Skip to main content
SpringerLink
Log in

Parallel Efficiency for Poroelasticity

  • Conference paper
  • First Online:
Supercomputing (RuSCDays 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13708))

Included in the following conference series:

  • 752 Accesses

Abstract

Poroelasticity is an example of coupled processes which are crucial for many applications including safety assessment of radioactive waste repositories. Numerical solution of poroelasticity problems discretized with finite volume – virtual element scheme leads to systems of algebraic equations, which may be solved simultaneously or iteratively. In this work, parallel scalability of the monolithic strategy and of the fixed-strain splitting strategy is examined, which depends mostly on linear solver performance. It was expected that splitting strategy would show better scalability due to better performance of a black-box linear solver on systems with simpler structure. However, this is not always the case.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Birkholzer, J.T., Tsang, C.F., Bond, A.E., Hudson, J.A., Jing, L., Stephansson, O.: 25 years of DECOVALEX-scientific advances and lessons learned from an international research collaboration in coupled subsurface processes. Int. J. Rock Mech. Min. Sci. 122, 103995 (2019)

    Google Scholar 

  2. Kapyrin, I.V., Ivanov, V.A., Kopytov, G.V., Utkin, S.S.: Integral code GeRa for radioactive waste disposal safety validation. Gornyi Zh (10), 44–50 (2015)

    Google Scholar 

  3. GeRa website. gera.ibrae.ac.ru

  4. Grigor’ev, F.V., Kapyrin, I.V., Vassilevski, Y.V.: Modeling of thermal convection in porous media with volumetric heat source using the GeRa code. Chebyshevskii Sbornik 18(3), 235–254 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kapyrin, I., Konshin, I., Kramarenko, V., Grigoriev, F.: Modeling groundwater flow in unconfined conditions of variable density solutions in dual-porosity media using the GeRa code. In: Voevodin, V., Sobolev, S. (eds.) RuSCDays 2018. CCIS, vol. 965, pp. 266–278. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-05807-4_23

    Chapter  Google Scholar 

  6. Biot, M.A.: General theory of three-dimensional consolidation. J. Appl. Phys. 12(2), 155–164 (1941)

    Article  MATH  Google Scholar 

  7. Keilegavlen, E., Nordbotten, J.M.: Finite volume methods for elasticity with weak symmetry. Int. J. Numer. Meth. Eng. 112(8), 939–962 (2017)

    Article  MathSciNet  Google Scholar 

  8. Terekhov, K.M., Tchelepi, H.A.: Cell-centered finite-volume method for elastic deformation of heterogeneous media with full-tensor properties. J. Comput. Appl. Math. 364, 112331 (2020)

    Google Scholar 

  9. Nordbotten, J.M., Keilegavlen, E.: An introduction to multi-point flux (MPFA) and stress (MPSA) finite volume methods for thermo-poroelasticity. In: Di Pietro, D.A., Formaggia, L., Masson, R. (eds.) Polyhedral Methods in Geosciences. SSSS, vol. 27, pp. 119–158. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-69363-3_4

    Chapter  MATH  Google Scholar 

  10. Terekhov, K.M.: Cell-centered finite-volume method for heterogeneous anisotropic poromechanics problem. J. Comput. Appl. Math. 365, 112357 (2020)

    Google Scholar 

  11. Terekhov, K.M., Vassilevski, Y.V.: Finite volume method for coupled subsurface flow problems, II: Poroelasticity. J. Comput. Phys. 462, 111225 (2022)

    Google Scholar 

  12. Beirão da Veiga, L., Brezzi, F., Marini, L.D., Russo, A.: The hitchhiker’s guide to the virtual element method. Math. Models Methods Appl. Sci. 24(08), 1541–1573 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gain, A.L., Talischi, C., Paulino, G.H.: On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes. Comput. Methods Appl. Mech. Eng. 282, 132–160 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Coulet, J., Faille, I., Girault, V., Guy, N., Nataf, F.: A fully coupled scheme using virtual element method and finite volume for poroelasticity. Comput. Geosci. 24(2), 381–403 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  15. Aavatsmark, I., Barkve, T., Bøe, O., Mannseth, T.: Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: derivation of the methods. SIAM J. Sci. Comput. 19(5), 1700–1716 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Eng. 200, 1591–1606 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Frigo, M., Castelletto, N., Ferronato, M.: Enhanced relaxed physical factorization preconditioner for coupled poromechanics. Comput. Math. Appl. 106, 27–39 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  18. INMOST website. inmost.org

  19. Vassilevski, Y., Terekhov, K., Nikitin, K., Kapyrin, I.: Parallel Finite Volume Computation on General Meshes. Springer, New York (2020). https://doi.org/10.1007/978-3-030-47232-0

  20. Anuprienko, D., Kapyrin, I.: Nonlinearity continuation method for steady-state groundwater flow modeling in variably saturated conditions. J. Comput. Appl. Math. 393, 113502 (2021)

    Google Scholar 

  21. Kolditz, O., Shao, H., Wang, W., Bauer, S.: Thermo-Hydro-Mechanical Chemical Processes in Fractured Porous Media: Modelling and Benchmarking, vol. 25. Springer, Berlin (2016)

    Book  Google Scholar 

  22. INM RAS cluster. cluster2.inm.ras.ru

  23. Karypis, G., Schloegel, K., Kumar, V.: Parmetis: Parallel graph partitioning and sparse matrix ordering library (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nuclear Safety Institute RAS, Moscow, 115191, Russian Federation

    Denis Anuprienko

Authors
  1. Denis Anuprienko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Denis Anuprienko .

Editor information

Editors and Affiliations

  1. Research Computing Center (RCC), Moscow State University, Moscow, Russia

    Vladimir Voevodin

  2. Research Computing Center (RCC), Moscow State University, Moscow, Russia

    Sergey Sobolev

  3. Keldysh Institute of Applied Mathematics, Moscow, Russia

    Mikhail Yakobovskiy

  4. Russian Federal Nuclear Center, Sarov, Russia

    Rashit Shagaliev

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Anuprienko, D. (2022). Parallel Efficiency for Poroelasticity. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds) Supercomputing. RuSCDays 2022. Lecture Notes in Computer Science, vol 13708. Springer, Cham. https://doi.org/10.1007/978-3-031-22941-1_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-22941-1_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22940-4

  • Online ISBN: 978-3-031-22941-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation