A Parallel Preconditioned Bi-Conjugate Gradient Stabilized Solver for the Poisson Problem

Ning Zhao, Xuben Wang
College of Geophysics, ChengDu University of Technology, ChengDu, China
Journal of Computers, Vol 7, No 12 (2012), 3088-3095, 2012
@article{JCPjcp071230883095,

   author={Ning Zhao and Xuben Wang},

   title={A Parallel Preconditioned Bi-Conjugate Gradient Stabilized Solver for the Poisson Problem},

   journal={Journal of Computers},

   volume={7},

   number={12},

   year={2012},

   keywords={sparse matrix solver; Bi-Conjugate Gradient Stabilized; ELLPACK-R; NVIDIA CUDA; AINV precondition},

   url={http://ojs.academypublisher.com/index.php/jcp/article/view/jcp071230883095}

}

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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.
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