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

D’Ambra, Pasqua; Filippone, Salvatore; Vassilevski, Panayot S.

doi:10.1145/3190647

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

Journal Article · Fri Jun 01 00:00:00 EDT 2018 · ACM Transactions on Mathematical Software

DOI:https://doi.org/10.1145/3190647· OSTI ID:1670548

D’Ambra, Pasqua ^[1]; Filippone, Salvatore ^[2]; Vassilevski, Panayot S. ^[3]

National Research Council, Napoli (Italy)
Cranfield Univ., England (United Kingdom)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

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.

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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; DMS-1619640; 676629

OSTI ID:: 1670548

Report Number(s):: LLNL-JRNL-729959; 880696

Journal Information:: ACM Transactions on Mathematical Software, Vol. 44, Issue 4; ISSN 0098-3500

Publisher:: Association for Computing MachineryCopyright Statement

Country of Publication:: United States

Language:: English

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SParSH-AMG: A library for hybrid CPU-GPU algebraic multigrid and preconditioned iterative methods Ganesan, Sashikumaar; Shah, Manan arXiv https://doi.org/10.48550/arxiv.2007.00056	preprint	January 2020
AMG preconditioners for Linear Solvers towards Extreme Scale D'Ambra, Pasqua; Durastante, Fabio; Filippone, Salvatore arXiv https://doi.org/10.48550/arxiv.2006.16147	text	January 2020
Bootstrap AMG for spectral clustering D'Ambra, Pasqua; Cutillo, Luisa; Vassilevski, Panayot S. Computational and Mathematical Methods, Vol. 1, Issue 2 https://doi.org/10.1002/cmm4.1020	journal	March 2019
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