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Efficient implementation of Jacobi iterative method for large sparse linear systems on graphic processing units

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Abstract

In this paper, an original Jacobi implementation is considered for the solution of sparse linear systems of equations. The proposed algorithm helps to optimize the parallel implementation on GPU. The performance analysis of GPU-based (using CUDA) algorithm of the implementation of this algorithm is compared to the corresponding serial CPU-based algorithm. Numerical experiments performed on a set of matrices arising from the finite element discretization of various equations (3D Laplace equation, 3D gravitational potential equation, 3D Heat equation) with different meshes, illustrate the performance, robustness and efficiency of our algorithm, with a speed up to 23\(\times \) in double-precision arithmetics.

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Acknowledgments

The authors acknowledge partial financial support from the OpenGPU project (Pôle de Compétitivité Systematic, France), and from the CRESTA (Collaborative Research into Exascale Systemware, Tools and Applications) project (European Commission). The authors also acknowledge the CUDA Research Center at CentraleSupélec (formerly, École Centrale Paris), Université Paris Saclay, France, for its support and for providing the computing facilities.

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  1. CentraleSupélec, Université Paris-Saclay, Grande Voie des Vignes, 92295, Châtenay-Malabry Cedex, France

    Abal-Kassim Cheik Ahamed & Frédéric Magoulès

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  1. Abal-Kassim Cheik Ahamed
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  2. Frédéric Magoulès
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Correspondence to Abal-Kassim Cheik Ahamed.

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Cheik Ahamed, AK., Magoulès, F. Efficient implementation of Jacobi iterative method for large sparse linear systems on graphic processing units. J Supercomput 73, 3411–3432 (2017). https://doi.org/10.1007/s11227-016-1701-3

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