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An improved convergence analysis of smoothed aggregation algebraic multigrid

Journal Article · · Numerical Linear Algebra with Applications
DOI:https://doi.org/10.1002/nla.775· OSTI ID:1227005
 [1];  [2];  [3]
  1. Univ. of Colorado, Boulder, CO (United States). Dept. of Applied Mathematics
  2. University of West Bohemia (Czech Republic). Dept. of Mathematics
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
+ Show Author Affiliations
We present an improved analysis of the smoothed aggregation (SA) alge- braic multigrid method (AMG) extending the original proof in [SA] and its modification in [Va08]. The new result imposes fewer restrictions on the aggregates that makes it eas- ier to verify in practice. Also, we extend a result in [Van] that allows us to use aggressive coarsening at all levels due to the special properties of the polynomial smoother, that we use and analyze, and thus provide a multilevel convergence estimate with bounds independent of the coarsening ratio.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
DOE Contract Number:
AC52-07NA27344
OSTI ID:
1227005
Report Number(s):
LLNL-JRNL--448115
Journal Information:
Numerical Linear Algebra with Applications, Journal Name: Numerical Linear Algebra with Applications Journal Issue: 3 Vol. 19; ISSN 1070-5325
Publisher:
Wiley
Country of Publication:
United States
Language:
English

References (7)

Convergence of algebraic multigrid based on smoothed aggregation journal May 2001
Two-grid Method for Linear Elasticity on Unstructured Meshes journal January 1999
Two-level Preconditioner with Small Coarse Grid Appropriate for Unstructured Meshes journal July 1996
Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems journal September 1996
The cascadic multigrid method for elliptic problems journal December 1996
Multigrid Methods for Finite Elements book January 1995
The method of alternating projections and the method of subspace corrections in Hilbert space journal April 2002

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Related Subjects

97 MATHEMATICS AND COMPUTING
aggressive coarsening
algebraic multigrid
convergence analysis
polynomial smoother
smoothed aggregation