¹College of Geophysics,ChengDu University of Technology ,ChengDu,China
²School of Computer Science and Technology,Henan Polytechnic University
³Key Lab of Earth Exploration&Information Techniques of Ministry of Education. ChengDu University of Technology ,ChengDu,China

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Abstract—We present a parallel Preconditioned Bi- Conjugate Gradient Stabilized(BICGstab) solver for the Poisson problem. Given a real, nosymmetric and positive definite coefficient matrix , the parallized Preconditioned BICGstab -solver is able to find a solution for that system by exploiting the massive compute power of todays GPUs.Comparing sequential CPU implementations and that algorithm.we achieve a speed up from 8 to 10 depending on the dimension of the coefficient matrix. Additionally the concept of preconditioners to decrease the time to find a solution is evaluated using the AINV method.

Index Terms—Sparse matrix solver, Bi-Conjugate Gradient Stabilized, ELLPACK-R, NVIDIA CUDA, AINV precondition.

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Cite: Zhao Ning, Wang XuBen, "A Parallel Preconditioned Bi-Conjugate Gradient Stabilized Solver for the Poisson Problem," Journal of Computers vol. 7, no. 12, pp. 3088-3095, 2012.