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. Farrell, Patrick E.; Pearson, John W.: A preconditioner for the Ohta-Kawasaki equation (2017)
  2. Luo, Li; Zhang, Qian; Wang, Xiao-Ping; Cai, Xiao-Chuan: A parallel two-phase flow solver on unstructured mesh in 3D (2017)
  3. Ulrich Wilbrandt, Clemens Bartsch, Naveed Ahmed, Najib Alia, Felix Anker, Laura Blank, Alfonso Caiazzo, Sashikumaar Ganesan, Swetlana Giere, Gunar Matthies, Raviteja Meesala, Abdus Shamim, Jagannath Venkatesan, Volker John: ParMooN - a modernized program package based on mapped finite elements (2017) arXiv
  4. Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot: Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation (2016)
  5. Beams, Natalie N.; Olson, Luke N.; Freund, Jonathan B.: A finite element based P$^3$M method for $N$-body problems (2016)
  6. Bienz, Amanda; Falgout, Robert D.; Gropp, William; Olson, Luke N.; Schroder, Jacob B.: Reducing parallel communication in algebraic multigrid through sparsification (2016)
  7. Chen, Zhiming; Huang, Guanghui: A direct imaging method for electromagnetic scattering data without phase information (2016)
  8. Grasedyck, Lars; Wang, Lu; Xu, Jinchao: A nearly optimal multigrid method for general unstructured grids (2016)
  9. Guo, Li; Zhang, Xing; He, Guowei: Large-eddy simulation of circular cylinder flow at subcritical Reynolds number: turbulent wake and sound radiation (2016)
  10. Huber, Markus; Gmeiner, Björn; Rüde, Ulrich; Wohlmuth, Barbara: Resilience for massively parallel multigrid solvers (2016)
  11. Klawonn, Axel; Lanser, Martin; Rheinbach, Oliver: A nonlinear FETI-DP method with an inexact coarse problem (2016)
  12. Liu, Hui; Wang, Kun; Chen, Zhangxin: A family of constrained pressure residual preconditioners for parallel reservoir simulations. (2016)
  13. Napov, Artem; Notay, Yvan: An efficient multigrid method for graph Laplacian systems (2016)
  14. Zampini, Stefano: PCBDDC: a class of robust dual-primal methods in PETSc (2016)
  15. Bank, R.; Falgout, R.; Jones, T.; Manteuffel, T.A.; McCormick, S.F.; Ruge, J.W.: Algebraic multigrid domain and range decomposition (AMG-DD/AMG-RD) (2015)
  16. Chamakuri, Nagaiah; Kunisch, Karl; Plank, Gernot: Application of optimal control to the cardiac defibrillation problem using a physiological model of cellular dynamics (2015)
  17. Colli Franzone, P.; Pavarino, L.F.; Scacchi, S.: Parallel multilevel solvers for the cardiac electro-mechanical coupling (2015)
  18. 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)
  19. Gremse, Felix; Höfter, Andreas; Schwen, Lars Ole; Kiessling, Fabian; Naumann, Uwe: GPU-accelerated sparse matrix-matrix multiplication by iterative row merging (2015)
  20. Klawonn, Axel; Lanser, Martin; Rheinbach, Oliver: Toward extremely scalable nonlinear domain decomposition methods for elliptic partial differential equations (2015)

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