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. Pereira, Fabio Henrique; Nabeta, Sílvio Ikuyo: A parallel wavelet-based algebraic multigrid black-box solver and preconditioner (2012)
  2. Adler, J. H.; Manteuffel, T. A.; McCormick, S. F.; Nolting, J. W.; Ruge, J. W.; Tang, L.: Efficiency based adaptive local refinement for first-order system least-squares formulations (2011)
  3. Baker, Allison H.; Falgout, Robert D.; Kolev, Tzanio V.; Meier Yang, Ulrike: Multigrid smoothers for ultraparallel computing (2011)
  4. Baker, Allison H.; Schulz, Martin; Yang, Ulrike M.: On the performance of an algebraic multigrid solver on multicore clusters (2011)
  5. Brunner, Thomas A.; Kolev, Tzanio V.: Algebraic multigrid for linear systems obtained by explicit element reduction (2011)
  6. Nasr-Azadani, M. M.; Meiburg, E.: TURBINS: an immersed boundary, Navier-Stokes code for the simulation of gravity and turbidity currents interacting with complex topographies (2011)
  7. Aprovitola, Andrea; D’Ambra, Pasqua; Denaro, Filippo; Di Serafino, Daniela; Filippone, Salvatore: Scalable algebraic multilevel preconditioners with application to CFD (2010)
  8. Barham, Matthew I.; White, Daniel A.; Steigmann, David J.: Finite element modeling of the deformation of magnetoelastic film (2010)
  9. Boyle, Jonathan; Mihajlovi, Milan; Scott, Jennifer: HSL_MI20: an efficient AMG preconditioner for finite element problems in 3D (2010)
  10. Brown, Jed: Efficient nonlinear solvers for nodal high-order finite elements in 3D (2010)
  11. Buckeridge, Sean; Scheichl, Robert: Parallel geometric multigrid for global weather prediction (2010)
  12. D’Ambra, Pasqua; Di Serafino, Daniela; Filippone, Salvatore: MLD2P4: a package of parallel algebraic multilevel domain decomposition preconditioners in Fortran 95 (2010)
  13. Emans, Maximilian: Performance of parallel AMG-preconditioners in CFD-codes for weakly compressible flows (2010)
  14. Emans, Maximilian: Efficient parallel AMG methods for approximate solutions of linear systems in CFD applications (2010)
  15. Henniger, R.; Obrist, D.; Kleiser, L.: High-order accurate solution of the incompressible Navier-Stokes equations on massively parallel computers (2010)
  16. Karer, E.; Kraus, J. K.: Algebraic multigrid for finite element elasticity equations: determination of nodal dependence via edge-matrices and two-level convergence (2010)
  17. Kerrache, Said; Nakauchi, Yasushi: Optrans: a parallel software library for optimal transport (2010)
  18. Montagnier, J.; Buffat, M.; Guibert, D.: Parallel computation of pollutant dispersion in industrial sites (2010)
  19. Raghavan, Padma; Teranishi, Keita: Parallel hybrid preconditioning: incomplete factorization with selective sparse approximate inversion (2010)
  20. Yang, Ulrike Meier: On long-range interpolation operators for aggressive coarsening (2010)

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