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. Salinas, P.; Rodrigo, C.; Gaspar, F. J.; Lisbona, F. J.: An efficient cell-centered multigrid method for problems with discontinuous coefficients on semi-structured triangular grids (2013)
  2. Vasconcelos, Paulo B.; d’Almeida, Filomena D.; Roman, Jose E.: A Jacobi-Davidson type method with a correction equation tailored for integral operators (2013)
  3. Wang, Lu; Hu, Xiaozhe; Cohen, Jonathan; Xu, Jinchao: A parallel auxiliary grid algebraic multigrid method for graphic processing units (2013)
  4. Bell, Nathan; Dalton, Steven; Olson, Luke N.: Exposing fine-grained parallelism in algebraic multigrid methods (2012)
  5. Buchan, A. G.; Pain, C. C.; Umpleby, A. P.; Smedley-Stevenson, R. P.: A sub-grid scale finite element agglomeration multigrid method with application to the Boltzmann transport equation (2012)
  6. Emans, Maximilian: Krylov-accelerated algebraic multigrid for semi-definite and nonsymmetric systems in computational fluid dynamics. (2012)
  7. Ferronato, Massimiliano: Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives (2012)
  8. Jönsthövel, T. B.; van Gijzen, M. B.; MacLachlan, S.; Vuik, C.; Scarpas, A.: Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials (2012)
  9. Kolev, Tzanio V.; Vassilevski, Panayot S.: Parallel auxiliary space AMG solver for (H(\operatornamediv)) problems (2012)
  10. Kosturski, N.; Margenov, S.; Vutov, Y.: Improving the efficiency of parallel FEM simulations on voxel domains (2012)
  11. Li, Dan; Greif, Chen; Schötzau, Dominik: Parallel numerical solution of the time-harmonic Maxwell equations in mixed form. (2012)
  12. MacLachlan, S. P.; Moulton, J. D.; Chartier, T. P.: Robust and adaptive multigrid methods: comparing structured and algebraic approaches. (2012)
  13. Melchior, S. A.; Legat, V.; Van Dooren, P.; Wathen, A. J.: Analysis of preconditioned iterative solvers for incompressible flow problems (2012)
  14. Muddle, Richard L.; Mihajlović, Milan; Heil, Matthias: An efficient preconditioner for monolithically-coupled large-displacement fluid-structure interaction problems with pseudo-solid mesh updates (2012)
  15. Pereira, Fabio Henrique; Nabeta, Sílvio Ikuyo: A parallel wavelet-based algebraic multigrid black-box solver and preconditioner (2012)
  16. 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)
  17. Baker, Allison H.; Falgout, Robert D.; Kolev, Tzanio V.; Meier Yang, Ulrike: Multigrid smoothers for ultraparallel computing (2011)
  18. Baker, Allison H.; Schulz, Martin; Yang, Ulrike M.: On the performance of an algebraic multigrid solver on multicore clusters (2011)
  19. Brunner, Thomas A.; Kolev, Tzanio V.: Algebraic multigrid for linear systems obtained by explicit element reduction (2011)
  20. 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)

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