Advertisement

Multi-GPU Acceleration of Algebraic Multigrid Preconditioners

  • Christian RichterEmail author
  • Sebastian Schöps
  • Markus Clemens
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 23)

Abstract

A multi-GPU implementation of Krylov subspace methods with an algebraic multigrid preconditioners is proposed. With this, large linear system are solved which result from electrostatic field problems after discretization with the Finite Element Method. As data is distributed across multiple GPUs the resulting impact on memory and execution time are discussed for a given problem solved with either first or second order ansatz functions.

References

  1. 1.
    Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM, Boston (2003)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bell, N., Garland, M.: Efficient sparse matrix-vector multiplication on CUDA, NVIDIA Corporation, NVIDIA Technical Report NVR-2008-004 (2008)Google Scholar
  3. 3.
    Mehri Dehnavi, M., Fernández, D.M., Giannacopoulos, D.: Finite-Element sparse matrix vector multiplication on graphic processing units. IEEE Trans. Magn. 46(8), 2982–2985 (2010)CrossRefGoogle Scholar
  4. 4.
    Richter, C., Schöps, S., Clemens, M.: GPU acceleration of finite differences in coupled electromagnetic/thermal simulations. IEEE Trans. Magn. 49(5), 1649–1652 (2013)CrossRefGoogle Scholar
  5. 5.
    Mehri Dehnavi, M., Fernández, D.M., Giannacopoulos, D.: Enhancing the performance of conjugate gradient solvers on graphic processing units. IEEE Trans. Magn. 47(5), 1162–1165 (2011)CrossRefGoogle Scholar
  6. 6.
    Mehri Dehnavi, M., Fernández, D.M., Gaudiot, J.-L.: Parallel sparse approximate inverse preconditioning on graphic processing units. IEEE Trans. Parallel Distrib. Syst. 24(9), 1852–1862 (2013)CrossRefGoogle Scholar
  7. 7.
    Verschoor, M., Jalba, A.C.: Analysis and performance estimation of the conjugate gradient method on multiple GPUs. Parallel Comput. 38(10–11), 552–575 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    C. Richter; S. Schöps; M. Clemens Multi-GPU acceleration of algebraic multigrid preconditioners for elliptic field problems, IEEE Trans. Magn., 51(3), 1–4 (2015). DOI: 10.1109/TMAG.2014.2357332CrossRefGoogle Scholar
  9. 9.
    Steinmetz, T., Helias, M., Wimmer, G., et al.: Electro-quasistatic field simulations based on a discrete electromagnetism formulation. IEEE Trans. Magn. 42(4), 755–758 (2006)CrossRefGoogle Scholar
  10. 10.
    Monk, P.: Finite Element Methods for Maxwell’s Equations. Oxford University Press, Oxford (2003)CrossRefzbMATHGoogle Scholar
  11. 11.
    Ye, H., Clemens, M., Seifert, J.: Electro-quasistatic field simulation for the layout optimization of outdoor insulation using microvaristor material. IEEE Trans. Magn. 49(5), 1709–1712 (2013)CrossRefGoogle Scholar
  12. 12.
    Stüben, K.: Algebraic multigrid (AMG): an introduction with applications, GMD, Report 53 (1999)Google Scholar
  13. 13.
    Vanek, P., Mandel, J., Bresina, M.: Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing 56, 179–196 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Shapira, Y.: Matrix-Based Multigrid: Theory and Applications. Numerical Methods and Algorithms. Springer, New York (2008)CrossRefzbMATHGoogle Scholar
  15. 15.
    Trottenberg, U., Oosterlee, C., Schuller, A.: Multigrid. Academic, New York (2001)zbMATHGoogle Scholar
  16. 16.
    Bell, N., Garland, M.: CUSP: generic parallel algorithms for sparse matrix and graph computations, version 0.4.0. (2012)Google Scholar
  17. 17.
    Bell, N., Dalton, S., Olson, L.N.: Exposing fine-grained parallelism in algebraic multigrid methods. SIAM J. Sci. Comput. 34(4), C123–C152 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Richter, C., Schöps, S., Clemens, M.: GPU acceleration of algebraic multigrid preconditioners for discrete elliptic field problems. IEEE Trans. Magn. 50(2), 461–464 (2014)CrossRefGoogle Scholar
  19. 19.
    Balay, S., Brown, J., Buschelman, K., et al.: PETSc users manual, Argonne National Laboratory, Technical Report ANL-95/11 - Review 3.4, (2013)Google Scholar
  20. 20.
    Gee, M., Siefert, C., et al.: ML 5.0 smoothed aggregation user’s guide, Sandia National Laboratories, Technical Report SAND2006-2649 (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Christian Richter
    • 1
    Email author
  • Sebastian Schöps
    • 2
  • Markus Clemens
    • 3
  1. 1.University of Wuppertal, Chair of Electromagnetic TheoryWuppertalGermany
  2. 2.Graduate School of Computational Engineering Institut für Theorie Elektromagnetischer FelderTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Chair of Electromagnetic TheoryBergische Universität WuppertalWuppertalGermany

Personalised recommendations