Algebraic multigrid (AMG) is often viewed as a scalable O ( n ) solver for sparse linear systems. Yet, AMG lacks parallel scalability due to increasingly large costs associated with communication, both in the initial construction of a multigrid hierarchy and in the iterative solve phase. This work introduces a parallel implementation of AMG that reduces the cost of communication, yielding improved parallel scalability. It is common in Message Passing Interface (MPI), particularly in the MPI-everywhere approach, to arrange inter-process communication, so that communication is transported regardless of the location of the send and receive processes. Performance tests show notable differences in the cost of intra- and internode communication, motivating a restructuring of communication. In this case, the communication schedule takes advantage of the less costly intra-node communication, reducing both the number and the size of internode messages. Node-centric communication extends to the range of components in both the setup and solve phase of AMG, yielding an increase in the weak and strong scaling of the entire method.

中文翻译：

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使用多步节点感知通信减少代数多重网格中的通信

代数多重网格 (AMG) 通常被视为稀疏线性系统的可扩展 O ( n ) 求解器。然而，由于与通信相关的成本越来越大，AMG 缺乏并行可扩展性，无论是在多重网格层次结构的初始构建还是在迭代求解阶段。这项工作引入了 AMG 的并行实现，它降低了通信成本，提高了并行可扩展性。在消息传递接口 (MPI) 中，特别是在 MPI-everywhere 方法中，安排进程间通信是很常见的，这样无论发送和接收进程的位置如何，都可以传输通信。性能测试显示节点内和节点间通信的成本存在显着差异，从而推动通信重组。在这种情况下，通信调度利用了成本较低的节点内通信，减少了节点间消息的数量和大小。以节点为中心的通信扩展到 AMG 的设置和求解阶段的组件范围，从而增加了整个方法的弱缩放和强缩放。