BoomerAMG: A parallel algebraic multigrid solver and preconditioner. Driven by the need to solve linear systems arising from problems posed on extremely large, unstructured grids, there has been a recent resurgence of interest in algebraic multigrid (AMG). AMG is attractive in that it holds out the possibility of multigrid-like performance on unstructured grids. The sheer size of many modern physics and simulation problems has led to the development of massively parallel computers, and has sparked much research into developing algorithms for them. Parallelizing AMG is a difficult task, however. While much of the AMG method parallelizes readily, the process of coarse-grid selection, in particular, is fundamentally sequential in nature. We have previously introduced a parallel algorithm [cf. A. J. Cleary, R. D. Falgout, V. E. Henson and J. E. Jones, Coarse grid selection for parallel algebraic multigrid, in: A. Ferriera, J. Rollin, H. Simon, S.-H. Teng (eds.), Proceedings of the Fifth International Symposium on Solving Irregularly Structured Problems in Parallel, Lecture Notes in Computer Science, Vol. 1457, Springer, New York (1998)] for the selection of coarse-grid points, based on modifications of certain parallel independent set algorithms and the application of heuristic designed to insure the quality of the coarse grids, and shown results from a prototype serial version of the algorithm. In this paper we describe an implementation of a parallel AMG code, using the algorithm of A. J. Cleary, R. D. Falgout and V. E. Henson [loc. cit.] as well as other approaches to parallelizing the coarse-grid selection. We consider three basic coarsening schemes and certain modifications to the basic schemes, designed to address specific performance issues. We present numerical results for a broad range of problem sizes and descriptions, and draw conclusion regarding the efficacy of the method. Finally, we indicate the current directions of the research.

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  1. Allen, Jeffery M.; Chang, Justin; Usseglio-Viretta, Francois L. E.; Graf, Peter; Smith, Kandler: A segregated approach for modeling the electrochemistry in the 3-D microstructure of li-ion batteries and its acceleration using block preconditioners (2021)
  2. Büsing, Henrik: Efficient solution techniques for two-phase flow in heterogeneous porous media using exact Jacobians (2021)
  3. Ye, Shuai; Xu, Xinhai; An, Hengbin; Yang, Xuejun: A supplementary strategy for coarsening in algebraic multigrid (2021)
  4. Bui, Quan M.; Osei-Kuffuor, Daniel; Castelletto, Nicola; White, Joshua A.: A scalable multigrid reduction framework for multiphase poromechanics of heterogeneous media (2020)
  5. Dassi, F.; Scacchi, S.: Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems (2020)
  6. Demidov, D.; Rossi, R.: Subdomain deflation combined with local AMG: a case study using AMGCL library (2020)
  7. Gratien, Jean-Marc: A robust and scalable multi-level domain decomposition preconditioner for multi-core architecture with large number of cores (2020)
  8. Heinlein, Alexander; Klawonn, Axel; Lanser, Martin; Weber, Janine: A frugal FETI-DP and BDDC coarse space for heterogeneous problems (2020)
  9. Kong, Fande; Wang, Yaqi; Gaston, Derek R.; Permann, Cody J.; Slaughter, Andrew E.; Lindsay, Alexander D.; DeHart, Mark D.; Martineau, Richard C.: A highly parallel multilevel Newton-Krylov-Schwarz method with subspace-based coarsening and partition-based balancing for the multigroup neutron transport equation on three-dimensional unstructured meshes (2020)
  10. Lee, Chak Shing; Hamon, François; Castelletto, Nicola; Vassilevski, Panayot S.; White, Joshua A.: Nonlinear multigrid based on local spectral coarsening for heterogeneous diffusion problems (2020)
  11. Moncorgé, A.; Møyner, O.; Tchelepi, H. A.; Jenny, P.: Consistent upwinding for sequential fully implicit multiscale compositional simulation (2020)
  12. Pazner, Will: Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods (2020)
  13. Rhebergen, Sander; Wells, Garth N.: An embedded-hybridized discontinuous Galerkin finite element method for the Stokes equations (2020)
  14. Roy, Thomas; Jönsthövel, Tom B.; Lemon, Christopher; Wathen, Andrew J.: A constrained pressure-temperature residual (CPTR) method for non-isothermal multiphase flow in porous media (2020)
  15. Xiao, Yingxiong; Li, Zhenyou: Preconditioned conjugate gradient methods for the refined FEM discretizations of nearly incompressible elasticity problems in three dimensions (2020)
  16. Yushu, Dewen; Matouš, Karel: The image-based multiscale multigrid solver, preconditioner, and reduced order model (2020)
  17. Bassett, Brody; Kiedrowski, Brian: Meshless local Petrov-Galerkin solution of the neutron transport equation with streamline-upwind Petrov-Galerkin stabilization (2019)
  18. D’Ambra, Pasqua; Vassilevski, Panayot S.: Improving solve time of aggregation-based adaptive AMG. (2019)
  19. Dobrev, V.; Kolev, T.; Lee, C. S.; Tomov, V.; Vassilevski, P. S.: Algebraic hybridization and static condensation with application to scalable (H)(div) preconditioning (2019)
  20. Johansson, August; Kehlet, Benjamin; Larson, Mats G.; Logg, Anders: Multimesh finite element methods: solving PDEs on multiple intersecting meshes (2019)

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