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

作者：Gu Tong Xiang^*; Zuo Xian Yu; Liu Xing Ping; Li Pei Lu

来源：Journal of Computational and Applied Mathematics, 2009, 226(1): 55-65.

DOI：10.1016/j.cam.2008.05.017

• Sparse nonsymmetric linear system
• IBiCGSTAB(2) method
• Krylov subspace method
• Distributed parallel environments
• Global communication

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%.

• 出版日期2009-4-1
• 单位濮阳职业技术学院; 河南师范大学; 北京应用物理与计算数学研究所