Parallel performance of algebraic multigrid domain decomposition

Abstract

SummaryAlgebraic 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.