A space-time parallel solver for the three-dimensional heat equation
Forschungszentrum Jülich（于利希研究中心）；Università della Svizzera italiana（瑞士意大利大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Bergische Universität Wuppertal（伍珀塔尔大学）
Robert Speck, Daniel Ruprecht, Matthew Emmett, Matthias Bolten, Rolf Krause
本文提出将时间并行的PFASST方法与空间并行的多网格方法结合，实现三维热方程的高效并行求解，通过在Cray XE6和IBM Blue Gene/Q上进行并行扩展测试，展示了空间和时间并行化的有效性。
摘要：
本文介绍了将时间并行的“空间和时间并行全近似方案”（PFASST）与空间并行的多网格方法（PMG）结合，从而得到一个基于网格的三维热方程求解器，具有独特的高效并发性。报告了在Cray XE6机器“Monte Rosa”上至多16,384个核心和IBM Blue Gene/Q系统“JUQUEEN”上至多65,536个核心上的并行扩展测试。通过展示PFASST与PMG结合后显著扩展强标度极限，证明了空间和时间并行化的效果。讨论了在PFASST的多级层次结构中使用空间粗化策略在大规模并行模拟中的影响。
英文摘要：
The paper presents a combination of the time-parallel "parallel full approximation scheme in space and time" (PFASST) with a parallel multigrid method (PMG) in space, resulting in a mesh-based solver for the three-dimensional heat equation with a uniquely high degree of efficient concurrency. Parallel scaling tests are reported on the Cray XE6 machine "Monte Rosa" on up to 16,384 cores and on the IBM Blue Gene/Q system "JUQUEEN" on up to 65,536 cores. The efficacy of the combined spatial- and temporal parallelization is shown by demonstrating that using PFASST in addition to PMG significantly extends the strong-scaling limit. Implications of using spatial coarsening strategies in PFASST's multi-level hierarchy in large-scale parallel simulations are discussed.
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