Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication has become a significant bottleneck that limits its scalability as processor counts continue to grow on modern machines. This paper examines the design, implementation, and parallel performance of a novel algorithm, Algebraic Multigrid Domain Decomposition (AMG-DD), designed specifically to limit communication. The goal of AMG-DD is to provide a low-communication alternative to standard AMG V-cycles by trading some additional computational overhead for a significant reduction in communication cost. Numerical results show that AMG-DD achieves superior accuracy per communication cost compared to AMG, and speedup over AMG is demonstrated on a large GPU cluster.

中文翻译：

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代数多重网格域分解 (AMG-DD) 的并行性能

代数多重网格 (AMG) 是一种广泛使用的可扩展求解器和预处理器，适用于由各种椭圆偏微分方程离散化产生的大规模线性系统。尽管 AMG 具有最佳的计算复杂度，但随着现代机器上处理器数量的不断增长，通信成本已成为限制其可扩展性的重要瓶颈。本文研究了一种专为限制通信而设计的新算法代数多重网格域分解 (AMG-DD) 的设计、实现和并行性能。AMG-DD 的目标是通过交换一些额外的计算开销来显着降低通信成本，从而提供标准 AMG V 循环的低通信替代方案。数值结果表明，与 AMG 相比，AMG-DD 在单位通信成本上实现了更高的准确性，