Intel Corporation, University of Notre Dame, Notre Dame, IN, United States of America.
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, United States of America.
PLoS One. 2022 Nov 22;17(11):e0277940. doi: 10.1371/journal.pone.0277940. eCollection 2022.
Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of time and energy. In this paper, we propose communication-efficient parallel algorithms for solving partial differential equations that alleviate this overhead. First, we describe an asynchronous algorithm that removes the requirement of synchronization and checks for termination in a distributed fashion while maintaining the provision to restart iterations if necessary. Then, we build on the asynchronous algorithm to propose an event-triggered communication algorithm that communicates the boundary values to neighboring processors only at certain iterations, thereby reducing the number of messages while maintaining similar accuracy of solution. We demonstrate our algorithms on a successive over-relaxation solver for the pressure Poisson equation arising from variable density incompressible multiphase flows in 3-D and show that our algorithms improve time and energy efficiency.
在并行计算机上使用区域分解方法求解偏微分方程的数值解通常需要处理器之间的同步和通信。这些操作在时间和能量方面通常会有很大的开销。在本文中，我们提出了一种用于求解偏微分方程的通信高效并行算法，以减轻这种开销。首先，我们描述了一种异步算法，该算法以分布式的方式去除了同步的要求，并检查终止情况，同时在必要时提供重新启动迭代的功能。然后，我们基于异步算法提出了一种事件触发的通信算法，该算法仅在某些迭代时将边界值通信到相邻的处理器，从而减少了消息的数量，同时保持了类似的解的准确性。我们在三维可变密度不可压缩多相流的压力泊松方程的逐次超松弛求解器上验证了我们的算法，并表明我们的算法提高了时间和能量效率。
