Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bebendorf, M., Rjasanow, S.: Adaptive low-rank approximation of collocation matrices. Computing 70(1), 1–24 (2003)
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)
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)
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)
Langer, U., Steinbach, O.: Boundary element tearing and interconnecting methods. Computing 71(3), 205–228 (2003)
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). http://dx.doi.org/10.1007/s11227-014-1107-z
Lukáš, D., Kovář, P., Kovářová, T., Merta, M.: A parallel fast boundary element method using cyclic graph decompositions. Numer. Algorithms 70, 807–824 (2015)
McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000)
Merta, M., Zapletal, J.: Acceleration of boundary element method by explicit vectorization. Adv. Eng. Softw. 86, 70–79 (2015)
Of, G., Steinbach, O.: The all-floating boundary element tearing and interconnecting method. J. Numer. Math. 17(4), 277–298 (2009)
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)
Rjasanow, S., Steinbach, O.: The Fast Solution of Boundary Integral Equations. Springer, Heidelberg (2007)
Rokhlin, V.: Rapid solution of integral equations of classical potential theory. J. Comput. Phys. 60(2), 187–207 (1985)
Sauter, S., Schwab, C.: Boundary Element Methods. Springer Series in Computational Mathematics. Springer, Heidelberg (2010)
Sirtori, S.: General stress analysis method by means of integral equations and boundary elements. Meccanica 14(4), 210–218 (1979)
Steinbach, O.: Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements. Texts in Applied Mathematics. Springer, Heidelberg (2008)
Intel Xeon Phi Coprocessor Peak Theoretical Maximums. http://www.intel.com/content/www/us/en/benchmarks/server/xeon-phi/xeon-phi-theoretical-maximums.html. Accessed 9 Oct 2015
Acknowledgments
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Merta, M., Zapletal, J., Jaros, J. (2016). Many Core Acceleration of the Boundary Element Method. In: Kozubek, T., Blaheta, R., Šístek, J., Rozložník, M., Čermák, M. (eds) High Performance Computing in Science and Engineering. HPCSE 2015. Lecture Notes in Computer Science(), vol 9611. Springer, Cham. https://doi.org/10.1007/978-3-319-40361-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-40361-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40360-1
Online ISBN: 978-3-319-40361-8
eBook Packages: Computer ScienceComputer Science (R0)