一种调优且可扩展的快速多极方法作为百亿亿级系统的卓越算法
A Tuned and Scalable Fast Multipole Method as a Preeminent Algorithm for Exascale Systems
AI总结：
本文通过多核CPU上的性能调优和可扩展性研究，展示了快速多极方法（FMM）在百亿亿级计算中的潜力，实现了高达32768个进程的弱扩展和2048个进程的强扩展，并讨论了其适用于异构大规模并行架构的特性。
摘要：
在可能在未来百亿亿级计算中发挥重要作用的算法中，快速多极方法（FMM）似乎是一颗冉冉升起的新星。我们之前的工作展示了FMM在GPU集群上的扩展性，问题规模达数十亿未知量。该工作产生了一个极其并行的FMM，可扩展到数千个GPU或数万个CPU。本文报告了在Kraken超级计算机上使用多核CPU进行的性能调优和可扩展性研究。FMM中的所有内核均使用OpenMP并行化，对随机分布在立方体中的10^7个粒子的测试显示，在8个线程上效率为78%。使用SIMD指令对粒子-粒子内核进行调优，使得单核测试中（粒子数10^3-10^7）整体算法加速4倍。并行可扩展性在强扩展和弱扩展中均进行了研究。强扩展测试使用10^8个粒子，非SIMD代码在2048个进程上实现了93%的并行效率，而SIMD优化代码为54%（但仍快2倍）。弱扩展测试使用每个进程10^6个粒子，在32768个进程上实现了72%的效率，最大计算耗时约40秒，评估了超过320亿个未知量。这项工作为我们的观点——FMM有望在百亿亿级计算中发挥主导作用——提供了证据，并在论文末尾讨论了使其特别适合新兴异构大规模并行架构的特征。
英文摘要：
Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the order of billions of unknowns. That work led to an extremely parallel FMM, scaling to thousands of GPUs or tens of thousands of CPUs. This paper reports on a a campaign of performance tuning and scalability studies using multi-core CPUs, on the Kraken supercomputer. All kernels in the FMM were parallelized using OpenMP, and a test using 10^7 particles randomly distributed in a cube showed 78% efficiency on 8 threads. Tuning of the particle-to-particle kernel using SIMD instructions resulted in 4x speed-up of the overall algorithm on single-core tests with 10^3 - 10^7 particles. Parallel scalability was studied in both strong and weak scaling. The strong scaling test used 10^8 particles and resulted in 93% parallel efficiency on 2048 processes for the non-SIMD code and 54% for the SIMD-optimized code (which was still 2x faster). The weak scaling test used 10^6 particles per process, and resulted in 72% efficiency on 32,768 processes, with the largest calculation taking about 40 seconds to evaluate more than 32 billion unknowns. This work builds up evidence for our view that FMM is poised to play a leading role in exascale computing, and we end the paper with a discussion of the features that make it a particularly favorable algorithm for the emerging heterogeneous and massively parallel architectural landscape.
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