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基于时间分解求解时间依赖问题的并行算法研究

李永刚,欧阳洁,肖曼玉   

  1. 西北工业大学应用数学系;西北工业大学应用数学系;西北工业大学应用数学系 西安710072;西安710072;西安710072
  • 出版日期:2007-01-20 发布日期:2007-01-20

李永刚,欧阳洁,肖曼玉. 基于时间分解求解时间依赖问题的并行算法研究[J]. 数值计算与计算机应用, 2007, 28(1): 27-37.

A TIME DECOMPOSITION PARALLEL ALGORITHM FOR SOLVING TIME-DEPENDENT PROBLEMS

  1. Li Yonggang Ouyang Jie Xiao Manyu (Department of Applied Mathematics Northwestern Polytechnical University,Xi'an 710072,China)
  • Online:2007-01-20 Published:2007-01-20
基于Lions等建立的Parareal模型,提出了改进的时间分解并行算法,并给出收敛性证明.采用主从模式构造了通用的MPI算法流程,通过分析算法的并行加速比给出了最佳的粗细网格步长之比.在集群系统下分别对热传导方程和对流扩散方程进行并行计算,证明了算法无论对线性还是非线性的问题均具有良好的适应性和扩展性.数值模拟结果表明:时间分解并行算法仅需极少的迭代次数即能取得很高的计算精度,且具有较好的并行加速比和并行效率.
A time decomposition parallel algorithm is developed based on the parareal model proposed by J Lions.The convergence of algorithm is also proved.The general MPI flow process is constructed in Master/Slave mode.Analysis of par- allel speed-up indicates the optimal time-step sizes ratio between the coarse and fine grids.The well adaptability and expansibility of algorithm to both linear and nonlinear cases have been certified by computing the heat conduction and convective-diffusion equations on PC cluster.The numerical simulation results demonstrate that very high accuracy can be acquired by few times of iteration,so that better parallel speed-up is obtained.
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[1]Jacques-Louis Lions,Yvon Maday,and Gabriel Turinici.A Parareal in time discretization of PDE's. C.R.Acard.Sci.Paris,Serie I,2001.332:661-668.
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[3]Yvon Maday,Gabriel Turinici.The Parareal in Time Iterative Solver:a Further Direction to Parallel Implementation.In Fifteen International Conference on Domain Decomposition Methods, Berlin,2003.
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[5]陈国良著,并行计算-结构-算法·编程(修订版),高等教育出版社,2003.
[6]张涵倌,沈孟育著,计算流体力学-差分方法的原理和应用,国防工业出版社,2003.
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