BootCMatch: A software package for bootstrap AMG based on graph weighted matching

Date published

2018-07-14

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Association for Computing Machinery (ACM)

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Article

ISSN

0098-3500

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Citation

D'Ambra P, Filippone S, Vassilevski P. (2018) BootCMatch: a software package for bootstrap AMG based on graph weighted matching. ACM Transactions on Mathematical Software, Volume 44, Issue 4, July 2018, Article number 39

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.

Description

Software Description

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Github

Keywords

Mathematics of computing, Solvers, Algebraic multigrid, Preconditioner, Iterative solver, Graph matching

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Attribution 4.0 International

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