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Coarse-grid selection for parallel algebraic multigrid

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Solving Irregularly Structured Problems in Parallel (IRREGULAR 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1457))

Abstract

The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG). To date, however, no parallel AMG algorithms exist. We introduce a parallel algorithm for the selection of coarse-grid points, a crucial component of AMG, based on modifications of certain parallel independent set algorithms and the application of heuristics designed to insure the quality of the coarse grids. A prototype serial version of the algorithm is implemented, and tests are conducted to determine its effect on multigrid convergence, and AMG complexity.

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References

  1. S. Balay, W. Gropp, L. C. McInnes, and B. Smith, Petsc 2.0 user's manual, Tech. Rep. ANL-95/11, Argonne National Laboratory, Nov. 1995.

    Google Scholar 

  2. A. Brandt, Algebraic multigrid theory: The symmetric case, in Preliminary Proceedings for the International Multigrid Conference, Copper Mountain, Colorado, April 1983.

    Google Scholar 

  3. A. Brandt, Algebraic multigrid theory: The symmetric case, Appl. Math. Comput., 19 (1986), pp. 23–56.

    Google Scholar 

  4. A. Brandt, S. F. McCormick, and J. W. Ruge, Algebraic multigrid (AMG) for automatic multigrid solutions with application to geodetic computations. Report, Inst. for Computational Studies, Fort Collins, Colo., October 1982.

    Google Scholar 

  5. —, Algebraic multigrid (AMG) for sparse matrix equations, in Sparsity and Its Applications, D. J. Evans, ed., Cambridge University Press, Cambridge, 1984.

    Google Scholar 

  6. M. Brezina, A. J. Cleary, R. D. Falgout, V. E. Henson, J. E. Jones, T. A. Manteuffel, S. F. McCormick, and J. W. Ruge, Algebraic multigrid based on element interpolation (AMGe). Submitted to the SIAM Journal on Scientific Computing special issue on the Fifth Copper Mountain Conference on Iterative Methods, 1998.

    Google Scholar 

  7. A. J. Cleary, R. D. Falgout, V. E. Henson, J. E. Jones, T. A. Manteuffel, S. F. McCormick, G. N. Miranda, and J. W. Ruge, Robustness and scalability of algebraic multigrid. Submitted to the SIAM Journal on Scientific Computing special issue on the Fifth Copper Mountain Conference on Iterative Methods, 1998.

    Google Scholar 

  8. R. K. Gjertsen, Jr., M. T. Jones, and P. E. Plassman, Parallel heuristics for improved; balanced graph colorings, Journal of Parallel and Distributed Computing, 37 (1996), pp. 171–186.

    Google Scholar 

  9. G. Golubovici and C. Popa, Interpolation and related coarsening techniques for the algebraic multigrid method, in Multigrid Methods IV, Proceedings of the Fourth European Multigrid Conference, Amsterdam, July 6-9, 1993, vol. 116 of ISNM, Basel, 1994, Birkhäuser, pp, 201–213.

    Google Scholar 

  10. J. E. Jones and S. F. McCormick, Parallel multigrid methods, in Parallel Numerical Algorithms, D. E. Keys, A. H. Sameh, and V. Venkatakrishnan, eds., Dordrecht, Netherlands, 1997, Kluwer Academic Publications.

    Google Scholar 

  11. M. T. Jones and P. E. Plassman, A parallel graph coloring heuristic, SIAM Journal on Scientific Computing, 14 (1993), pp. 654–669.

    Google Scholar 

  12. G. Karypis and V. Kumar, A coarse-grain parallel multilevel k-way partitioning algorithm, in Proceedings of the 8th SIAM Conference on Parallel Processing for Scientific Computing, 1997.

    Google Scholar 

  13. M. Luby, A simple parallel algorithm for the maximal independent set problem, SIAM Journal on Computing, 15 (1986), pp. 1036–1053.

    Google Scholar 

  14. S. F. McCormick, Multigrid methods for variational problems: general theory for the V-cycle, SIAM J. Numer. Anal., 22 (1985), pp. 634–643.

    Google Scholar 

  15. MPI Forum, MPI: A message-passing interface standard, International J. Supercomputing Applications, 8(3/4) (1994), pp. 654–669.

    Google Scholar 

  16. J. W. Ruge and K. Stüben, Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG), in Multigrid Methods for Integral and Differential Equations, D. J. Paddon and H. Holstein, eds., The Institute of Mathematics and its Applications Conference Series, Clarendon Press, Oxford, 1985, pp. 169–212.

    Google Scholar 

  17. —, Algebraic multigrid (AMC), in Multigrid Methods, S. F. McCormick, ed., vol. 3 of Frontiers in Applied Mathematics, SIAM; Philadelphia, PA, 1987, pp. 73–130.

    Google Scholar 

  18. K. Stüben, Algebraic multigrid (AMG): experiences and comparisons, Appl. Math. Comput., 13 (1983), pp. 419–452.

    Google Scholar 

  19. K. Stüben, U. Trottenberg, and K. Witsch, Software development based on multigrid techniques, in Proc. IFIP-Conference on PDE Software, Modules, Interfaces and Systems, B. Enquist and T. Smedsaas, eds., Sweden, 1983, Söderköping.

    Google Scholar 

  20. P. Vaněk, J. Mandel, and M. Brezina, Algebraic multigrid based on smoothed aggregation for second and fourth order problems, Computing, 56 (1996), pp. 179–196.

    Google Scholar 

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Authors and Affiliations

  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA

    Andrew J. Cleary, Robert D. Falgout, Van Emden Henson & Jim E. Jones

Authors
  1. Andrew J. Cleary
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  2. Robert D. Falgout
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  3. Van Emden Henson
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  4. Jim E. Jones
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Editor information

Alfonso Ferreira José Rolim Horst Simon Shang-Hua Teng

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© 1998 Springer-Verlag Berlin Heidelberg

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Cleary, A.J., Falgout, R.D., Henson, V.E., Jones, J.E. (1998). Coarse-grid selection for parallel algebraic multigrid. In: Ferreira, A., Rolim, J., Simon, H., Teng, SH. (eds) Solving Irregularly Structured Problems in Parallel. IRREGULAR 1998. Lecture Notes in Computer Science, vol 1457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018531

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  • DOI: https://doi.org/10.1007/BFb0018531

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64809-3

  • Online ISBN: 978-3-540-68533-3

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