Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: BootCMatch: A Software Package for Bootstrap AMG Based on GraphWeighted Matching

Abstract

This article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the goal of adaptivity is to achieve a method with a prescribed convergence rate. The presented method exploits a general coarsening process based on aggregation of unknowns, obtained by a maximum weight matching in the adjacency graph of the system matrix. More specifically, a maximum product matching is employed to define an effective smoother subspace (complementary to the coarse space), a process referred to as compatible relaxation, at every level of the recursive two-level hierarchical AMG process. Results on a large variety of test cases and comparisons with related work demonstrate the reliability and efficiency of the method and of themore » software.« less

Authors:
 [1];  [2];  [3]
+ Show Author Affiliations
  1. National Research Council, Napoli (Italy)
  2. Cranfield Univ., England (United Kingdom)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF); European Research Council (ERC)
OSTI Identifier:
1670548
Report Number(s):
LLNL-JRNL-729959
Journal ID: ISSN 0098-3500; 880696
Grant/Contract Number:  
AC52-07NA27344; DMS-1619640; 676629
Resource Type:
Accepted Manuscript
Journal Name:
ACM Transactions on Mathematical Software
Additional Journal Information:
Journal Volume: 44; Journal Issue: 4; Journal ID: ISSN 0098-3500
Publisher:
Association for Computing Machinery
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; algebraic multigrid; preconditioner; iterative solver; graph matching

Citation Formats

D’Ambra, Pasqua, Filippone, Salvatore, and Vassilevski, Panayot S. BootCMatch: A Software Package for Bootstrap AMG Based on GraphWeighted Matching. United States: N. p., 2018. Web. doi:10.1145/3190647.
Copy to clipboard
D’Ambra, Pasqua, Filippone, Salvatore, & Vassilevski, Panayot S. BootCMatch: A Software Package for Bootstrap AMG Based on GraphWeighted Matching. United States. https://doi.org/10.1145/3190647
Copy to clipboard
D’Ambra, Pasqua, Filippone, Salvatore, and Vassilevski, Panayot S. Fri . "BootCMatch: A Software Package for Bootstrap AMG Based on GraphWeighted Matching". United States. https://doi.org/10.1145/3190647. https://www.osti.gov/servlets/purl/1670548.
Copy to clipboard
@article{osti_1670548,
title = {BootCMatch: A Software Package for Bootstrap AMG Based on GraphWeighted Matching},
author = {D’Ambra, Pasqua and Filippone, Salvatore and Vassilevski, Panayot S.},
abstractNote = {This article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the goal of adaptivity is to achieve a method with a prescribed convergence rate. The presented method exploits a general coarsening process based on aggregation of unknowns, obtained by a maximum weight matching in the adjacency graph of the system matrix. More specifically, a maximum product matching is employed to define an effective smoother subspace (complementary to the coarse space), a process referred to as compatible relaxation, at every level of the recursive two-level hierarchical AMG process. Results on a large variety of test cases and comparisons with related work demonstrate the reliability and efficiency of the method and of the software.},
doi = {10.1145/3190647},
journal = {ACM Transactions on Mathematical Software},
number = 4,
volume = 44,
place = {United States},
year = {Fri Jun 01 00:00:00 EDT 2018},
month = {Fri Jun 01 00:00:00 EDT 2018}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1145/3190647
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal

Figures / Tables:

Algorithm 1 Algorithm 1: Pairwise aggregation based on maximum product matching
All figures and tables (17 total)
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

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
  • DOI: 10.1002/nla.688

Recursive Krylov-based multigrid cycles
journal, January 2008

  • Notay, Yvan; Vassilevski, Panayot S.
  • Numerical Linear Algebra with Applications, Vol. 15, Issue 5
  • DOI: 10.1002/nla.542

An auction-based weighted matching implementation on massively parallel architectures
journal, December 2012

Recursive Krylov-based multigrid cycles
journal, January 2008

  • Notay, Yvan; Vassilevski, Panayot S.
  • Numerical Linear Algebra with Applications, Vol. 15, Issue 5
  • DOI: 10.1002/nla.542

Approximate weighted matching on emerging manycore and multithreaded architectures
journal, August 2012

  • Halappanavar, Mahantesh; Feo, John; Villa, Oreste
  • The International Journal of High Performance Computing Applications, Vol. 26, Issue 4
  • DOI: 10.1177/1094342012452893

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
  • DOI: 10.4208/nmtma.2015.w06si

Optimal Weighted Matchings for Rank-Deficient Sparse Matrices
journal, January 2013

  • Hogg, J. D.; Scott, J. A.
  • SIAM Journal on Matrix Analysis and Applications, Vol. 34, Issue 4
  • DOI: 10.1137/120884262

Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
journal, September 1996

Bootstrap AMG
journal, January 2011

  • Brandt, A.; Brannick, J.; Kahl, K.
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 2
  • DOI: 10.1137/090752973

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
  • DOI: 10.1007/s00791-014-0224-9

An overview of SuperLU: Algorithms, implementation, and user interface
journal, September 2005

On Generalizing the Algebraic Multigrid Framework
journal, January 2004

  • Falgout, Robert D.; Vassilevski, Panayot S.
  • SIAM Journal on Numerical Analysis, Vol. 42, Issue 4
  • DOI: 10.1137/S0036142903429742

