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Title: Improving solve time of aggregation-based adaptive AMG

Abstract

In this paper, we propose improving the solve time of a bootstrap algebraic multigrid (AMG) designed previously by the authors. This is achieved by incorporating the information, a set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by using sufficiently large aggregates, and these aggregates are compositions of aggregates already built throughout the bootstrap algorithm. The modified AMG method has good convergence properties and shows significant reduction in both memory and solve time. These savings with respect to the original bootstrap AMG are illustrated on some difficult (for standard AMG) linear systems arising from discretization of scalar and vector function elliptic partial differential equations in both 2D and 3D.

Authors:
ORCiD logo [1];  [2]
  1. National Research Council (CNR), Naples (Italy). Inst. for Applied Computing
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Portland State Univ., OR (United States). Dept. of Mathematics and Statistics
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); European Union (EU); National Science Foundation (NSF)
OSTI Identifier:
1669235
Alternate Identifier(s):
OSTI ID: 1571299
Report Number(s):
LLNL-JRNL-776759
Journal ID: ISSN 1070-5325; 968776
Grant/Contract Number:  
AC52-07NA27344; 824158; DMS-1619640
Resource Type:
Accepted Manuscript
Journal Name:
Numerical Linear Algebra with Applications
Additional Journal Information:
Journal Volume: 26; Journal Issue: 6; Journal ID: ISSN 1070-5325
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; adaptive AMG; compatible relaxation; solve time; unsmoothed aggregation; weighted matching

Citation Formats

D'Ambra, Pasqua, and Vassilevski, Panayot S. Improving solve time of aggregation-based adaptive AMG. United States: N. p., 2019. Web. doi:10.1002/nla.2269.
D'Ambra, Pasqua, & Vassilevski, Panayot S. Improving solve time of aggregation-based adaptive AMG. United States. https://doi.org/10.1002/nla.2269
D'Ambra, Pasqua, and Vassilevski, Panayot S. Sun . "Improving solve time of aggregation-based adaptive AMG". United States. https://doi.org/10.1002/nla.2269. https://www.osti.gov/servlets/purl/1669235.
@article{osti_1669235,
title = {Improving solve time of aggregation-based adaptive AMG},
author = {D'Ambra, Pasqua and Vassilevski, Panayot S.},
abstractNote = {In this paper, we propose improving the solve time of a bootstrap algebraic multigrid (AMG) designed previously by the authors. This is achieved by incorporating the information, a set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by using sufficiently large aggregates, and these aggregates are compositions of aggregates already built throughout the bootstrap algorithm. The modified AMG method has good convergence properties and shows significant reduction in both memory and solve time. These savings with respect to the original bootstrap AMG are illustrated on some difficult (for standard AMG) linear systems arising from discretization of scalar and vector function elliptic partial differential equations in both 2D and 3D.},
doi = {10.1002/nla.2269},
journal = {Numerical Linear Algebra with Applications},
number = 6,
volume = 26,
place = {United States},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 6 works
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Table 1 Table 1: ANI1 test case for increasing size.

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Works referenced in this record:

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