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

Journal Article · · ACM Transactions on Mathematical Software
DOI:https://doi.org/10.1145/3190647· OSTI ID:1670548
 [1];  [2];  [3]
  1. National Research Council, Napoli (Italy)
  2. Cranfield Univ., England (United Kingdom)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
+ Show Author Affiliations
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.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF); European Research Council (ERC)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1670548
Report Number(s):
LLNL-JRNL--729959; 880696
Journal Information:
ACM Transactions on Mathematical Software, Journal Name: ACM Transactions on Mathematical Software Journal Issue: 4 Vol. 44; ISSN 0098-3500
Publisher:
Association for Computing MachineryCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (4)

AMG based on compatible weighted matching for GPUs preprint January 2018
AMG preconditioners for Linear Solvers towards Extreme Scale text January 2020
SParSH-AMG: A library for hybrid CPU-GPU algebraic multigrid and preconditioned iterative methods preprint January 2020
Bootstrap AMG for spectral clustering journal March 2019

Figures / Tables (17)

Algorithm 1(p. 8)figure Algorithm 1
Algorithm 2(p. 9)figure Algorithm 2
Algorithm 3(p. 10)figure Algorithm 3
Algorithm 4(p. 11)figure Algorithm 4
Fig. 1(p. 13)figure Fig. 1
Table 1(p. 17)table Table 1
Table 2(p. 18)table Table 2
Table 3(p. 18)table Table 3
Table 4(p. 19)table Table 4
Table 5(p. 19)table Table 5
Table 6(p. 20)table Table 6
Table 7(p. 21)table Table 7
Table 8(p. 22)table Table 8
Table 9(p. 23)table Table 9
Table 10(p. 24)table Table 10
Table 11(p. 24)table Table 11
Table 12(p. 25)table Table 12

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Related Subjects

97 MATHEMATICS AND COMPUTING
algebraic multigrid
graph matching
iterative solver
preconditioner