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BootCMatch: A Software Package for Bootstrap AMG Based on Graph Weighted Matching

Authors:

Pasqua D’ambra,

Salvatore Filippone,

Panayot S. VassilevskiAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 44, Issue 4

Article No.: 39, Pages 1 - 25

https://doi.org/10.1145/3190647

Published: 16 June 2018 Publication History

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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 the software.

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De Marchi NXotta GFerronato MSalomoni V(2024)An efficient multi-field dynamic model for 3D wave propagation in saturated anisotropic porous mediaJournal of Computational Physics10.1016/j.jcp.2024.113082510(113082)Online publication date: Aug-2024
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Owen HLehmkuhl OD’Ambra PDurastante FFilippone S(2024)Alya toward exascale: algorithmic scalability using PSCToolkitThe Journal of Supercomputing10.1007/s11227-024-05989-y80:10(13533-13556)Online publication date: 1-Jul-2024
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Index Terms

BootCMatch: A Software Package for Bootstrap AMG Based on Graph Weighted Matching
1. Mathematics of computing
  1. Mathematical software
    1. Solvers

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 44, Issue 4

December 2018

305 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/3233179

Editors:
Zhaojun Bai
University of California at Davis, USA
,
Wolfgang Bangerth
Colorado State University, USA

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Copyright © 2018 ACM.

© 2018 Association for Computing Machinery. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of the United States government. As such, the United States Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 June 2018

Accepted: 01 February 2018

Revised: 01 February 2018

Received: 01 April 2017

Published in TOMS Volume 44, Issue 4

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EC under the Horizon 2020 Project Energy oriented Centre of Excellence for computing applications âĂŞ Project Energy oriented Centre of Excellence for computing applications (EoCoE)

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Cited By

Wang YChang FWei BGao JJi W(2024)Optimization of Sparse Matrix Computation for Algebraic Multigrid on GPUsACM Transactions on Architecture and Code Optimization10.1145/366492421:3(1-27)Online publication date: 15-May-2024
https://dl.acm.org/doi/10.1145/3664924
De Marchi NXotta GFerronato MSalomoni V(2024)An efficient multi-field dynamic model for 3D wave propagation in saturated anisotropic porous mediaJournal of Computational Physics10.1016/j.jcp.2024.113082510(113082)Online publication date: Aug-2024
https://doi.org/10.1016/j.jcp.2024.113082
Owen HLehmkuhl OD’Ambra PDurastante FFilippone S(2024)Alya toward exascale: algorithmic scalability using PSCToolkitThe Journal of Supercomputing10.1007/s11227-024-05989-y80:10(13533-13556)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s11227-024-05989-y
Lee B(2024)Least angle regression, relaxed lasso, and elastic net for algebraic multigrid of systems of elliptic partial differential equationsNumerical Linear Algebra with Applications10.1002/nla.257231:5Online publication date: 18-Jun-2024
https://doi.org/10.1002/nla.2572
Bernaschi MCelestini AVella FD'Ambra P(2023)A Multi-GPU Aggregation-Based AMG Preconditioner for Iterative Linear SolversIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2023.328723834:8(2365-2376)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1109/TPDS.2023.3287238
D'Ambra PDurastante FFerdous SFilippone SHalappanavar MPothen A(2023)AMG Preconditioners based on Parallel Hybrid Coarsening and Multi-objective Graph Matching2023 31st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP)10.1109/PDP59025.2023.00017(59-67)Online publication date: Mar-2023
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D’Ambra PDurastante FFilippone S(2023)Parallel Sparse Computation ToolkitSoftware Impacts10.1016/j.simpa.2022.100463(100463)Online publication date: Jan-2023
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D'Ambra PDurastante FFilippone SZikatanov L(2023)Automatic coarsening in Algebraic Multigrid utilizing quality measures for matching-based aggregationsComputers & Mathematics with Applications10.1016/j.camwa.2023.06.026144:C(290-305)Online publication date: 15-Aug-2023
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D’Ambra PVassilevski PCutillo L(2023)Extending bootstrap AMG for clustering of attributed graphsApplied Mathematics and Computation10.1016/j.amc.2023.127904447:COnline publication date: 15-Jun-2023
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Bertaccini DD'Ambra PDurastante FFilippone S(2023)Why diffusion‐based preconditioning of Richards equation works: Spectral analysis and computational experiments at very large scaleNumerical Linear Algebra with Applications10.1002/nla.252331:1Online publication date: 19-Jul-2023
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