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Parallel Assembly of ACA BEM Matrices on Xeon Phi Clusters

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Parallel Processing and Applied Mathematics (PPAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10777))

Abstract

The paper presents parallelization of the boundary element method in distributed memory of a cluster equipped with many-core based compute nodes. A method for efficient distribution of boundary element matrices among MPI processes based on the cyclic graph decompositions is described. In addition, we focus on the intra-node optimization of the code, which is necessary in order to fully utilize the many-core processors with wide SIMD registers. Numerical experiments carried out on a cluster consisting of the Intel Xeon Phi processors of the Knights Landing generation are presented.

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Notes

  1. 1.

    November 2016 version.

References

  1. Bebendorf, M.: Approximation of boundary element matrices. Numer. Math. 86(4), 565–589 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bebendorf, M., Kriemann, R.: Fast parallel solution of boundary integral equations and related problems. Comp. Vis. Sci. 8(3–4), 121–135 (2005)

    Article  MathSciNet  Google Scholar 

  3. Bebendorf, M., Rjasanow, S.: Adaptive low-rank approximation of collocation matrices. Computing 70(1), 1–24 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Börm, S.: H2Lib (2017). http://www.h2lib.org/. Accessed 14 Feb 2017

  5. Dongarra, J.: Report on the Sunway TaihuLight system. Technical report. University of Tennessee, Oak Ridge National Laboratory, June 2016

    Google Scholar 

  6. Karypis, G., Kumar, V.: A fast and highly quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1999)

    Article  MATH  Google Scholar 

  7. Kravcenko, M., Merta, M., Zapletal, J.: Using discrete mathematics to optimize parallelism in boundary element method, Paper 2. In: Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering. Civil-Comp Press, Stirlingshire (2017). https://doi.org/10.4203/ccp.111.2

  8. Kreutzer, M., Hager, G., Wellein, G., Fehske, H., Bishop, A.R.: A unified sparse matrix data format for efficient general sparse matrix-vector multiplication on modern processors with wide SIMD units. SIAM J. Sci. Comput. 36(5), C401–C423 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lukáš, D., Kovář, P., Kovářová, T., Merta, M.: A parallel fast boundary element method using cyclic graph decompositions. Numer. Algorithms 70(4), 807–824 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Merta, M., Zapletal, J.: BEM4I (2014). http://bem4i.it4i.cz. Accessed 17 Jan 2017

  11. Merta, M., Zapletal, J., Jaros, J.: Many core acceleration of the boundary element method. In: Kozubek, T., Blaheta, R., Šístek, J., Rozložník, M., Čermák, M. (eds.) HPCSE 2015. LNCS, vol. 9611, pp. 116–125. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40361-8_8

    Chapter  Google Scholar 

  12. Merta, M., Riha, L., Meca, O., Markopoulos, A., Brzobohaty, T., Kozubek, T., Vondrak, V.: Intel Xeon Phi acceleration of hybrid total FETI solver. Adv. Eng. Softw. 112, 124–135 (2017)

    Article  Google Scholar 

  13. Říha, L., Brzobohatý, T., Markopoulos, A., Kozubek, T., Meca, O., Schenk, O., Vanroose, W.: Efficient implementation of total FETI solver for graphic processing units using schur complement. In: Kozubek, T., Blaheta, R., Šístek, J., Rozložník, M., Čermák, M. (eds.) HPCSE 2015. LNCS, vol. 9611, pp. 85–100. Springer, Cham (2016)

    Chapter  Google Scholar 

  14. Rjasanow, S., Steinbach, O.: The Fast Solution of Boundary Integral Equations. Springer, Boston (2007). https://doi.org/10.1007/0-387-34042-4

    MATH  Google Scholar 

  15. Sauter, S.A., Schwab, C.: Boundary element methods. In: Sauter, S.A., Schwab, C. (eds.) Boundary Element Methods. Springer Series in Computational Mathematics, vol. 39, pp. 183–287. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-540-68093-2_4

    Chapter  Google Scholar 

  16. Steinbach, O.: Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements. Texts in Applied Mathematics. Springer, New York (2008). https://doi.org/10.1007/978-0-387-68805-3

    Book  MATH  Google Scholar 

  17. Zapletal, J., Merta, M., Malý, L.: Boundary element quadrature schemes for multi-and many-core architectures. Comput. Math. Appl. 74(1), 157–173 (2017). 5th European Seminar on Computing ESCO 2016

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by The Ministry of Educations, Youth and Sports from the Large Infrastructures for Research, Experimental Development and Innovations project “IT4Innovations National Supercomputing Center – LM2015070”. The work was supported by The Ministry of Educations, Youth and Sports from the National Programme of Sustainability (NPU II) project “IT4Innovations excellence in science – LQ1602”. This work was partially supported by grant of SGS No. SP2017/165 “Efficient implementation of the boundary element method III”, VŠB – Technical University of Ostrava, Czech Republic. The authors thank HLRN for providing us with access to the HLRN Berlin Test and Development System.

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Authors and Affiliations

  1. IT4Innovations, VŠB – Technical University of Ostrava, 17. listopadu 15/2172, 708 33, Ostrava-Poruba, Czech Republic

    Michal Kravcenko, Lukas Maly, Michal Merta & Jan Zapletal

  2. Department of Applied Mathematics, VŠB – Technical University of Ostrava, 17. listopadu 15/2172, 708 33, Ostrava-Poruba, Czech Republic

    Michal Kravcenko, Lukas Maly, Michal Merta & Jan Zapletal

Authors
  1. Michal Kravcenko
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  2. Lukas Maly
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  3. Michal Merta
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  4. Jan Zapletal
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Corresponding author

Correspondence to Michal Merta .

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Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  3. University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  4. Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

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Kravcenko, M., Maly, L., Merta, M., Zapletal, J. (2018). Parallel Assembly of ACA BEM Matrices on Xeon Phi Clusters. In: Wyrzykowski, R., Dongarra, J., Deelman, E., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2017. Lecture Notes in Computer Science(), vol 10777. Springer, Cham. https://doi.org/10.1007/978-3-319-78024-5_10

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  • DOI: https://doi.org/10.1007/978-3-319-78024-5_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78023-8

  • Online ISBN: 978-3-319-78024-5

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