FFT, FMM, and multigrid methods are widely used fast and highly scalable solvers for elliptic PDEs. However, emerging large-scale computing systems are introducing challenges in comparison to current petascale computers. Recent efforts (Dongarra et al. 2011) have identified several constraints in the design of exascale software that includes massive concurrency, resilience management, exploiting the high performance of heterogeneous systems, energy efficiency, and utilizing the deeper and more complex memory hierarchy expected at exascale. In this paper, we perform a model-based comparison of the FFT, FMM, and multigrid methods in the context of these projected constraints. In addition, we use performance models to offer predictions about the expected performance on upcoming exascale system configurations based on current technology trends.

中文翻译：

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Exascale 之路上的 FFT、FMM 和多重网格：性能挑战和机遇

FFT、FMM 和多重网格方法被广泛用于椭圆偏微分方程的快速且高度可扩展的求解器。然而，与当前的千万亿级计算机相比，新兴的大规模计算系统带来了挑战。最近的努力（Dongarra 等人，2011 年）已经确定了百亿亿级软件设计中的几个限制，包括大规模并发、弹性管理、利用异构系统的高性能、能源效率以及利用百亿亿级预期的更深更复杂的内存层次. 在本文中，我们在这些投影约束的背景下对 FFT、FMM 和多重网格方法进行了基于模型的比较。此外，我们使用性能模型根据当前技术趋势对即将到来的百亿亿次系统配置的预期性能进行预测。