Skip to main content
Log in

CUDA-based solver for large-scale groundwater flow simulation

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

This article presents a parallel simulation solver for groundwater flow on CUDA. Preconditioned conjugate gradient (PCG) algorithm is used to solve the large linear systems arising from the finite-difference discretization of three-dimensional groundwater flow problems. CUDA implementing methods for the two most time-consuming operations in PCG, sparse matrix–vector multiplication and vector inner-product, are given. The experimental results show that CUDA can speed up the solving process of the groundwater simulation significantly. 1.8–3.7 speedup can be achieved with different GPUs for a transient groundwater flow problem.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Algorithm 1
Fig. 2
Algorithm 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Mills RT et al (2007) Simulating subsurface flow and transport on ultrascale computers using pflotran. J Phys Conf Series 78(1):012051

    Article  Google Scholar 

  2. Wu Y-S, Zhang K, Ding C, Pruess K, Elmroth E, Bodvarsson GS (2002) An efficient parallel-computing method for modeling nonisothermal multiphase flow and multicomponent transport in porous and fractured media. Adv Water Resour 25(3):243–261

    Article  Google Scholar 

  3. Saied F, Mahinthakumar G (1998) Efficient parallel multigrid based solvers for large scale groundwater flow simulations. Comput Math Appl 35(7):45–54

    Article  MATH  Google Scholar 

  4. Harbaugh AW, Banta ER, Hill MC, Mcdonald MG (2000) Modflow-2000, the U. S. Geological survey modular ground-water model-user guide to modularization concepts and the ground-water flow process. US Geological Survey OpenFile Report 0092

  5. Dong Y, Li G (2009) A parallel pcg solver for modflow. Ground Water 47(6):845–850. doi:10.1111/j.1745-6584.2009.00598.x

    Article  Google Scholar 

  6. Owens J, Houston M, Luebke D, Green S, Stone J, Phillips J (2008) Gpu computing. Proc IEEE 96(5):879–899. doi:citeulike-article-id:2767438

    Article  Google Scholar 

  7. NVIDIA (2009) Nvidia cudatm programming guide version 2.2

  8. Kirk DB, W-mW Hwu (2010) Programming massively parallel processors: a hands-on approach, 1st edn. Morgan Kaufmann, Burlington

    Google Scholar 

  9. Xue Y, Xie C (2007) Numerical simulation for groundwater, 1st edn. Science, Beijing

    Google Scholar 

  10. Barrett R (1994) Templates for the solution of linear systems: Building blocks for iterative methods. Society for Industrial Mathematics, Philadelphia

    Book  Google Scholar 

  11. Shewchuk J (1994) An introduction to the conjugate gradient method without the agonizing pain. Technical report CS-94–125. Carnegie Mellon University, Pittsburgh

    Google Scholar 

  12. Ian J, Farmer I, Grinspun E, Schrder P (2003) Sparse matrix solvers on the gpu: conjugate gradients and multigrid. ACM Trans Graph 22:917–924

    Article  Google Scholar 

  13. NVIDIA (2009) Cuda cublas library version 2.2

  14. Vuduc RW (2003) Automatic performance tuning of sparse matrix kernels. University of California, Berkeley

    Google Scholar 

  15. Baskaran M, Bordawekar R (2009) Optimizing sparse matrix-vector multiplication on gpus. IBM Research Report RC24704, IBM

  16. Goumas G, Kourtis K, Anastopoulos N, Karakasis V, Koziris N (2009) Performance evaluation of the sparse matrix-vector multiplication on modern architectures. J Supercomput 50(1):36–77

    Article  Google Scholar 

  17. Cheng T, Ji X, Wang Q (2009) An efficient parallel method for large-scale groundwater flow equation based on petsc. Paper presented at the 2009 IEEE youth conference on information, computing and telecommunications

Download references

Acknowledgments

The authors are thankful for the help from Prof. Xusheng Wang. This research is supported in part by the Fundamental Research Funds for the Central Universities of China.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qun Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ji, X., Cheng, T. & Wang, Q. CUDA-based solver for large-scale groundwater flow simulation. Engineering with Computers 28, 13–19 (2012). https://doi.org/10.1007/s00366-011-0213-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-011-0213-2

Keywords

Navigation