Accelerating iterative linear solvers using multiple graphical processing units

References

• S. Balay, W. Gropp, L. McInnes, and B. Smith, The Portable, Extensible Toolkit for Scientific Computing, version 2.0.13, 1996. Available at http://www.mcs.anl.gov/petsc/.
   Google Scholar
• R. Barrett, M. Berry, T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd ed., SIAM, Chicago, 1994.
   Google Scholar
• N. Bell and M. Garland, Efficient sparse matrix–vector multiplication on CUDA, NVIDIA Technical Report, NVR-2008-004, NVIDIA Corporation, 2008.
   Google Scholar
• N. Bell and M. Garland, Implementing sparse matrix–vector multiplication on throughput-oriented processors, Proceedings of the Supercomputing, New York, November 2009, pp. 1–11.
   Google Scholar
• N. Bell, S. Dalton, and L. Olson, Exposing fine-grained parallelism in algebraic multigrid methods, SIAM J. Sci. Comput. 34(4) (2012), pp. 123–152. doi: 10.1137/110838844
   Web of Science ®Google Scholar
• J. Bolz, I. Farmer, E. Grinspun, and P. Schröder, Sparse matrix solvers on the GPU: Conjugate gradients and multigrid, Symp. Q. J. Modern Foreign Literatures 22(3) (2007), pp. 917–924.
   Google Scholar
• J. Brannick, Y. Chen, X. Hu, and L. Zikatanov, Parallel unsmoothed aggregation algebraic multigrid algorithms on GPUs, Springer Process. Math. Stat. 45 (2013), pp. 81–102. doi: 10.1007/978-1-4614-7172-1_5
   Google Scholar
• L. Buatois, G. Caumon, and B. Lévy, Concurrent number cruncher: an efficient sparse linear solver on the GPU, High Perform. Comput. Commun. 4782 (2007), pp. 358–371.
   Google Scholar
• X.C. Cai and M. Sarkis, A restricted additive Schwarz preconditioner for general sparse linear systems, SIAM J. Sci. Comput. 21 (1999), pp. 792–797. doi: 10.1137/S106482759732678X
   Web of Science ®Google Scholar
• J.W. Cao and J.C. Sun, An efficient and effective nonlinear solver in a parallel software for large scale petroleum reservoir simulation, Int. J. Numer. Anal. Model. 2 (2005), pp. 15–27.
   Web of Science ®Google Scholar
• Z. Chen, G. Huan, and Y. Ma, Computational Methods for Multiphase Flows in Porous Media, Computational Science and Engineering Series, Vol. 2, SIAM, Philadelphia, 2006.
   Google Scholar
• Z. Chen, H. Liu, S. Yu, B. Hsieh, and L. Shao, GPU-based parallel reservoir simulators, Proceedings of the 21st International Conference on Domain Decomposition Methods, Rennes, France, 2012.
   Google Scholar
• T.A. Davis, University of Florida Sparse Matrix Collection, NA digest, Gainesville, 1994. Available at http://www.cise.ufl.edu/research/sparse/matrices/
   Google Scholar
• D. Goddeke, R. Strzodka, J. Mohd-Yusof, P. McCormick, H. Wobker, C. Becker, and S. Turek, Using GPUs to improve multigrid solver performance on a cluster, Int. J. Comput. Sci. Eng. 4(1) (2008), pp. 36–55.
   Google Scholar
• R. Grimes, D. Kincaid, and D. Young, ITPACK 2.0 User's Guide, Technical Report CNA-150, Center for Numerical Analysis, University of Texas, August 1979.
   Google Scholar
• G. Haase, M. Liebmann, C.C. Douglas, and G. Plank, A parallel algebraic multigrid solver on graphics processing units, in High Performance Computing and Applications, Second International Conference, HPCA 2009, Shanghai, China, August 10–12, 2009, Revised Selected Papers, Lecture Notes in Computer Science, Vol. 5938, W. Zhang, Z. Chen, C.C. Douglas, and W. Tong, eds., Springer, Berlin, Heidelberg, 2010, pp. 38–47.
   Google Scholar
• G. Karypis and V. Kumar, A fast and highly quality multilevel scheme for partitioning irregular graphs, SIAM J. Sci. Comput. 20(1) (1999), pp. 359–392. doi: 10.1137/S1064827595287997
   Web of Science ®Google Scholar
• H. Klie, H. Sudan, R. Li, and Y. Saad, Exploiting capabilities of many core platforms in reservoir simulation, SPE RSS Reservoir Simulation Symposium, Houston, 21–23 February 2011.
   Google Scholar
• R. Li and Y. Saad, GPU-accelerated preconditioned iterative linear solvers, Tech. Rep. umsi-2010-112, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN, 2010.
   Google Scholar
• H. Liu, S. Yu, Z. Chen, B. Hsieh, and L. Shao, Parallel preconditioners for reservoir simulation on GPU, SPE-152811, SPE Latin America and Caribbean Petroleum Engineering Conference, Mexico City, Mexico, 16–18 April 2012.
   Google Scholar
• H. Liu, S. Yu, Z. Chen, B. Hsieh, and L. Shao, Sparse matrix-vector multiplication on NVIDIA GPU, Int. J. Numer. Anal. Model. Ser. B, 3(2) (2012), pp. 185–191.
   Google Scholar
• H. Liu, S. Yu, and Z. Chen, Development of algebraic multigrid solvers using GPUs, SPE Reservoir Simulation Symposium, Houston, USA, February 2013.
   Google Scholar
• NVIDIA Corporation, Nvidia CUDA Programming Guide (version 3.2), 2010. Available at http://docs.nvidia.com/cuda/cuda-c-programming-guide/
   Google Scholar
• NVIDIA Corporation, CUSP: Generic Parallel Algorithms for Sparse Matrix and Graph, 2012. Available at http://code.google.com/p/cusp-library/.
   Google Scholar
• Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, Houston, 2003.
   Google Scholar
• Song Yu, Hui Liu, Zhangxin Chen, Ben Hsieh, and Lei Shao, GPU-based parallel reservoir simulation for large-scale simulation problems, SPE Europec/EAGE Annual Conference, Copenhagen, Denmark, 2012.
   Google Scholar
• L. Wang, X. Hu, J. Cohen, and J. Xu, A parallel auxiliary grid algebraic multigrid method for graphic processing unit, SIAM J. Sci. Comput. 35(3) (2013), pp. 263–283. doi: 10.1137/120894452
   Web of Science ®Google Scholar
• Zhangxin Chen, Hui Liu, Song Yu, Ben Hsieh, and Lei Shao, Reservoir simulation on NVIDIA Tesla GPUs, The Eighth International Conference on Scientific Computing and Applications, University of Nevada, Las Vegas, April 2012.
   Google Scholar