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

References in zbMATH (referenced in 10 articles , 1 standard article )

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  1. Franceschini, Andrea; Castelletto, Nicola; White, Joshua A.; Tchelepi, Hamdi A.: Scalable preconditioning for the stabilized contact mechanics problem (2022)
  2. Franceschini, Andrea; Gazzola, Laura; Ferronato, Massimiliano: A scalable preconditioning framework for stabilized contact mechanics with hydraulically active fractures (2022)
  3. D’Ambra, Pasqua; Durastante, Fabio; Filippone, Salvatore: AMG preconditioners for linear solvers towards extreme scale (2021)
  4. Massimo Bernaschi, Pasqua D’Ambra, Dario Pasquini: BootCMatchG: An adaptive Algebraic MultiGrid linear solver for GPUs (2020) not zbMATH
  5. Sashikumaar Ganesan, Manan Shah: SParSH-AMG: A library for hybrid CPU-GPU algebraic multigrid and preconditioned iterative methods (2020) arXiv
  6. D’Ambra, Pasqua; Vassilevski, Panayot S.: Improving solve time of aggregation-based adaptive AMG. (2019)
  7. Franceschini, Andrea; Paludetto Magri, Victor A.; Mazzucco, Gianluca; Spiezia, Nicolò; Janna, Carlo: A robust adaptive algebraic multigrid linear solver for structural mechanics (2019)
  8. Paludetto Magri, Victor A.; Franceschini, Andrea; Janna, Carlo: A novel algebraic multigrid approach based on adaptive smoothing and prolongation for ill-conditioned systems (2019)
  9. Abdullahi, Ambra; D’Ambra, Pasqua; Di Serafino, Daniela; Filippone, Salvatore: Parallel aggregation based on compatible weighted matching for AMG (2018)
  10. D’Ambra, Pasqua; Filippone, Salvatore; Vassilevski, Panayot S.: BootCMatch: a software package for bootstrap AMG based on graph weighted matching (2018)