Parallel Processing and Applied Mathematics - 13th International Conference, PPAM 2019, Bialystok, Poland, September 8-11, 2019, Revised Selected Papers, Part I
Parallel Processing and Applied Mathematics - 13th International Conference, PPAM 2019, Bialystok, Poland, September 8-11, 2019, Revised Selected Papers, Part I
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并行处理和应用数学 - 第 13 届国际会议，PPAM 2019，波兰比亚韦斯托克，2019 年 9 月 8-11 日，修订后的精选论文，第一部分
DOI：
10.1007/978-3-030-43229-4_3
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Murray C
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文献类型：
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作者：
Murray C
多重网格算法是椭圆偏微分方程最有效的求解器之一。然而，在开始实际求解之前，我们必须投入昂贵的矩阵设置阶段。这种装配工作是不可忽视的；特别是如果细网格模板集成很费力的话。我们的手稿建议使用非常不准确的几何精细网格模板开始多重网格求解，然后与实际求解并行更新和改进。这种更新可以贪婪地、自适应地实现。我们还建议任何算子更新一次最多传播一层，这确保多尺度信息传播不会阻碍实际求解。如果我们使网格更新序列考虑到多尺度算子信息以有限速度传播，那么增加的异步性（即惰性）会提高运行时间而不损失稳定性。
Multigrid algorithms are among the most efficient solvers for elliptic partial differential equations. However, we have to invest into an expensive matrix setup phase before we kick off the actual solve. This assembly effort is non-negligible; particularly if the fine grid stencil integration is laborious. Our manuscript proposes to start multigrid solves with very inaccurate, geometric fine grid stencils which are then updated and improved in parallel to the actual solve. This update can be realised greedily and adaptively. We furthermore propose that any operator update propagates at most one level at a time, which ensures that multiscale information propagation does not hold back the actual solve. The increased asynchronicity, i.e. the laziness improves the runtime without a loss of stability if we make the grid update sequence take into account that multiscale operator information propagates at finite speed.