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Toward Cost-Effective Reservoir Simulation Solvers on GPUs

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  19 September 2016

Zheng Li ,
Shuhong Wu ,
Jinchao Xu  and
Chensong Zhang
Zheng Li*
Affiliation:
Kunming University of Science and Technology, Kunming 650093, China
Shuhong Wu*
Affiliation:
Research Institute of Petroleum Exploration and Development, CNPC, Beijing 100083, China
Jinchao Xu*
Affiliation:
Department of Mathematics, Penn State University, University Park, PA 16802, USA
Chensong Zhang*
Affiliation:
LSEC & NCMIS, Academy of Mathematics and Systems Science, Beijing 100190, China
*
*Corresponding author. Email:[email protected] (Z. Li), [email protected] (S.Wu), [email protected] (J. Xu), [email protected] (C. Zhang)
*Corresponding author. Email:[email protected] (Z. Li), [email protected] (S.Wu), [email protected] (J. Xu), [email protected] (C. Zhang)
*Corresponding author. Email:[email protected] (Z. Li), [email protected] (S.Wu), [email protected] (J. Xu), [email protected] (C. Zhang)
*Corresponding author. Email:[email protected] (Z. Li), [email protected] (S.Wu), [email protected] (J. Xu), [email protected] (C. Zhang)
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Abstract

In this paper, we focus on graphical processing unit (GPU) and discuss how its architecture affects the choice of algorithm and implementation of fully-implicit petroleum reservoir simulation. In order to obtain satisfactory performance on new many-core architectures such as GPUs, the simulator developers must know a great deal on the specific hardware and spend a lot of time on fine tuning the code. Porting a large petroleum reservoir simulator to emerging hardware architectures is expensive and risky. We analyze major components of an in-house reservoir simulator and investigate how to port them to GPUs in a cost-effective way. Preliminary numerical experiments show that our GPU-based simulator is robust and effective. More importantly, these numerical results clearly identify the main bottlenecks to obtain ideal speedup on GPUs and possibly other many-core architectures.

Keywords

GPUsreservoir simulationfully-implicit method

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016 , pp. 971 - 991
Copyright
Copyright © Global-Science Press 2016 

