An improved parallel hybrid bi-conjugate gradient method suitable for distributed parallel computing

Authors:
Tong-Xiang Gu;Xian-Yu Zuo;Xing-Ping Liu;Pei-Lu Li
Affiliations:
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing 100088, PR China;Mathematics and Information Science College, Henan Normal University, Xinxiang 453007, PR China;Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O.Box 8009, Beijing 100088, PR China;Department of Mathematics and Information Engineering, Puyang Vocational and Technical College, Puyang 457001, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

An improved parallel hybrid bi-conjugate gradient method (IBiCGSTAB(2) method, in brief) for solving large sparse linear systems with nonsymmetric coefficient matrices is proposed for distributed parallel environments. The method reduces five global synchronization points to two by reconstructing the BiCGSTAB(2) method in [G.L.G. Sleijpen, H.A. van der Vorst, Hybrid bi-conjugate gradient methods for CFD problems, in: M. Hafez, K. Oshima (Eds.), Computational Fluid Dynamics Review 1995, John Wiley & Sons Ltd, Chichester, 1995, pp. 457-476] and the communication time required for the inner product can be efficiently overlapped with useful computation. The cost is only slightly increased computation time, which can be ignored, compared with the reduction of communication time. Performance and isoefficiency analysis shows that the IBiCGSTAB(2) method has better parallelism and scalability than the BiCGSTAB(2) method. Numerical experiments show that the scalability can be improved by a factor greater than 2.5 and the improvement in parallel communication performance approaches 60%.