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. Duarte, Max; Bonaventura, Zdeněk; Massot, Marc; Bourdon, Anne: A numerical strategy to discretize and solve the Poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations (2015)
  2. Gremse, Felix; Höfter, Andreas; Schwen, Lars Ole; Kiessling, Fabian; Naumann, Uwe: GPU-accelerated sparse matrix-matrix multiplication by iterative row merging (2015)
  3. Klawonn, Axel; Lanser, Martin; Rheinbach, Oliver: Toward extremely scalable nonlinear domain decomposition methods for elliptic partial differential equations (2015)
  4. Kosturski, Nikola; Margenov, Svetozar; Popov, Peter; Simeonov, Nikola; Vutov, Yavor: Performance analysis of block AMG preconditioning of poroelasticity equations (2015)
  5. Liu, Hui; Yang, Bo; Chen, Zhangxin: Accelerating algebraic multigrid solvers on NVIDIA GPUs (2015)
  6. Liu, Lulu; Keyes, David E.: Field-split preconditioned inexact Newton algorithms (2015)
  7. Notay, Yvan; Napov, Artem: A massively parallel solver for discrete Poisson-like problems (2015)
  8. Ottino, D.; Scacchi, S.: BPX preconditioners for the Bidomain model of electrocardiology (2015)
  9. Rhebergen, Sander; Wells, Garth N.; Wathen, Andrew J.; Katz, Richard F.: Three-field block preconditioners for models of coupled magma/mantle dynamics (2015)
  10. Treister, Eran; Yavneh, Irad: Non-Galerkin multigrid based on sparsified smoothed aggregation (2015)
  11. Xiao, Yingxiong; Zhou, Zhiyang; Shu, Shi: An efficient algebraic multigrid method for quadratic discretizations of linear elasticity problems on some typical anisotropic meshes in three dimensions. (2015)
  12. Della Rocca, G.; Blanquart, G.: Level set reinitialization at a contact line (2014)
  13. Feng, Chunsheng; Shu, Shi; Xu, Jinchao; Zhang, Chen-Song: A multi-stage preconditioner for the black oil model and its OpenMP implementation (2014)
  14. Fu, Zhisong; Lewis, T. James; Kirby, Robert M.; Whitaker, Ross T.: Architecting the finite element method pipeline for the GPU (2014)
  15. Jiang, Xue; Zheng, Weiying: Homogenization of quasi-static Maxwell’s equations (2014)
  16. MacLachlan, Scott P.; Olson, Luke N.: Theoretical bounds for algebraic multigrid performance: review and analysis. (2014)
  17. Siefert, C.; Tuminaro, R.; Gerstenberger, A.; Scovazzi, G.; Collis, S. S.: Algebraic multigrid techniques for discontinuous Galerkin methods with varying polynomial order (2014)
  18. Vassilevski, Panayot S.; Yang, Ulrike Meier: Reducing communication in algebraic multigrid using additive variants. (2014)
  19. Brannick, James; Chen, Yao; Hu, Xiaozhe; Zikatanov, Ludmil: Parallel unsmoothed aggregation algebraic multigrid algorithms on GPUs (2013)
  20. Brown, Jed; Smith, Barry; Ahmadia, Aron: Achieving textbook multigrid efficiency for hydrostatic ice sheet flow (2013)

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