Parallel performance of algebraic multigrid domain decomposition
Abstract
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.
- Authors:
-
[1];
- Universität Heidelberg (Germany)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); German Research Foundation (DFG)
- OSTI Identifier:
- 1776659
- Report Number(s):
- LLNL-JRNL-801850
Journal ID: ISSN 1070-5325; 1005848
- Grant/Contract Number:
- AC52-07NA27344; INST 35/1134/1
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Numerical Linear Algebra with Applications
- Additional Journal Information:
- Journal Volume: 28; Journal Issue: 3; Journal ID: ISSN 1070-5325
- Publisher:
- Wiley
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; algebraic multigrid; low-communication algorithms; parallel performance
Citation Formats
Mitchell, Wayne B., Strzodka, Robert, and Falgout, Robert D. Parallel performance of algebraic multigrid domain decomposition. United States: N. p., 2020.
Web. doi:10.1002/nla.2342.
Mitchell, Wayne B., Strzodka, Robert, & Falgout, Robert D. Parallel performance of algebraic multigrid domain decomposition. United States. https://doi.org/10.1002/nla.2342
Mitchell, Wayne B., Strzodka, Robert, and Falgout, Robert D. Mon .
"Parallel performance of algebraic multigrid domain decomposition". United States. https://doi.org/10.1002/nla.2342. https://www.osti.gov/servlets/purl/1776659.
@article{osti_1776659,
title = {Parallel performance of algebraic multigrid domain decomposition},
author = {Mitchell, Wayne B. and Strzodka, Robert and Falgout, Robert D.},
abstractNote = {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.},
doi = {10.1002/nla.2342},
journal = {Numerical Linear Algebra with Applications},
number = 3,
volume = 28,
place = {United States},
year = {Mon Oct 12 00:00:00 EDT 2020},
month = {Mon Oct 12 00:00:00 EDT 2020}
}
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