一种流行的互连拓扑结构，支持组件之间的分层连接。我们表明，如果我们将 FFT 的 all-to-all 通信与 Dragonfly 拓扑的物理连接对齐，我们将实现更好的扩展并减少通信时间。