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. Wang, Kun; Liu, Hui; Luo, Jia; Chen, Zhangxin: Efficient CPR-type preconditioner and its adaptive strategies for large-scale parallel reservoir simulations (2018)
  2. Farrell, Patrick E.; Pearson, John W.: A preconditioner for the Ohta-Kawasaki equation (2017)
  3. Heil, Matthias; Rosso, Jordan; Hazel, Andrew L.; Brøns, Morten: Topological fluid mechanics of the formation of the Kármán-vortex street (2017)
  4. Lee, Chak S.; Vassilevski, Panayot S.: Parallel solver for $\boldsymbolH(\operatornamediv)$ problems using hybridization and AMG (2017)
  5. Luo, Li; Zhang, Qian; Wang, Xiao-Ping; Cai, Xiao-Chuan: A parallel finite element method for 3D two-phase moving contact line problems in complex domains (2017)
  6. Luo, Li; Zhang, Qian; Wang, Xiao-Ping; Cai, Xiao-Chuan: A parallel two-phase flow solver on unstructured mesh in 3D (2017)
  7. Maddison, J.R.; Hiester, H.R.: Optimal constrained interpolation in mesh-adaptive finite element modeling (2017)
  8. Manteuffel, Thomas A.; Olson, Luke N.; Schroder, Jacob B.; Southworth, Ben S.: A root-node-based algebraic multigrid method (2017)
  9. Pavarino, L.F.; Scacchi, S.; Verdi, C.; Zampieri, E.; Zampini, S.: Scalable BDDC algorithms for cardiac electromechanical coupling (2017)
  10. 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
  11. Wilbrandt, Ulrich; Bartsch, Clemens; Ahmed, Naveed; Alia, Najib; Anker, Felix; Blank, Laura; Caiazzo, Alfonso; Ganesan, Sashikumaar; Giere, Swetlana; Matthies, Gunar; Meesala, Raviteja; Shamim, Abdus; Venkatesan, Jagannath; John, Volker: ParMooN -- a modernized program package based on mapped finite elements (2017)
  12. Wu, Lingfei; Romero, Eloy; Stathopoulos, Andreas: PRIMME_SVDS: a high-performance preconditioned SVD solver for accurate large-scale computations (2017)
  13. Xu, Xiaowen; Mo, Zeyao: Algebraic interface-based coarsening AMG preconditioner for multi-scale sparse matrices with applications to radiation hydrodynamics computation. (2017)
  14. 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)
  15. Beams, Natalie N.; Olson, Luke N.; Freund, Jonathan B.: A finite element based P$^3$M method for $N$-body problems (2016)
  16. Bienz, Amanda; Falgout, Robert D.; Gropp, William; Olson, Luke N.; Schroder, Jacob B.: Reducing parallel communication in algebraic multigrid through sparsification (2016)
  17. Chen, Zhiming; Huang, Guanghui: A direct imaging method for electromagnetic scattering data without phase information (2016)
  18. Ervik, Åsmund; Lysgaard, Morten Olsen; Herdes, Carmelo; Jiménez-Serratos, Guadalupe; Müller, Erich A.; Munkejord, Svend Tollak; Müller, Bernhard: A multiscale method for simulating fluid interfaces covered with large molecules such as asphaltenes (2016)
  19. Grasedyck, Lars; Wang, Lu; Xu, Jinchao: A nearly optimal multigrid method for general unstructured grids (2016)
  20. Gratton, Serge; Hénon, Pascal; Jiránek, Pavel; Vasseur, Xavier: Reducing complexity of algebraic multigrid by aggregation. (2016)

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