[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.

[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.

[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.

[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.

[5]
Bell, N. and Garland, M., *Efficient sparse matrix-vector multiplication on CUDA*, Technical report, Nvidia Technical Report NVR-2008-004, Nvidia Corporation, 2008.

[6]
Braess, D., Towards algebraic multigrid for elliptic problems of second order, Computing, 55(4) (1995), pp. 379–393.

[7]
Brandt, A., Algebraic multigrid theory: the symmetric case, Appl. Math. Comput., 19(1) (1986), pp. 23–56.

[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.

[9]
Brandt, A., McCoruick, S. and Ruge, J., Algebraic multigrid (amg) for sparse matrix equations, Sparsity Appl., (1985), pp. 257–284.

[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.

[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.

[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.

[13]
Chen, Z., Huan, G. and Ma, Y., Computational Methods for Multiphase Flows in Porous Media, Volume 2, SIAM, 2006.

[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.

[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.

[16]
Coats, K. H.
et al., A note on IMPES and some IMPES-based simulation models, SPE J., 5(03) (2000), pp. 245–251.

[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.

[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.

[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.

[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.

[22]
Falgout, R., An introduction to algebraic multigrid computing, Comput. Sci. Eng., 8(6) (2006).

[23]
Feng, C., Multilevel Iterative Methods and Solvers for Reservoir Simulation on CPU-GPU Heterogenous Computers, PhD thesis, Xiangtan University, 2014.

[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.

[25]
Gandham, R., Esler, K. and Zhang, Y., A GPU accelerated aggregation algebraic multigrid method, Comput. Math. Appl., 68(10) (2014), pp. 1151–1160.

[26]
Hayder, M. E. and Baddourah, M.
et al., Challenges in high performance computing for reservoir simulation, Paper SPE, 152414 (2012), pp. 4–7.

[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.

[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.

[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.

[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.

[31]
Li, R. and Saad, Y., GPU-accelerated preconditioned iterative linear solvers, J. Supercomput., 63(2) (2013), pp. 443–466.

[32]
Liu, H., Yang, B. and Chen, Z., Accelerating algebraic multigrid solvers on NVIDIA GPUs, Comput. Math. Appl., 70(5) (2015), pp. 1162–1181.

[35]
Napov, A. and Notay, Y., An algebraic multigrid method with guaranteed convergence rate, SIAM J. Sci. Comput., 34(2) (2012), pp. A1079–A1109.

[36]
Notay, Y., Flexible conjugate gradients, SIAM J. Sci. Comput., 22(4) (2000), pp. 1444–1460.

[37]
Notay, Y., *Aggregation-based algebraic multigrid for convection-diffusion equations*, SIAM J. Sci. Comput., 2012.

[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.

[39]
Peaceman, D. W., *Presentation of a horizontal well in numerical reservoir simulation*, The 11th SPE Symposium on Reservoir Simulation, 1991.

[40]
Saad, Y., Iterative methods for sparse linear systems, SIAM, 2003.

[41]
Stüben, K., Algebraic Multigrid (AMG): an Introduction with Applications, GMD Forschungszentrum Informationstechnik, 1999.

[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.

[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.

[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.

[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.

[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.

[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.

[50]
Wallis, J., Kendall, R., Little, T. and Nolen, J., Constrained residual acceleration of conjugate residual methods, SPE, 13536 (1985), pp. 10–13.

[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.

[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.

[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.