Many Core Acceleration of the Boundary Element Method

  • Michal Merta
  • Jan ZapletalEmail author
  • Jiri Jaros
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9611)


The paper presents the boundary element method accelerated by the Intel Xeon Phi coprocessors. An overview of the boundary element method for the 3D Laplace equation is given followed by the discretization and its parallelization using OpenMP and the offload features of the Xeon Phi coprocessor are discussed. The results of numerical experiments for both single- and double-layer boundary integral operators are presented. In most cases the accelerated code significantly outperforms the original code running solely on Intel Xeon processors.


Boundary element method Intel Many Integrated Core architecture Acceleration OpenMP parallelization 



This work was supported by the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070), funded by the European Regional Development Fund and the national budget of the Czech Republic via the Research and Development for Innovations Operational Programme, as well as Czech Ministry of Education, Youth and Sports via the project Large Research, Development and Innovations Infrastructures (LM2011033). MM and JZ acknowledge the support of VŠB-TU Ostrava under the grant SGS SP2015/160. JJ was supported by the research project Architecture of parallel and embedded computer systems, Brno University of Technology, FIT-S-14-2297, 2014–2016 and by the SoMoPro II Programme co-financed by the European Union and the South-Moravian Region. This work reflects only the author’s view and the European Union is not liable for any use that may be made of the information contained therein.


  1. 1.
    Bebendorf, M., Rjasanow, S.: Adaptive low-rank approximation of collocation matrices. Computing 70(1), 1–24 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Dautray, R., Lions, J., Amson, J.: Mathematical Analysis and Numerical Methods for Science and Technology. Integral Equations and Numerical Methods, vol. 4. Springer, Heidelberg (1999)Google Scholar
  3. 3.
    Deslippe, J., Austin, B., Daley, C., Yang, W.S.: Lessons learned from optimizing science kernels for Intel’s Knights Corner architecture. Comput. Sci. Eng. 17(3), 30–42 (2015)CrossRefGoogle Scholar
  4. 4.
    Dongarra, J., Gates, M., Haidar, A., Jia, Y., Kabir, K., Luszczek, P., Tomov, S.: HPC programming on intel many-integrated-core hardware with MAGMA port to Xeon Phi. Sci. Program. 2015, 11 (2015)Google Scholar
  5. 5.
    Langer, U., Steinbach, O.: Boundary element tearing and interconnecting methods. Computing 71(3), 205–228 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    López-Portugués, M., López-Fernández, J., Díaz-Gracia, N., Ayestarán, R., Ranilla, J.: Aircraft noise scattering prediction using different accelerator architectures. J. Supercomputing 70(2), 612–622 (2014). CrossRefGoogle Scholar
  7. 7.
    Lukáš, D., Kovář, P., Kovářová, T., Merta, M.: A parallel fast boundary element method using cyclic graph decompositions. Numer. Algorithms 70, 807–824 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  9. 9.
    Merta, M., Zapletal, J.: Acceleration of boundary element method by explicit vectorization. Adv. Eng. Softw. 86, 70–79 (2015)CrossRefGoogle Scholar
  10. 10.
    Of, G., Steinbach, O.: The all-floating boundary element tearing and interconnecting method. J. Numer. Math. 17(4), 277–298 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Of, G.: Fast multipole methods and applications. In: Schanz, M., Steinbach, O. (eds.) Boundary Element Analysis. Lecture Notes in Applied and Computational Mechanics, vol. 29, pp. 135–160. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Rjasanow, S., Steinbach, O.: The Fast Solution of Boundary Integral Equations. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  13. 13.
    Rokhlin, V.: Rapid solution of integral equations of classical potential theory. J. Comput. Phys. 60(2), 187–207 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Sauter, S., Schwab, C.: Boundary Element Methods. Springer Series in Computational Mathematics. Springer, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  15. 15.
    Sirtori, S.: General stress analysis method by means of integral equations and boundary elements. Meccanica 14(4), 210–218 (1979)CrossRefzbMATHGoogle Scholar
  16. 16.
    Steinbach, O.: Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements. Texts in Applied Mathematics. Springer, Heidelberg (2008)CrossRefzbMATHGoogle Scholar
  17. 17.
    Intel Xeon Phi Coprocessor Peak Theoretical Maximums. Accessed 9 Oct 2015

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.IT4Innovations National Supercomputing CenterVŠB-Technical University of OstravaOstravaCzech Republic
  2. 2.Department of Computer SystemsBrno University of TechnologyBrnoCzech Republic

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