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 article 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 with 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的并行性能

代数多重网格（AMG）是由大范围的椭圆PDE离散化而成的大规模线性系统的一种广泛使用的可扩展求解器和预处理器。尽管AMG具有最佳的计算复杂度，但随着现代计算机上处​​理器数量的不断增长，通信成本已成为制约其可扩展性的重要瓶颈。本文研究了专为限制通信而设计的新型算法，代数多网格域分解（AMG-DD）的设计，实现和并行性能。AMG-DD的目标是通过交易一些额外的计算开销来显着降低通信成本，从而为标准AMG V周期提供一种低通信替代方案。数值结果表明，与AMG相比，AMG‐DD在每次通信成本上实现了更高的精度，