Improving solve time of aggregation-based adaptive AMG

D'Ambra, Pasqua; Vassilevski, Panayot S.

doi:10.1002/nla.2269

Title: Improving solve time of aggregation-based adaptive AMG

Journal Article · 20 October 2019 · Numerical Linear Algebra with Applications

DOI: https://doi.org/10.1002/nla.2269 · OSTI ID:1669235

^[1]; Vassilevski, Panayot S. ^[2]

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

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: European Union (EU); National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1669235

Report Number(s):: LLNL-JRNL--776759; 968776

Journal Information:: Numerical Linear Algebra with Applications, Journal Name: Numerical Linear Algebra with Applications Journal Issue: 6 Vol. 26; ISSN 1070-5325

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

References (24)

On the use of suboptimal matchings for scaling and ordering sparse symmetric matrices: SCALING OF SPARSE SYMMETRIC MATRICES USING AN AUCTION ALGORITHM Hogg, Jonathan; Scott, Jennifer Numerical Linear Algebra with Applications, Vol. 22, Issue 4 https://doi.org/10.1002/nla.1978	journal	March 2015
Coarsening by compatible relaxation Livne, O. E. Numerical Linear Algebra with Applications, Vol. 11, Issue 23 https://doi.org/10.1002/nla.378	journal	March 2004
AMG by element agglomeration and constrained energy minimization interpolation Kolev, Tzanio V.; Vassilevski, Panayot S. Numerical Linear Algebra with Applications, Vol. 13, Issue 9 https://doi.org/10.1002/nla.494	journal	January 2006
Improving algebraic multigrid interpolation operators for linear elasticity problems Baker, A. H.; Kolev, Tz. V.; Yang, U. M. Numerical Linear Algebra with Applications https://doi.org/10.1002/nla.688	journal	January 2009
Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems Vaněk, P.; Mandel, J.; Brezina, M. Computing, Vol. 56, Issue 3 https://doi.org/10.1007/BF02238511	journal	September 1996
Adaptive AMG with coarsening based on compatible weighted matching D’Ambra, Pasqua; Vassilevski, Panayot S. Computing and Visualization in Science, Vol. 16, Issue 2 https://doi.org/10.1007/s00791-014-0224-9	journal	April 2013
AMG for problems of elasticity Ruge, J. Applied Mathematics and Computation, Vol. 19, Issue 1-4 https://doi.org/10.1016/0096-3003(86)90109-8	journal	July 1986
BoomerAMG: A parallel algebraic multigrid solver and preconditioner Henson, Van Emden; Yang, Ulrike Meier Applied Numerical Mathematics, Vol. 41, Issue 1 https://doi.org/10.1016/S0168-9274(01)00115-5	journal	April 2002
A parallel generalized relaxation method for high-performance image segmentation on GPUs D’Ambra, Pasqua; Filippone, Salvatore Journal of Computational and Applied Mathematics, Vol. 293 https://doi.org/10.1016/j.cam.2015.04.035	journal	February 2016
Algebraic multigrid methods Xu, Jinchao; Zikatanov, Ludmil Acta Numerica, Vol. 26 https://doi.org/10.1017/S0962492917000083	journal	May 2017
Challenges of Scaling Algebraic Multigrid Across Modern Multicore Architectures Baker, Allison H.; Gamblin, Todd; Schulz, Martin Distributed Processing Symposium (IPDPS), 2011 IEEE International Parallel & Distributed Processing Symposium https://doi.org/10.1109/IPDPS.2011.35	conference	May 2011
An Aggregation Multilevel Method Using Smooth Error Vectors Chow, Edmond SIAM Journal on Scientific Computing, Vol. 27, Issue 5 https://doi.org/10.1137/040608192	journal	January 2006
Adaptive Algebraic Multigrid Brezina, M.; Falgout, R.; MacLachlan, S. SIAM Journal on Scientific Computing, Vol. 27, Issue 4 https://doi.org/10.1137/040614402	journal	January 2006
Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems Hagemann, Michael; Schenk, Olaf SIAM Journal on Scientific Computing, Vol. 28, Issue 2 https://doi.org/10.1137/040615614	journal	January 2006
Algebraic Multigrid Based on Computational Molecules, 2: Linear Elasticity Problems Kraus, J. K. SIAM Journal on Scientific Computing, Vol. 30, Issue 1 https://doi.org/10.1137/050641156	journal	January 2008
Bootstrap AMG Brandt, A.; Brannick, J.; Kahl, K. SIAM Journal on Scientific Computing, Vol. 33, Issue 2 https://doi.org/10.1137/090752973	journal	January 2011
Compatible Relaxation and Coarsening in Algebraic Multigrid Brannick, James J.; Falgout, Robert D. SIAM Journal on Scientific Computing, Vol. 32, Issue 3 https://doi.org/10.1137/090772216	journal	January 2010
On Generalizing the Algebraic Multigrid Framework Falgout, Robert D.; Vassilevski, Panayot S. SIAM Journal on Numerical Analysis, Vol. 42, Issue 4 https://doi.org/10.1137/S0036142903429742	journal	January 2004
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix Duff, I. S.; Koster, J. SIAM Journal on Matrix Analysis and Applications, Vol. 22, Issue 4 https://doi.org/10.1137/S0895479899358443	journal	January 2001
Spectral AMGe ($\rho$AMGe) Chartier, T.; Falgout, R. D.; Henson, V. E. SIAM Journal on Scientific Computing, Vol. 25, Issue 1 https://doi.org/10.1137/S106482750139892X	journal	January 2003
AMGE Based on Element Agglomeration Jones, Jim E.; Vassilevski, Panayot S. SIAM Journal on Scientific Computing, Vol. 23, Issue 1 https://doi.org/10.1137/S1064827599361047	journal	January 2001
An overview of SuperLU: Algorithms, implementation, and user interface Li, Xiaoye S. ACM Transactions on Mathematical Software, Vol. 31, Issue 3 https://doi.org/10.1145/1089014.1089017	journal	September 2005
Bootstrap Algebraic Multigrid: Status Report, Open Problems, and Outlook Brandt, Achi; Brannick, James; Kahl, Karsten Numerical Mathematics: Theory, Methods and Applications, Vol. 8, Issue 1 https://doi.org/10.4208/nmtma.2015.w06si	journal	February 2015
Algebraic Multigrid Methods Xu, Jinchao; Zikatanov, Ludmil T. arXiv https://doi.org/10.48550/arxiv.1611.01917	preprint	January 2016

Similar Records

Adaptive AMG with Coarsening Based on Compatible Weighted Matching

Technical Report · 2013 · OSTI ID:1062221

D'Ambra, Pasqua; Vassilevski, Panayot S.

Generalized Bootstrap AMG and AIR-AMG for coupled PDE systems with a focus on spacetime discretizatoins

Technical Report · 2022 · OSTI ID:1876687

Brannick, James

αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods

Conference · 2014 · OSTI ID:1144751

D'Ambra, P.; Vassilevski, P. S.

Related Subjects

97 MATHEMATICS AND COMPUTING
adaptive AMG
compatible relaxation
solve time
unsmoothed aggregation
weighted matching

Title: Improving solve time of aggregation-based adaptive AMG

Citation Formats

References (24)

Similar Records

Related Subjects