A Parallel CFD Model for Wind Farms
journal, January 2013

AMG for problems of elasticity
journal, July 1986

A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
journal, January 2001

  • Amestoy, Patrick R.; Duff, Iain S.; L'Excellent, Jean-Yves
  • SIAM Journal on Matrix Analysis and Applications, Vol. 23, Issue 1
  • DOI: 10.1137/S0895479899358194

Adaptive Smoothed Aggregation ($\alpha$SA) Multigrid
journal, January 2005

  • Brezina, M.; Falgout, R.; MacLachlan, S.
  • SIAM Review, Vol. 47, Issue 2
  • DOI: 10.1137/050626272

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
  • DOI: 10.1002/nla.1978

The university of Florida sparse matrix collection
journal, November 2011

  • Davis, Timothy A.; Hu, Yifan
  • ACM Transactions on Mathematical Software, Vol. 38, Issue 1
  • DOI: 10.1145/2049662.2049663

On two-grid convergence estimates
journal, January 2005

  • Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T.
  • Numerical Linear Algebra with Applications, Vol. 12, Issue 5-6
  • DOI: 10.1002/nla.437

The auction algorithm: A distributed relaxation method for the assignment problem
journal, December 1988

  • Bertsekas, D. P.
  • Annals of Operations Research, Vol. 14, Issue 1
  • DOI: 10.1007/BF02186476

Coarsening by compatible relaxation
journal, March 2004

  • Livne, O. E.
  • Numerical Linear Algebra with Applications, Vol. 11, Issue 23
  • DOI: 10.1002/nla.378

An Algebraic Multigrid Method with Guaranteed Convergence Rate
journal, January 2012

  • Napov, Artem; Notay, Yvan
  • SIAM Journal on Scientific Computing, Vol. 34, Issue 2
  • DOI: 10.1137/100818509

Auction algorithms for network flow problems: A tutorial introduction
journal, October 1992

  • Bertsekas, Dimitri P.
  • Computational Optimization and Applications, Vol. 1, Issue 1
  • DOI: 10.1007/BF00247653

Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems
journal, January 2005

  • Duff, Iain S.; Pralet, Stéphane
  • SIAM Journal on Matrix Analysis and Applications, Vol. 27, Issue 2
  • DOI: 10.1137/04061043x

An Algebraic Multigrid Method with Guaranteed Convergence Rate
journal, January 2012

  • Napov, Artem; Notay, Yvan
  • SIAM Journal on Scientific Computing, Vol. 34, Issue 2
  • DOI: 10.1137/100818509

On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
journal, January 2001

An algebraic multilevel method for anisotropic elliptic equations based on subgraph matching: AN AMG METHOD FOR ANISOTROPIC EQUATIONS BASED ON SUBGRAPH MATCHING
journal, January 2012

  • Brannick, James; Chen, Yao; Zikatanov, Ludmil
  • Numerical Linear Algebra with Applications, Vol. 19, Issue 2
  • DOI: 10.1002/nla.1804

The Hungarian method for the assignment problem
journal, March 1955

Algebraic Multilevel Preconditioners for the Graph Laplacian Based on Matching in Graphs
journal, January 2013

  • Brannick, J.; Chen, Y.; Kraus, J.
  • SIAM Journal on Numerical Analysis, Vol. 51, Issue 3
  • DOI: 10.1137/120876083

Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems
journal, January 2006

  • Hagemann, Michael; Schenk, Olaf
  • SIAM Journal on Scientific Computing, Vol. 28, Issue 2
  • DOI: 10.1137/040615614

Adaptive Algebraic Multigrid
journal, January 2006

  • Brezina, M.; Falgout, R.; MacLachlan, S.
  • SIAM Journal on Scientific Computing, Vol. 27, Issue 4
  • DOI: 10.1137/040614402
    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    AMG preconditioners for Linear Solvers towards Extreme Scale
    text, January 2020

    Bootstrap AMG for spectral clustering
    journal, March 2019

    • D'Ambra, Pasqua; Cutillo, Luisa; Vassilevski, Panayot S.
    • Computational and Mathematical Methods, Vol. 1, Issue 2
    • DOI: 10.1002/cmm4.1020

    AMG based on compatible weighted matching for GPUs
    preprint, January 2018

      Sort by:
      [ × clear filter / sort ]

      Figures / Tables found in this record:

      Algorithm 1 (p. 8)figure
      Algorithm 2 (p. 9)figure
      Algorithm 3 (p. 10)figure
      Algorithm 4 (p. 11)figure
      Fig. 1 (p. 13)figure
      Table 1 (p. 17)table
      Table 2 (p. 18)table
      Table 3 (p. 18)table
      Table 4 (p. 19)table
      Table 5 (p. 19)table
      Table 6 (p. 20)table
      Table 7 (p. 21)table
      Table 8 (p. 22)table
      Table 9 (p. 23)table
      Table 10 (p. 24)table
      Table 11 (p. 24)table
      Table 12 (p. 25)table
        [ × clear filter / sort ]
        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

        Similar Records in DOE PAGES and OSTI.GOV collections: