Time-Domain BEM for the Wave Equation: Optimization and Hybrid Parallelization

  • Berenger Bramas
  • Olivier Coulaud
  • Guillaume Sylvand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8632)


The problem of time-domain BEM for the wave equation in acoustics and electromagnetism can be expressed as a sparse linear system composed of multiple interaction/convolution matrices. It can be solved using sparse matrix-vector products which are inefficient to achieve high Flop-rate. In this paper we present a novel approach based on the re-ordering of the interaction matrices in slices. We end up with a custom multi-vectors/vector product operation and compute it using SIMD intrinsic functions. We take advantage of the new order of the computation to parallelize in shared and distributed memory. We demonstrate the performance of our system by studying the sequential Flop-rate and the parallel scalability, and provide results based on an industrial test-case with up to 32 nodes.


Boundary element method (BEM) time domain sparse matrix-vector product (SpMV) shared/distributed memory parallelization SIMD 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Liu, Y.J., Mukherjee, S., Nishimura, N., Schanz, M., Ye, W., Sutradhar, A., Pan, E., Dumont, N.A., Frangi, A., Saez, A.: Recent advances and emerging applications of the boundary element method. ASME Applied Mechanics Review 64(5), 138 (2011)Google Scholar
  2. 2.
    I. Terrasse, Résolution mathématique et numérique des équations de Maxwell instationnaires par une méthode de potentiels retardés, PhD dissertation, Ecole Polytechnique Palaiseau France (1993)Google Scholar
  3. 3.
    Abboud, T., Pallud, M., Teissedre, C.: SONATE: A Parallel Code for Acoustics Nonlinear oscillations and boundary-value problems for Hamiltonian systems, Technical report (1982),
  4. 4.
    Hu, F.Q.: An efficient solution of time domain boundary integral equations for acoustic scattering and its acceleration by Graphics Processing Units. In: 19th AIAA/CEAS Aeroacoustics Conference, ch. (2013), doi:10.2514/6.2013-2018Google Scholar
  5. 5.
    Langer, S., Schanz, M.: Time Domain Boundary Element Method. In: Marburg, S., Nolte (eds.) Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods, pp. 495–516. Springer, Heidelberg (2008)Google Scholar
  6. 6.
    Takahashi, T.: A Time-domain BIEM for Wave Equation accelerated by Fast Multipole Method using Interpolation, pp. 191–192 (2013), doi:10.1115/1.400549Google Scholar
  7. 7.
    Karakasis, V., Goumas, G., Koziris, N.: Perfomance Models for Blocked Sparse Matrix-Vector Multiplication Kernels. In: International Conference on Parallel Processing 2009, pp. 356–364 (2009), doi:10.1109/ICPP.2009.21Google Scholar
  8. 8.
    Nishtala, R., Vuduc, R.W.: When Cache Blocking of Sparse Matrix Vector Multiply Works and Why. In: Proceedings of the PARA 2004 Workshop on the State-of-the-art in Scientific Computing (2004)Google Scholar
  9. 9.
    Toledo, S.: Improving the memory-system performance of sparse-matrix vector multiplication. IBM Journal of Research and Development 41(6), 711–725 (1997)CrossRefGoogle Scholar
  10. 10.
    Pinar, A., Heath, M.T.: Improving performance of sparse matrix-vector multiplication. In: Proceedings of the 1999 ACM/IEEE Conference on Supercomputing. ACM (1999)Google Scholar
  11. 11.
    Yzelman, A.N., Bisseling, R.H.: Cache-Oblivious Sparse MatrixVector Multiplication by Using Sparse Matrix Partitioning Methods. SIAM Journal on Scientific Computing 31(4), 3128–3154 (2009), doi:10.1137/080733243MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Vuduc, R.W., Moon, H.-J.: Fast sparse matrix-vector multiplication by exploiting variable block structure. In: Yang, L.T., Rana, O.F., Di Martino, B., Dongarra, J. (eds.) HPCC 2005. LNCS, vol. 3726, pp. 807–816. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Goto, K., Advanced, T.: High-Performance Implementation of the Level-3 BLAS, 117 (2006)Google Scholar
  14. 14.
    Morton, G.M.: A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing. International Business Machines Company (1966)Google Scholar
  15. 15.
    Amestoy, P.R., Duff, I.S., L’Excellent, J.-Y.: MUMPS MUltifrontal Massively Parallel Solver Version 2.0 (1998)Google Scholar
  16. 16.
    Snir, M., Otto, S., et al.: The MPI core, 2nd edn (1998)Google Scholar
  17. 17.
    OpenMP specifications, Version 3.1 (2011),

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Berenger Bramas
    • 1
  • Olivier Coulaud
    • 1
  • Guillaume Sylvand
    • 2
  1. 1.Inria Bordeaux, Sud-OuestTalenceFrance
  2. 2.Airbus Group InnovationsApplied Mathematics and SimulationToulouseFrance

Personalised recommendations