Performance of Time and Frequency Domain Cluster Solvers Compared to Geophysical Applications

  • Victor Kostin
  • Sergey SolovyevEmail author
  • Andrey Bakulin
  • Maxim Dmitriev
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 965)


In the framework of frequency-domain full waveform inversion (FWI), we compare the performance of two MPI-based acoustic solvers. One of the solvers is the time-domain solver developed by the SEISCOPE consortium. The other solver is a frequency-domain multifrontal direct solver developed by us. For the high-contrast 3D velocity model, we perform the series of experiments for varying numbers of cluster nodes and shots, and conclude that in FWI applications the solvers complement each other in terms of performance. Theoretically, the conclusion follows from considerations of structures of the solvers and their scalabilities. Relations between the number of cluster nodes, the size of the geophysical model and the number of shots define which solver would be preferable in terms of performance.


Geophysical problem 3D acoustic solvers Frequency-domain Time-domain Modeling Sparse matrix Low-rank approximation 



We also appreciate KAUST for providing access to Shaheen II supercomputer.


  1. 1.
    Aminzadeh, F., Brac, J., Kuntz, T.: 3-D salt and overthrust models. In: SEG/EAGE Modelling Series. SEG Book Series (1997)Google Scholar
  2. 2.
    Belonosov, M., Dmitriev, M., Kostin, V., Neklyudov, D., Tcheverda, V.: An iterative solver for the 3D Helmholtz equation. J. Comput. Phys. 345, 330–344 (2017). Scholar
  3. 3.
    Collino, F., Tsogka, C.: Application of the perfectly matched layer absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media. Geophysics 66, 294–307 (2001)CrossRefGoogle Scholar
  4. 4.
    Duff, I.S., Reid, J.K.: The multifrontal solution of indefinite sparse symmetric linear systems. ACM Trans. Math. Softw. (TOMS) 9(3), 302–325 (1983). Scholar
  5. 5.
    Hackbusch, W.: A sparse matrix arithmetic based on H-Matrices. Part I: introduction to H-matrices. Computing 62(2), 89–108 (1999). Scholar
  6. 6.
    Kostin, V., Solovyev, S., Liu, H., Bakulin, A.: HSS cluster-based direct solver for acoustic wave equation. In: 87th Annual International Meeting, SEG Technical Program Expanded Abstracts, pp. 4017–4021 (2017)Google Scholar
  7. 7.
    Martinsson, P.G.: A fast randomized algorithm for computing a hierarchically semiseparable representation of a matrix. SIAM J. Matrix Anal. Appl. 32(4), 1251–1274 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Mulder, W.A., Plessix, R.E.: How to choose a subset of frequencies in frequency-domain finite-difference migration. Geophys. J. Int. 158(3), 801–812 (2004)CrossRefGoogle Scholar
  9. 9.
    Plessix, R.E.: A Helmholtz iterative solver for 3D seismic-imaging problems. Geophysics 72(5), SM185–SM194 (2007). Scholar
  10. 10.
    Shin, C., Cha, Y.H.: Waveform inversion in the Laplace domain. Geophys. J. Int. 173(3), 922–931 (2008)CrossRefGoogle Scholar
  11. 11.
    Solovyev, S., Vishnevsky, D., Liu, H.: Multifrontal hierarchically semi-separable solver for 3D Helmholtz problem using optimal 27-point finite-difference scheme. In: 77th EAGE Conference and Exhibition Expanded Abstracts (2015)Google Scholar
  12. 12.
    Virieux, J., et al.: Seismic wave modeling for seismic imaging. Lead. Edge 28(5), 538–544 (2009)CrossRefGoogle Scholar
  13. 13.
    Wang, S., de Hoop, M., Xia, J.: On 3D modeling of seismic wave propagation via a structured parallel multifrontal direct Helmholtz solver. Geophys. Prospect. 59, 857–873 (2011). Scholar
  14. 14.
    Xia, J.: Efficient structured multifrontal factorization for large sparse matrices. SIAM J. Sci. Comput. 35, A832–A860 (2013). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Victor Kostin
    • 1
  • Sergey Solovyev
    • 1
    Email author
  • Andrey Bakulin
    • 2
  • Maxim Dmitriev
    • 2
  1. 1.Institute of Petroleum Geology and Geophysics SB RASNovosibirskRussia
  2. 2.Geophysics Technology, EXPEC ARC, Saudi AramcoDhahranSaudi Arabia

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