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References

[1] Appleyard, J. R., Appleyard, J. D., Wakefield, M. A. and Desitter, A. L., Accelerating reservoir simulators using GPU technology, SPE Reservoir Simulation Symposium, 2011.CrossRefGoogle Scholar
[2] Baker, A. H., Falgout, R. D., Kolev, T. V. and Yang, U. M., Multigrid smoothers for ultraparallel computing, SIAM J. Sci. Comput., 33(5) (2011), pp. 2864–2887.CrossRefGoogle Scholar
[3] Bank, R. E., Chan, T. F., Coughran, W. M. Jr and Smith, R. K., The Alternate-Block-Factorization procedure for systems of partial differential equations, BIT Numer. Math., 29(4) (1989), pp. 938–954.CrossRefGoogle Scholar
[4] Bell, N., Dalton, S. and Olson, L. N., Exposing fine-grained parallelism in algebraic multigrid methods, SIAM J. Sci. Comput., 34(4) (2012), pp. C123–C152.CrossRefGoogle Scholar
[5] Bell, N. and Garland, M., Efficient sparse matrix-vector multiplication on CUDA, Technical report, Nvidia Technical Report NVR-2008-004, Nvidia Corporation, 2008.Google Scholar
[6] Braess, D., Towards algebraic multigrid for elliptic problems of second order, Computing, 55(4) (1995), pp. 379–393.CrossRefGoogle Scholar
[7] Brandt, A., Algebraic multigrid theory: the symmetric case, Appl. Math. Comput., 19(1) (1986), pp. 23–56.Google Scholar
[8] Brandt, A., McCormick, S. and Ruge, J., Algebraic multigrid (amg) for automatic multigrid solutions with application to geodetic computations, Report, Inst. for Computational Studies, Fort Collins, Colo, 1982.Google Scholar
[9] Brandt, A., McCoruick, S. and Ruge, J., Algebraic multigrid (amg) for sparse matrix equations, Sparsity Appl., (1985), pp. 257–284.Google Scholar
[10] Brannick, J., Chen, Y., Hu, X. and Zikatanov, L., Parallel unsmoothed aggregation algebraic multigrid algorithms on gpus, Numerical Solution of Partial Differential Equations: Theory, Algorithms and Their Applications, pages 81–102, Springer, 2013.CrossRefGoogle Scholar
[11] Byun, J.-H., Lin, R., Yelick, K. A. and Demmel, J., Autotuning sparse matrix-vector multiplication for multicore, Technical Report UCB/EECS-2012-215, EECS Department, University of California, Berkeley, November 2012.Google Scholar
[12] Cao, H., Tchelepi, H., Wallis, J. and Yardumian, H., Parallel scalable unstructured CPR-type linear solver for reservoir simulation, Paper SPE 96809 presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 9-12 October, 2005.CrossRefGoogle Scholar
[13] Chen, Z., Huan, G. and Ma, Y., Computational Methods for Multiphase Flows in Porous Media, Volume 2, SIAM, 2006.CrossRefGoogle Scholar
[14] Choi, J. W., Singh, A. and Vuduc, R. W., Model-driven autotuning of sparse matrix-vector multiply on GPUs, ACM SIGPLAN Notices, 45(5) (2010), pp. 115.CrossRefGoogle Scholar
[15] Christie, M. and Blunt, M., Tenth SPE comparative solution project: A comparison of upscaling techniques, SPE Reservoir Evaluation & Engineering, 4(04) (2001), pp. 308–317.CrossRefGoogle Scholar
[16] Coats, K. H. et al., A note on IMPES and some IMPES-based simulation models, SPE J., 5(03) (2000), pp. 245–251.CrossRefGoogle Scholar
[17] CUSOLVER, https://developer.nvidia.com/cusolver.Google Scholar
[18] Dang, H. V. and Schmidt, B., CUDA-enabled sparse matrix-vector multiplication on GPUs using atomic operations, Parallel Comput., 39(11) (2013), pp. 737–750.CrossRefGoogle Scholar
[19] Dogru, A. H., Fung, L. S. and Middya, U. et al., A next-generation parallel reservoir simulator for giant reservoirs, SPE/EAGE Reservoir Characterization & Simulation Conference, 2009.CrossRefGoogle Scholar
[20] Douglas, J. Jr, Peaceman, D. and Rachford, H. Jr et al., A method for calculating multi-dimensional immiscible displacement, Trans. Amer. Inst. Min. Metallurgical Petroleum Eng., pages 297–306, 1959.Google Scholar
[21] Esler, K., Mukundakrishnan, K., Natoli, V., Shumway, J., Zhang, Y. and Gilman, J., Realizing the potential of GPUs for reservoir simulation, ECMOR XIV-14th European Conference on the Mathematics of Oil Recovery, 2014.CrossRefGoogle Scholar
[22] Falgout, R., An introduction to algebraic multigrid computing, Comput. Sci. Eng., 8(6) (2006).CrossRefGoogle Scholar
[23] Feng, C., Multilevel Iterative Methods and Solvers for Reservoir Simulation on CPU-GPU Heterogenous Computers, PhD thesis, Xiangtan University, 2014.Google Scholar
[24] Fung, L. S., Sindi, M. O. and Dogru, A. H. et al., Multi-paradigm parallel acceleration for reservoir simulation, SPE Reservoir Simulation Symposium, 2013.CrossRefGoogle Scholar
[25] Gandham, R., Esler, K. and Zhang, Y., A GPU accelerated aggregation algebraic multigrid method, Comput. Math. Appl., 68(10) (2014), pp. 1151–1160.CrossRefGoogle Scholar
