Abstract
The paper presents a multi-GPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrix-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multi-GPU configuration with eight GPUs is about 100 times faster than a typical server CPU core.
This publication is based on work supported in part by NSF grants OISE-0405349, ACI-0305466, CNS-0719626, and ACI-0324876, by DOE project DE-FC26-08NT4, by FWF project SFB032, by BMWF project AustrianGrid 2, and Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
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References
Baskaran, M.M., Bordawekar, R.: Optimizing sparse matrix-vector multiplication on gpus. IBM Technical Report RC24704 (2008)
Bell, N., Garland, M.: Efficient sparse matrix-vector multiplication on cuda. NVIDIA Technical Report NVR-2008-004 (2008)
Bornemann, F.A., Deuflhard, P.: The cascadic multigrid method for elliptic problems. Numer. Math. 75, 135–152 (1996)
Briggs, W.L., Henson, V.E., McCormick, S.: A Multigrid Tutorial, 2nd edn. SIAM, Philadelphia (2000)
Douglas, C.C.: Madpack: A family of abstract multigrid or multilevel solvers. Comput. Appl. Math. 14, 3–20 (1995)
Douglas, C.C., Haase, G., Langer, U.: A Tutorial on Elliptic Pde Solvers and Their Parallelization. Society for Industrial and Applied Mathematics (2003)
Barrett, R., et al.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, Philadelphia (1994)
Göddeke, D., Strzodka, R., Mohd-Yusof, J., McCormick, P., Wobker, H., Becker, C., Turek, S.: Using GPUs to improve multigrid solver performance on a cluster. International Journal of Computational Science and Engineering 4(1), 36–55 (2008)
Gropp, W., Lusk, E., Skjellum, A.: Using MPI: Portable Parallel Programming with the Message Passing Interface. The MIT Press, Cambridge (1999)
Haase, G., Kuhn, M., Reitzinger, S.: Parallel AMG on distributed memory computers. SIAM SISC 24(2), 410–427 (2002)
Im, E.-J., Yelick, K., Vuduc, R.: Sparsity: Optimization framework for sparse matrix kernels. Int. J. High Perform. Comput. Appl. 18(1), 135–158 (2004)
Liebmann, M.: Efficient PDE Solvers on Modern Hardware with Applications in Medical and Technical Sciences. PhD thesis, University of Graz, Department of Mathematics and Scientific Computing (July 2009)
Plank, G., Liebmann, M., Weber dos Santos, R., Vigmond, E.J., Haase, G.: Algebraic multigrid preconditioner for the cardiac bidomain model. IEEE Transactions on Biomedical Engineering 54(4), 585–596 (2007)
Ruge, J.W., Stüben, K.: Efficient solution of finite difference and finite element equations by algebraic multigrid (amg). In: Multigrid methods for integral and differential equations. The Institute of Mathematics and Its Applications Conference Series, pp. 169–212. Clarendon Press, Oxford (1985)
Thoman, P.: Multigrid Methods on GPUs, p. 62. VDM, Saarbrücken (2008)
Vassilevski, P.S.: Multilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving Finite Element Equations, 1st edn. Springer, New York (2008)
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Haase, G., Liebmann, M., Douglas, C.C., Plank, G. (2010). A Parallel Algebraic Multigrid Solver on Graphics Processing Units. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (eds) High Performance Computing and Applications. Lecture Notes in Computer Science, vol 5938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11842-5_5
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DOI: https://doi.org/10.1007/978-3-642-11842-5_5
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