CUDA 2D Stencil Computations for the Jacobi Method

Jose Maria Cecilia, Jose Manuel Garcia, Manuel Ujaldon
Computer Engineering and Technology Department, University of Murcia, Spain
Applied Parallel and Scientific Computing, Lecture Notes in Computer Science, Volume 7133/2012, 173-183, 2012


   title={CUDA 2D Stencil Computations for the Jacobi Method},

   author={Cecilia, J. and Garc{‘i}a, J. and Ujald{‘o}n, M.},

   journal={Applied Parallel and Scientific Computing},





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We are witnessing the consolidation of the GPUs streaming paradigm in parallel computing. This paper explores stencil operations in CUDA to optimize on GPUs the Jacobi method for solving Laplace’s differential equation. The code keeps constant the access pattern through a large number of loop iterations, that way being representative of a wide set of iterative linear algebra algorithms. Optimizations are focused on data parallelism, threads deployment and the GPU memory hierarchy, whose management is explicit by the CUDA programmer. Experimental results are shown on Nvidia Teslas C870 and C1060 GPUs and compared to a counterpart version optimized on a quadcore Intel CPU. The speed-up factor for our set of GPU optimizations reaches 3-4x and the execution times defeat those of the CPU by a wide margin, also showing great scalability when moving towards a more sophisticated GPU architecture and/or more demanding problem sizes.
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