Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

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Abstract—An improved implementation of the Preconditioned Conjugate Gradient method on GPU using CUDA (Compute Unified Device Architecture) is proposed. It aims to solving the Poisson equation arising in liquid animation with high efficiency. We consider the features of the linear system obtained from the Poisson equation and propose an optimization method to solve it. First, a novel storage format called mDIA (modified diagonal storage format) is presented to improve the efficiency of the Sparse Matrix-Vector product (SpMV) operation. Second, a parallel Jacobi iterative method is proposed when using the Incomplete Cholesky preconditioner to explore inherent parallelism. Third, CUDA streams are also introduced to overlap computations among separate streams. The proposed optimization technique is embedded into our GPU based PCG algorithm. Results on Geforce G100 show that our SpMV kernel yields an improvement of nearly 100% for large sparse matrix with more than 30, 0000 rows. Also, a speedup of more than 7 is obtained for PCG method, making the real-time physics engine possible.

Index Terms—CUDA, PCG, Incomplete Cholesky preconditioner, SpMV, Poisson equation

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Cite: Yechen Gui and Guijuan Zhang, "An Improved Implementation of Preconditioned Conjugate Gradient Method on GPU," Journal of Software vol. 7, no. 12, pp. 2695-2702, 2012.