D’Ambra, PasquaFilippone, SalvatoreVassilevski, Panayot S.2018-07-162018-07-162018-07-14D'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 390098-3500http://dx.doi.org/10.1145/3190647https://dspace.lib.cranfield.ac.uk/handle/1826/13344This 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.enAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Mathematics of computingSolversAlgebraic multigridPreconditionerIterative solverGraph matchingArticle19748203