Reducing communication in algebraic multigrid using additive variants



Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers; however, its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Additive AMG variants provide not only increased parallelism as well as decreased numbers of messages per cycle but also generally exhibit slower convergence. We present various new additive variants with convergence rates that are significantly improved compared to the classical additive algebraic multigrid method and investigate their potential for decreased communication, and improved communication-computation overlap, features that are essential for good performance on future exascale architectures. Published 2014. This article is a US Government work and is in the public domain in the USA.