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Reducing communication in algebraic multigrid using additive variants
Author(s) -
Vassilevski Panayot S.,
Yang Ulrike Meier
Publication year - 2014
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1928
Subject(s) - multigrid method , convergence (economics) , scalability , algebraic number , computer science , solver , computation , parallelism (grammar) , parallel computing , domain (mathematical analysis) , mathematics , theoretical computer science , algorithm , mathematical optimization , partial differential equation , mathematical analysis , database , economics , economic growth
SUMMARY 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.