PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method
PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method
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DOI：
10.1007/s00791-020-00330-5
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发表时间：
2019-12
影响因子：
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通讯作者：
Ruth Schöbel;R. Speck
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文献类型：
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作者：
Ruth Schöbel;R. Speck
为了在求解含时偏微分方程组时扩展现有的尺度极限，空间和时间并行全近似格式(PFASST)被证明是一种很有前途的时间并行积分器。与时空多重网格类似，PFASST能够同时计算多个时间步长，因此特别适合于高性能计算系统上的大规模应用。在这项工作中，我们将PFASST与并行谱延迟校正(SDC)方法相结合，形成了一种前所未有的双时间并行积分器。当PFASST提供全局、大规模的“跨步骤并行”时，内部并行SDC方法允许使用对角化的局部拟牛顿求解器来集成每个单独的时间步长“跨方法并行”。这种新方法，我们称之为“增强型并发的PFASST”(PFASST-ER)，因此公开了更多的时间并发性。对于两个具有挑战性的非线性反应扩散问题，我们证明了PFASST-ER比PFASST的经典变种更有效，并且可以使用比时间步长更多的处理器。
To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to space–time multigrid, PFASST is able to compute multiple time-steps simultaneously and is therefore in particular suitable for large-scale applications on high performance computing systems. In this work we couple PFASST with a parallel spectral deferred correction (SDC) method, forming an unprecedented doubly time-parallel integrator. While PFASST provides global, large-scale “parallelization across the step”, the inner parallel SDC method allows integrating each individual time-step “parallel across the method” using a diagonalized local Quasi-Newton solver. This new method, which we call “PFASST with Enhanced concuRrency” (PFASST-ER), therefore exposes even more temporal concurrency. For two challenging nonlinear reaction-diffusion problems, we show that PFASST-ER works more efficiently than the classical variants of PFASST and can use more processors than time-steps.