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AMG by element agglomeration and constrained energy minimization interpolation

Journal Article · · Numerical Linear Algebra with Applications, vol. 13, no. 9, September 10, 2006, pp. 771-788
DOI:https://doi.org/10.1002/nla.494· OSTI ID:898479
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This paper studies AMG (algebraic multigrid) methods that utilize energy minimization construction of the interpolation matrices locally, in the setting of element agglomeration AMG. The coarsening in element agglomeration AMG is done by agglomerating fine-grid elements, with coarse element matrices defined by a local Galerkin procedure applied to the matrix assembled from the individual fine-grid element matrices. This local Galerkin procedure involves only the coarse basis restricted to the agglomerated element. To construct the coarse basis, one exploits previously proposed constraint energy minimization procedures now applied to the local matrix. The constraints are that a given set of vectors should be interpolated exactly, not only globally, but also locally on every agglomerated element. The paper provides algorithmic details, as well as a convergence result based on a ''local-to-global'' energy bound of the resulting multiple-vector fitting AMG interpolation mappings. A particular implementation of the method is illustrated with a set of numerical experiments.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA
Sponsoring Organization:
USDOE
DOE Contract Number:
W-7405-ENG-48
OSTI ID:
898479
Report Number(s):
UCRL-JRNL-219462
Journal Information:
Numerical Linear Algebra with Applications, vol. 13, no. 9, September 10, 2006, pp. 771-788, Journal Name: Numerical Linear Algebra with Applications, vol. 13, no. 9, September 10, 2006, pp. 771-788
Country of Publication:
United States
Language:
English

References (15)

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Related Subjects

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE WASTES FROM NUCLEAR FACILITIES
99 GENERAL AND MISCELLANEOUS
AGGLOMERATION
CONSTRUCTION
CONVERGENCE
IMPLEMENTATION
INTERPOLATION
MATRICES
MINIMIZATION
VECTORS