Abstract
This paper introduces our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for a single GPU and multiple GPUs are implemented. A HEC matrix format and a communication mechanism are established. Also, a set of specific algorithms for solving preconditioned systems in parallel environments are designed, including ILU(k), RAS and parallel triangular solvers. Based on these work, several Krylov solvers and AMG solvers are developed. According to numerical experiments, favorable acceleration performance is obtained from our Krylov solver and AMG solver under various parameter conditions.
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Acknowledgments
The support of Department of Chemical and Petroleum Engineering, University of Calgary and Reservoir Simulation Research Group is gratefully acknowledged. The research is partly supported by NSERC/AIEES/Foundation CMG, AITF iCore, IBM Thomas J. Watson Research Center, and the Frank and Sarah Meyer FCMG Collaboration Centre for Visualization and Simulation. The research is also enabled in part by support provided by WestGrid (www.westgrid.ca) and Compute Canada Calcul Canada (www.computecanada.ca).
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Yang, B., Liu, H., Chen, Z. (2016). Development of Krylov and AMG Linear Solvers for Large-Scale Sparse Matrices on GPUs. In: Xie, J., Chen, Z., Douglas, C., Zhang, W., Chen, Y. (eds) High Performance Computing and Applications. HPCA 2015. Lecture Notes in Computer Science(), vol 9576. Springer, Cham. https://doi.org/10.1007/978-3-319-32557-6_6
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