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. Fu, Guosheng; Kuang, Wenzheng: A monolithic divergence-conforming HDG scheme for a linear fluid-structure interaction model (2022)
  2. Nathan Bell, Luke N. Olson, Jacob Schroder: PyAMG: Algebraic Multigrid Solvers in Python (2022) not zbMATH
  3. Rhebergen, Sander; Wells, Garth N.: Preconditioning for a pressure-robust HDG discretization of the Stokes equations (2022)
  4. Torun, Tugba; Torun, F. Sukru; Manguoglu, Murat; Aykanat, Cevdet: Partitioning and reordering for spike-based distributed-memory parallel Gauss-Seidel (2022)
  5. Yue, Xiaoqiang; Wang, Chunqing; Xu, Xiaowen; Wang, Libo; Shu, Shi: A new relaxed splitting preconditioner for multidimensional multi-group radiation diffusion equations (2022)
  6. Al Daas, Hussam; Grigori, Laura; Jolivet, Pierre; Tournier, Pierre-Henri: A multilevel Schwarz preconditioner based on a hierarchy of robust coarse spaces (2021)
  7. Allen, Jeffery M.; Chang, Justin; Usseglio-Viretta, Francois L. E.; Graf, Peter; Smith, Kandler: A segregated approach for modeling the electrochemistry in the 3-D microstructure of li-ion batteries and its acceleration using block preconditioners (2021)
  8. Augustin, Christoph M.; Gsell, Matthias A. F.; Karabelas, Elias; Willemen, Erik; Prinzen, Frits W.; Lumens, Joost; Vigmond, Edward J.; Plank, Gernot: A computationally efficient physiologically comprehensive 3D-0D closed-loop model of the heart and circulation (2021)
  9. Bui, Quan M.; Hamon, François P.; Castelletto, Nicola; Osei-Kuffuor, Daniel; Settgast, Randolph R.; White, Joshua A.: Multigrid reduction preconditioning framework for coupled processes in porous and fractured media (2021)
  10. Büsing, Henrik: Efficient solution techniques for two-phase flow in heterogeneous porous media using exact Jacobians (2021)
  11. D’Ambra, Pasqua; Durastante, Fabio; Filippone, Salvatore: AMG preconditioners for linear solvers towards extreme scale (2021)
  12. Fu, Guosheng: Uniform auxiliary space preconditioning for HDG methods for elliptic operators with a parameter dependent low order term (2021)
  13. Jolivet, P.; Badri, M. A.; Favennec, Y.: Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: efficient assembly and preconditioning (2021)
  14. Jost, Antoine Michael Diego; Glockner, Stéphane: Direct forcing immersed boundary methods: improvements to the ghost-cell method (2021)
  15. Klawonn, Axel; Lanser, Martin; Rheinbach, Oliver; Uran, Matthias: Fully-coupled micro-macro finite element simulations of the Nakajima test using parallel computational homogenization (2021)
  16. Kuchta, Miroslav; Mardal, Kent-André: Iterative solvers for EMI models (2021)
  17. Li, Lingxiao; Zhang, Donghang; Zheng, Weiying: A constrained transport divergence-free finite element method for incompressible MHD equations (2021)
  18. Li, Ruipeng; Sjögreen, Björn; Meier Yang, Ulrike: A new class of AMG interpolation methods based on matrix-matrix multiplications (2021)
  19. Schussnig, Richard; Pacheco, Douglas R. Q.; Fries, Thomas-Peter: Robust stabilised finite element solvers for generalised Newtonian fluid flows (2021)
  20. Świrydowicz, Katarzyna; Langou, Julien; Ananthan, Shreyas; Yang, Ulrike; Thomas, Stephen: Low synchronization Gram-Schmidt and generalized minimal residual algorithms. (2021)

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