BoomerAMG

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.


References in zbMATH (referenced in 144 articles , 1 standard article )

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  1. Bui, Quan M.; Osei-Kuffuor, Daniel; Castelletto, Nicola; White, Joshua A.: A scalable multigrid reduction framework for multiphase poromechanics of heterogeneous media (2020)
  2. Moncorgé, A.; Møyner, O.; Tchelepi, H. A.; Jenny, P.: Consistent upwinding for sequential fully implicit multiscale compositional simulation (2020)
  3. Rhebergen, Sander; Wells, Garth N.: An embedded-hybridized discontinuous Galerkin finite element method for the Stokes equations (2020)
  4. Xiao, Yingxiong; Li, Zhenyou: Preconditioned conjugate gradient methods for the refined FEM discretizations of nearly incompressible elasticity problems in three dimensions (2020)
  5. Bassett, Brody; Kiedrowski, Brian: Meshless local Petrov-Galerkin solution of the neutron transport equation with streamline-upwind Petrov-Galerkin stabilization (2019)
  6. 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)
  7. Johansson, August; Kehlet, Benjamin; Larson, Mats G.; Logg, Anders: Multimesh finite element methods: solving PDEs on multiple intersecting meshes (2019)
  8. Klawonn, Axel; Lanser, Martin; Rheinbach, Oliver; Weber, Janine: Preconditioning the coarse problem of BDDC methods -- three-level, algebraic multigrid, and vertex-based preconditioners (2019)
  9. Kunisch, Karl; Neic, Aurel; Plank, Gernot; Trautmann, Philip: Inverse localization of earliest cardiac activation sites from activation maps based on the viscous eikonal equation (2019)
  10. Li, Lingxiao; Ni, Mingjiu; Zheng, Weiying: A charge-conservative finite element method for inductionless MHD equations. II: A robust solver (2019)
  11. Maddison, James R.; Goldberg, Daniel N.; Goddard, Benjamin D.: Automated calculation of higher order partial differential equation constrained derivative information (2019)
  12. Manguoğlu, Murat; Mehrmann, Volker: A robust iterative scheme for symmetric indefinite systems (2019)
  13. Manteuffel, Thomas A.; MüNzenmaier, Steffen; Ruge, John; Southworth, Ben: Nonsymmetric reduction-based algebraic multigrid (2019)
  14. Paludetto Magri, Victor A.; Franceschini, Andrea; Janna, Carlo: A novel algebraic multigrid approach based on adaptive smoothing and prolongation for ill-conditioned systems (2019)
  15. Shahane, Shantanu; Aluru, Narayana; Ferreira, Placid; Kapoor, Shiv G.; Vanka, Surya Pratap: Finite volume simulation framework for die casting with uncertainty quantification (2019)
  16. Thomas, S. J.; Ananthan, S.; Yellapantula, S.; Hu, J. J.; Lawson, M.; Sprague, M. A.: A comparison of classical and aggregation-based algebraic multigrid preconditioners for high-fidelity simulation of wind turbine incompressible flows (2019)
  17. Tselepidis, N. A.; Filelis-Papadopoulos, C. K.; Gravvanis, G. A.: Distributed algebraic tearing and interconnecting techniques (2019)
  18. Adler, James H.; Lashuk, Ilya; MacLachlan, Scott P.: Composite-grid multigrid for diffusion on the sphere. (2018)
  19. Barker, A. T.; Dobrev, V.; Gopalakrishnan, J.; Kolev, T.: A scalable preconditioner for a primal discontinuous Petrov-Galerkin method (2018)
  20. Beaude, Laurence; Beltzung, Thibaud; Brenner, Konstantin; Lopez, Simon; Masson, Roland; Smai, Farid; Thebault, Jean-Frédéric; Xing, Feng: Parallel geothermal numerical model with fractures and multi-branch wells (2018)

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