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:
-
- National Research Council (CNR), Naples (Italy). Inst. for Applied Computing
- 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 = {Sun Oct 20 00:00:00 EDT 2019},
month = {Sun Oct 20 00:00:00 EDT 2019}
}
Web of Science
Figures / Tables:
Works referenced in this record:
Improving algebraic multigrid interpolation operators for linear elasticity problems
journal, January 2009
- Baker, A. H.; Kolev, Tz. V.; Yang, U. M.
- Numerical Linear Algebra with Applications
Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
journal, September 1996
- Vaněk, P.; Mandel, J.; Brezina, M.
- Computing, Vol. 56, Issue 3
Bootstrap Algebraic Multigrid: Status Report, Open Problems, and Outlook
journal, February 2015
- Brandt, Achi; Brannick, James; Kahl, Karsten
- Numerical Mathematics: Theory, Methods and Applications, Vol. 8, Issue 1
Bootstrap AMG
journal, January 2011
- Brandt, A.; Brannick, J.; Kahl, K.
- SIAM Journal on Scientific Computing, Vol. 33, Issue 2
Compatible Relaxation and Coarsening in Algebraic Multigrid
journal, January 2010
- Brannick, James J.; Falgout, Robert D.
- SIAM Journal on Scientific Computing, Vol. 32, Issue 3
Adaptive AMG with coarsening based on compatible weighted matching
journal, April 2013
- D’Ambra, Pasqua; Vassilevski, Panayot S.
- Computing and Visualization in Science, Vol. 16, Issue 2
An overview of SuperLU: Algorithms, implementation, and user interface
journal, September 2005
- Li, Xiaoye S.
- ACM Transactions on Mathematical Software, Vol. 31, Issue 3
BoomerAMG: A parallel algebraic multigrid solver and preconditioner
journal, April 2002
- Henson, Van Emden; Yang, Ulrike Meier
- Applied Numerical Mathematics, Vol. 41, Issue 1
A parallel generalized relaxation method for high-performance image segmentation on GPUs
journal, February 2016
- D’Ambra, Pasqua; Filippone, Salvatore
- Journal of Computational and Applied Mathematics, Vol. 293
On Generalizing the Algebraic Multigrid Framework
journal, January 2004
- Falgout, Robert D.; Vassilevski, Panayot S.
- SIAM Journal on Numerical Analysis, Vol. 42, Issue 4
AMG for problems of elasticity
journal, July 1986
- Ruge, J.
- Applied Mathematics and Computation, Vol. 19, Issue 1-4
On the use of suboptimal matchings for scaling and ordering sparse symmetric matrices: SCALING OF SPARSE SYMMETRIC MATRICES USING AN AUCTION ALGORITHM
journal, March 2015
- Hogg, Jonathan; Scott, Jennifer
- Numerical Linear Algebra with Applications, Vol. 22, Issue 4
Coarsening by compatible relaxation
journal, March 2004
- Livne, O. E.
- Numerical Linear Algebra with Applications, Vol. 11, Issue 23
AMG by element agglomeration and constrained energy minimization interpolation
journal, January 2006
- Kolev, Tzanio V.; Vassilevski, Panayot S.
- Numerical Linear Algebra with Applications, Vol. 13, Issue 9
Algebraic Multigrid Based on Computational Molecules, 2: Linear Elasticity Problems
journal, January 2008
- Kraus, J. K.
- SIAM Journal on Scientific Computing, Vol. 30, Issue 1
Spectral AMGe ($\rho$AMGe)
journal, January 2003
- Chartier, T.; Falgout, R. D.; Henson, V. E.
- SIAM Journal on Scientific Computing, Vol. 25, Issue 1
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
journal, January 2001
- Duff, I. S.; Koster, J.
- SIAM Journal on Matrix Analysis and Applications, Vol. 22, Issue 4
AMGE Based on Element Agglomeration
journal, January 2001
- Jones, Jim E.; Vassilevski, Panayot S.
- SIAM Journal on Scientific Computing, Vol. 23, Issue 1
Challenges of Scaling Algebraic Multigrid Across Modern Multicore Architectures
conference, May 2011
- Baker, Allison H.; Gamblin, Todd; Schulz, Martin
- Distributed Processing Symposium (IPDPS), 2011 IEEE International Parallel & Distributed Processing Symposium
An Aggregation Multilevel Method Using Smooth Error Vectors
journal, January 2006
- Chow, Edmond
- SIAM Journal on Scientific Computing, Vol. 27, Issue 5
Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems
journal, January 2006
- Hagemann, Michael; Schenk, Olaf
- SIAM Journal on Scientific Computing, Vol. 28, Issue 2
Adaptive Algebraic Multigrid
journal, January 2006
- Brezina, M.; Falgout, R.; MacLachlan, S.
- SIAM Journal on Scientific Computing, Vol. 27, Issue 4
Figures / Tables found in this record: