SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page C245-C264, January 2020.
Multidimensional discrete Fourier transforms (DFTs) are typically decomposed into multiple one-dimensional (1D) transforms. Hence, parallel implementations of any multidimentional DFT focus on parallelizing within or across the 1D DFT. Existing DFT packages exploit the inherent parallelism across the 1D DFTs and offer rigid frameworks, that cannot be extended to incorporate both forms of parallelism and various data layouts to enable some of the parallelism. However, in the era of exascale, where systems have thousand of nodes and intricate network topologies, flexibility and parallel efficiency are key aspects all multidimentional DFT frameworks need to have in order to map and scale the computation appropriately. In this work, we show the need for a versatile parallel framework that facilitates the development of a family of parallel multidimentional DFT algorithms by (1) using different data layouts to distribute the data across the compute nodes, (2) exploiting the two different parallelization schemes to different degrees, and (3) unifying the two parallelization schemes within a single framework. We show that the flexibility of selecting different parallel multidimentional DFT algorithms allows for almost linear strong scaling results for problem sizes of $1024^3$ on two supercomputers, namely, RIKEN's K-Computer and Oakridge's Summit.

中文翻译：

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多维DFT的灵活框架

SIAM科学计算杂志，第42卷，第5期，第C245-C264页，2020年1月。
多维离散傅里叶变换（DFT）通常分解为多个一维（1D）变换。因此，任何多维DFT的并行实现都集中在1D DFT内或跨1D DFT的并行化。现有的DFT软件包利用了一维DFT的固有并行性，并提供了严格的框架，这些框架无法扩展为结合并行形式和各种数据布局以实现某些并行性。但是，在亿万富翁时代，系统具有成千上万个节点，网络拓扑复杂，灵活性和并行效率是所有多维DFT框架都需要具备的关键方面，以便适当地映射和缩放计算。在这项工作中 我们显示出需要一种通用的并行框架，该框架通过（1）使用不同的数据布局在计算节点上分布数据，（2）在不同程度上利用两种不同的并行化方案，来促进一系列并行多维DFT算法的开发（3）将两个并行化方案统一在一个框架内。我们表明，选择不同的并行多维DFT算法的灵活性允许在两台超级计算机（即RIKEN的K-计算机和Oakridge的Summit）上对$ 1024 ^ 3 $的问题大小进行几乎线性的强缩放结果。（3）将两个并行化方案统一在一个框架内。我们表明，选择不同的并行多维DFT算法的灵活性允许在两台超级计算机（即RIKEN的K-计算机和Oakridge的Summit）上对$ 1024 ^ 3 $的问题大小进行几乎线性的强缩放结果。（3）将两个并行化方案统一在一个框架内。我们表明，选择不同的并行多维DFT算法的灵活性允许在两台超级计算机（即RIKEN的K-计算机和Oakridge的Summit）上对$ 1024 ^ 3 $的问题大小进行几乎线性的强缩放结果。