[26] Hayder, M. E. and Baddourah, M. et al., Challenges in high performance computing for reservoir simulation, Paper SPE, 152414 (2012), pp. 4–7.Google Scholar
[27] Hu, X., Vassilevski, P. S. and Xu, J., Comparative convergence analysis of nonlinear AMLI-cycle multigrid, SIAM J. Numer. Anal., 51(2) (2013), pp. 1349–1369.CrossRefGoogle Scholar
[28] Kim, H., Xu, J. and Zikatanov, L., A multigrid method based on graph matching for convection–diffusion equations, Numer. Linear Algebra Appl., 10(1-2) (2003), pp. 181–195.CrossRefGoogle Scholar
[29] Klie, H. M., Sudan, H. H., Li, R. and Saad, Y. et al., Exploiting capabilities of many core platforms in reservoir simulation, SPE Reservoir Simulation Symposium, Society of Petroleum Engineers, 2011.CrossRefGoogle Scholar
[30] Lacroix, S., Vassilevski, Y. V. and Wheeler, M. F., Decoupling preconditioners in the implicit parallel accurate reservoir simulator (IPARS), Numerical Linear Algebra Appl., 8(8) (2001), pp. 537–549.CrossRefGoogle Scholar
[31] Li, R. and Saad, Y., GPU-accelerated preconditioned iterative linear solvers, J. Supercomput., 63(2) (2013), pp. 443–466.CrossRefGoogle Scholar
[32] Liu, H., Yang, B. and Chen, Z., Accelerating algebraic multigrid solvers on NVIDIA GPUs, Comput. Math. Appl., 70(5) (2015), pp. 1162–1181.CrossRefGoogle Scholar
[33] MAGMA, http://icl.cs.utk.edu/magma/.Google Scholar
[34] MUMPS, http://mumps-solver.org.Google Scholar
[35] Napov, A. and Notay, Y., An algebraic multigrid method with guaranteed convergence rate, SIAM J. Sci. Comput., 34(2) (2012), pp. A1079–A1109.CrossRefGoogle Scholar
[36] Notay, Y., Flexible conjugate gradients, SIAM J. Sci. Comput., 22(4) (2000), pp. 1444–1460.CrossRefGoogle Scholar
[37] Notay, Y., Aggregation-based algebraic multigrid for convection-diffusion equations, SIAM J. Sci. Comput., 2012.CrossRefGoogle Scholar
[38] Pavlas, E. J. Jr et al., Fine-scale simulation of complex water encroachment in a large carbonate reservoir in saudi arabia, SPE Reservoir Evaluation & Engineering, 5(05) (2002), pp. 346–354.CrossRefGoogle Scholar
[39] Peaceman, D. W., Presentation of a horizontal well in numerical reservoir simulation, The 11th SPE Symposium on Reservoir Simulation, 1991.Google Scholar
[40] Saad, Y., Iterative methods for sparse linear systems, SIAM, 2003.CrossRefGoogle Scholar
[41] Stüben, K., Algebraic Multigrid (AMG): an Introduction with Applications, GMD Forschungszentrum Informationstechnik, 1999.Google Scholar
[42] Sudan, H., Klie, H., Li, R. and Saad, Y., High performance manycore solvers for reservoir simulation, 12th European Conference on the Mathematics of Oil Recovery, 2010.CrossRefGoogle Scholar
[43] SuperLU, http://crd-legacy.lbl.gov/~xiaoye/SuperLU/.Google Scholar
[44] Tchelepi, H. and Zhou, Y. et al., Multi-GPU parallelization of nested factorization for solving large linear systems, SPE Reservoir Simulation Symposium, Society of Petroleum Engineers, 2013.Google Scholar
[45] Trangenstein, J. A. and Bell, J. B., Mathematical structure of the black-oil model for petroleum reservoir simulation, SIAM J. Appl. Math., 49(3) (1989), pp. 749–783.CrossRefGoogle Scholar
[46] UMFPACK, http://faculty.cse.tamu.edu/davis/suitesparse.html.Google Scholar
[47] Vaněk, P., Brezina, M. and Mandel, J. et al., Convergence of algebraic multigrid based on smoothed aggregation, Numer. Math., 88(3) (2001), pp. 559–579.Google Scholar
[48] Vaněk, P., Mandel, J. and Brezina, M., Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems, Computing, 196 (1996), pp. 179–196.CrossRefGoogle Scholar
[49] Wallis, J., Incomplete Gaussian elimination as a preconditioning for generalized conjugate gradient acceleration, Paper SPE 12265 presented at the SPE Reservoir Simulation Symposium, San Francisco, California, 15-18 November, 1983.CrossRefGoogle Scholar
[50] Wallis, J., Kendall, R., Little, T. and Nolen, J., Constrained residual acceleration of conjugate residual methods, SPE, 13536 (1985), pp. 10–13.Google Scholar
[51] Wang, L., Hu, X., Cohen, J. and Xu, J., A parallel auxiliary grid algebraic multigrid method for graphic processing units, SIAM J. Sci. Comput., 35(3) (2013), pp. C263–C283.CrossRefGoogle Scholar
[52] Wu, S., Feng, C., Zhang, C.-S., Li, Q. and Al, E., A multilevel preconditioner and its shared memory implementation for new generation reservoir simulator, Petroleum Science, (2014), pp. 1–18.Google Scholar
[53] Yu, S., Liu, H., Chen, Z. J., Hsieh, B. and Shao, L. et al., GPU-based parallel reservoir simulation for large-scale simulation problems, SPE Europec/EAGE Annual Conference, Society of Petroleum Engineers, 2012.CrossRefGoogle Scholar