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Title: Compatible Relaxation and Coarsening in Algebraic Multigrid

Abstract

We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.

Authors:
;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
985488
Report Number(s):
LLNL-JRNL-417122
Journal ID: ISSN 1064-8275; SJOCE3; TRN: US201016%%2023
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 32; Journal Issue: 3; Journal ID: ISSN 1064-8275
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS; ALGORITHMS; METRICS; PERFORMANCE; RELAXATION

Citation Formats

Brannick, J J, and Falgout, R D. Compatible Relaxation and Coarsening in Algebraic Multigrid. United States: N. p., 2009. Web.
Brannick, J J, & Falgout, R D. Compatible Relaxation and Coarsening in Algebraic Multigrid. United States.
Brannick, J J, and Falgout, R D. 2009. "Compatible Relaxation and Coarsening in Algebraic Multigrid". United States. https://www.osti.gov/servlets/purl/985488.
@article{osti_985488,
title = {Compatible Relaxation and Coarsening in Algebraic Multigrid},
author = {Brannick, J J and Falgout, R D},
abstractNote = {We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.},
doi = {},
url = {https://www.osti.gov/biblio/985488}, journal = {SIAM Journal on Scientific Computing},
issn = {1064-8275},
number = 3,
volume = 32,
place = {United States},
year = {Tue Sep 22 00:00:00 EDT 2009},
month = {Tue Sep 22 00:00:00 EDT 2009}
}