Advertisement

Hardware-Based Efficiency Advances in the EXA-DUNE Project

  • Peter Bastian
  • Christian Engwer
  • Jorrit Fahlke
  • Markus Geveler
  • Dominik Göddeke
  • Oleg Iliev
  • Olaf Ippisch
  • René Milk
  • Jan Mohring
  • Steffen Müthing
  • Mario Ohlberger
  • Dirk Ribbrock
  • Stefan Turek
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 113)

Abstract

We present advances concerning efficient finite element assembly and linear solvers on current and upcoming HPC architectures obtained in the frame of the Exa-Dune project, part of the DFG priority program 1648 Software for Exascale Computing (SPPEXA). In this project, we aim at the development of both flexible and efficient hardware-aware software components for the solution of PDEs based on the DUNE platform and the FEAST library. In this contribution, we focus on node-level performance and accelerator integration, which will complement the proven MPI-level scalability of the framework. The higher-level aspects of the Exa-Dune project, in particular multiscale methods and uncertainty quantification, are detailed in the companion paper (Bastian et al., Advances concerning multiscale methods and uncertainty quantification in Exa-Dune. In: Proceedings of the SPPEXA Symposium, 2016).

Keywords

Discontinuous Galerkin Discontinuous Galerkin Method Unstructured Mesh Quadrature Point Memory Bandwidth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This research was funded by the DFG SPP 1648 Software for Exascale Computing.

References

  1. 1.
    Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Kornhuber, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE. Computing 82 (2–3), 121–138 (2008)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework. Computing 82 (2–3), 103–119 (2008)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Bastian, P., Engwer, C., Fahlke, J., Geveler, M., Göddeke, D., Iliev, O., Ippisch, O., Milk, R., Mohring, J., Müthing, S., Ohlberger, M., Ribbrock, D., Turek, S.: Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE. In: Proceedings of the SPPEXA Symposium 2016. Lecture Notes in Computational Science and Engineering. Springer (2016)Google Scholar
  4. 4.
    Bastian, P., Engwer, C., Göddeke, D., Iliev, O., Ippisch, O., Ohlberger, M., Turek, S., Fahlke, J., Kaulmann, S., Müthing, S., Ribbrock, D.: EXA-DUNE: flexible PDE solvers, numerical methods and applications. In: Lopes, L., et al. (eds.) Euro-Par 2014: Parallel Processing Workshops. Euro-Par 2014 International Workshops, Porto, 25–26 Aug 2014, Revised Selected Papers, Part II. Lecture Notes in Computer Science, vol. 8806, pp. 530–541. Springer (2014)Google Scholar
  5. 5.
    Bröker, O., Grote, M.J.: Sparse approximate inverse smoothers for geometric and algebraic multigrid. Appl. Numer. Math. 41 (1), 61–80 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Choi, J., Singh, A., Vuduc, R.: Model-driven autotuning of sparse matrix-vector multiply on GPUs. In: Principles and Practice of Parallel Programming, pp. 115–126. ACM, New York (2010)Google Scholar
  7. 7.
    Engwer, C., Fahlke, J.: Scalable hybrid parallelization strategies for the DUNE grid interface. In: Numerical Mathematics and Advanced Applications: Proceedings of ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol. 103, pp. 583–590. Springer (2014)Google Scholar
  8. 8.
    Ern, A., Stephansen, A., Zunino, P.: A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity. IMA J. Numer. Anal. 29 (2), 235–256 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Fog, A.: VCL vector class library, http://www.agner.org/optimize
  10. 10.
    Geveler, M., Ribbrock, D., Göddeke, D., Zajac, P., Turek, S.: Towards a complete FEM-based simulation toolkit on GPUs: unstructured grid finite element geometric multigrid solvers with strong smoothers based on sparse approximate inverses. Comput. Fluids 80, 327–332 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Grote, M.J., Huckle, T.: Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18, 838–853 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kretz, M., Lindenstruth, V.: Vc: A C++ library for explicit vectorization. Softw. Pract. Exp. 42 (11), 1409–1430 (2012)CrossRefGoogle Scholar
  13. 13.
    Kreutzer, M., Hager, G., Wellein, G., Fehske, H., Bishop, A.R.: A unified sparse matrix data format for modern processors with wide SIMD units. SIAM J. Sci. Comput. 36 (5), C401–C423 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kronbichler, M., Kormann, K.: A generic interface for parallel cell-based finite element operator application. Comput. Fluids 63, 135–147 (2012)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Melenk, J.M., Gerdes, K., Schwab, C.: Fully discrete hp-finite elements: fast quadrature. Comput. Methods Appl. Mech. Eng. 190 (32–33), 4339–4364 (2001)CrossRefzbMATHGoogle Scholar
  16. 16.
    Müthing, S., Ribbrock, D., Göddeke, D.: Integrating multi-threading and accelerators into DUNE-ISTL. In: Numerical Mathematics and Advanced Applications: Proceedings of ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol. 103, pp. 601–609. Springer (2014)Google Scholar
  17. 17.
    Sawyer, W., Vanini, C., Fourestey, G., Popescu, R.: SPAI preconditioners for HPC applications. PAMM 12 (1), 651–652 (2012)CrossRefGoogle Scholar
  18. 18.
    Turek, S., Göddeke, D., Becker, C., Buijssen, S., Wobker, S.: FEAST – realisation of hardware-oriented numerics for HPC simulations with finite elements. Concurr. Comput.: Pract. Exp. 22 (6), 2247–2265 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Peter Bastian
    • 1
  • Christian Engwer
    • 2
  • Jorrit Fahlke
    • 2
  • Markus Geveler
    • 4
  • Dominik Göddeke
    • 3
  • Oleg Iliev
    • 5
  • Olaf Ippisch
    • 6
  • René Milk
    • 2
  • Jan Mohring
    • 5
  • Steffen Müthing
    • 1
  • Mario Ohlberger
    • 2
  • Dirk Ribbrock
    • 4
  • Stefan Turek
    • 4
  1. 1.Interdisciplinary Center for Scientific ComputingHeidelberg UniversityHeidelbergGermany
  2. 2.Institute for Computational and Applied MathematicsUniversity of MünsterMünsterGermany
  3. 3.Institute of Applied Analysis and Numerical SimulationUniversity of StuttgartStuttgartGermany
  4. 4.Institute of Applied MathematicsDortmundGermany
  5. 5.Fraunhofer Institute for Industrial Mathematics ITWMKaiserslauternGermany
  6. 6.Institut für Mathematik, TU Clausthal-ZellerfeldClausthal-ZellerfeldGermany

Personalised recommendations