Abstract
We present an implementation of a Two-Level Preconditioned Conjugate Gradient Method for the GPU. We investigate a Truncated Neumann Series based preconditioner in combination with deflation. This combination exhibits fine-grain parallelism and hence we gain considerably in execution time when compared with a similar implementation on the CPU. Its numerical performance is comparable to the Block Incomplete Cholesky approach. Our method provides a speedup of up to 16 for a system of one million unknowns when compared to an optimized implementation on one core of the CPU.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gupta, R., van Gijzen, M.B., Vuik, C.: Efficient Two-Level Preconditioned Conjugate Gradient Method on the GPU, Reports of the Department of Applied Mathematical Analysis, Delft University of Technology, Delft, The Netherlands. Report 11–15 (2011)
Ament, M., Knittel, G., Weiskopf, D., Strasser, W.: A Parallel Preconditioned Conjugate Gradient Solver for the Poisson Problem on a Multi-GPU Platform. In: Proceedings of the 18th Euromicro Conference on Parallel, Distributed, and Network-based Processing, pp. 583–592 (2010)
Jacobsen, D.A., Senocak, I.: A Full-Depth Amalgamated Parallel 3D Geometric Multigrid Solver for GPU Clusters. In: Proceedings of 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA 2011-946, pp. 1–17 (January 2011)
Bolz, J., Farmer, I., Grinspun, E., Schröder, P.: Sparse matrix solvers on the GPU: conjugate gradients and multigrid. ACM Trans. Graph. 22, 917–924 (2003)
Bell, N., Garland, M.: Efficient Sparse Matrix-Vector Multiplication on CUDA, NVR-2008-04, NVIDIA Corporation (2008)
Van der Pijl, S.P., Segal, A., Vuik, C., Wesseling, P.: A mass conserving Level-Set Method for modeling of multi-phase flows. International Journal for Numerical Methods in Fluids 47, 339–361 (2005)
Tang, J.M., Vuik, C.: New Variants of Deflation Techniques for Pressure Correction in Bubbly Flow Problems. Journal of Numerical Analysis, Industrial and Applied Mathematics 2, 227–249 (2007)
Helfenstein, R., Koko, J.: Parallel preconditioned conjugate gradient algorithm on GPU. Journal of Computational and Applied Mathematics 236, 3584–3590 (2011)
Heuveline, V., Lukarski, D., Subramanian, C., Weiss, J.P.: Parallel Preconditioning and Modular Finite Element Solvers on Hybrid CPU-GPU Systems. In: Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, paper 36 (2011)
Meijerink, J.A., van der Vorst, H.A.: An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix. Mathematics of Computation 31, 148–162 (1977)
Jönsthövel, T.B., van Gijzen, M., MacLachlan, S., Vuik, C., Scarpas, A.: Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials. Computational Mechanics 50, 321–333 (2012)
MAGMABLAS documentation, http://icl.cs.utk.edu/magma/docs/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gupta, R., van Gijzen, M.B., Vuik, C.K. (2013). Efficient Two-Level Preconditioned Conjugate Gradient Method on the GPU. In: Daydé, M., Marques, O., Nakajima, K. (eds) High Performance Computing for Computational Science - VECPAR 2012. VECPAR 2012. Lecture Notes in Computer Science, vol 7851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38718-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-38718-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38717-3
Online ISBN: 978-3-642-38718-0
eBook Packages: Computer ScienceComputer Science (R0)