The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high performance computing systems and/or accelerators. However, these systems face scaling issues such as latency, the fixed cost of communicating information between devices in the system. The swept rule is a technique designed to minimize these costs by obtaining a solution to unsteady equations at as many possible spatial locations and times prior to communicating. In this study, we implemented and tested the swept rule for solving two-dimensional problems on heterogeneous computing systems across two distinct systems. Our solver showed a speedup range of 0.22-2.71 for the heat diffusion equation and 0.52-1.46 for the compressible Euler equations. We can conclude from this study that the swept rule offers both potential for speedups and slowdowns and that care should be taken when designing such a solver to maximize benefits. These results can help make decisions to maximize these benefits and inform designs.

中文翻译：

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二维扫描规则在异构架构中的应用

众所周知，描述可压缩流体流动的偏微分方程很难在实用规模上求解，并且经常需要使用高性能计算系统和/或加速器。但是，这些系统面临扩展问题，例如延迟，系统中设备之间传递信息的固定成本。扫描规则是一种设计用于通过在通信之前在尽可能多的空间位置和时间获得非定常方程的解的方法来最小化这些成本的技术。在这项研究中，我们实施并测试了用于解决跨两个不同系统的异构计算系统上的二维问题的清扫规则。我们的求解器对热扩散方程显示出0.22-2.71的加速范围，对于可压缩Euler方程显示出0.52-1.46的加速范围。从这项研究中我们可以得出结论，后掠规则提供了加速和减速的潜力，在设计这种求解器以最大程度地提高收益时应格外小心。这些结果可以帮助您做出决策，以最大程度地发挥这些优势并为设计提供依据。