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Parareal算法的均方稳定性分析
ANALYSIS OF MEAN-SQUARE STABILITY OF THE PARAREAL ALGORITHM

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吴树林 1   王志勇 2   黄乘明 3  
文摘 Parareal算法是一种非常有效的实时并行计算方法.与传统的并行计算方法相比, 该算法的显著特点是它的时间并行性一先将整个计算时间划分成若干个子区间, 然后在每个子区间内同时进行计算.Parareal算法收敛速度快, 并行效率高, 且易于编程实现, 从2001年由Lions, Maday和Tuinici等人首次提出至今, 在短短的几年间得到了广泛的研究和应用.最近, Parareal算法在随机微分方程数值解中的应用也得到了一些学者的关注.本文中, 我们研究Parareal算法在随机微分方程数值解中的均方稳定性, 分析保持算法稳定的充分性条件.通过分析, 我们得到了如下结论: a)Parareal算法在有限时间区间内是超线性收敛的; b)在无限时间区间内, 该算法是线性收敛的.最后, 通过数值试验, 我们验证了本文中的理论结果
其他语种文摘 Parareal algorithm is a very efficient parallel in time computation methods. Compared with traditional parallel methods, this algorithm has the advantages of faster convergence, higher parallel performance and easy coding. This algorithm was first proposed by Lions, Maday and Turinici in 2001 and has attracted many researchers over the past few years. Recently, the application and theoretical analysis of this algorithm for stochastic computation have been investigated by some researchers. In this paper, we analyze the Mean-square stability of the Parareal algorithm in stochastic computation. The sufficient conditions under which the Parareal algorithm is stable are obtained and it is shown that: a) the algorithm converges superlinearly on any bounded time interval and b) the convergence speed is only linear on unbounded time intervals. Finally, numerical results are given to validate our theoretical conclusions
来源 计算数学 ,2011,33(2):113-124 【核心库】
关键词 Parareal算法 ; 并行计算 ; 稳定性 ; 超线性收敛 ; 线性收敛 MR(2000)主题分类: 65L20 ; 65-04
地址

1. 四川理工学院理学院, 四川, 自贡, 643000  

2. 电子科技大学应用数学学院, 成都, 610054  

3. 华中科技大学数学与统计学院, 武汉, 430074

语种 中文
文献类型 研究性论文
ISSN 0254-7791
学科 数学
基金 四川理工学院人才引进项目资助项目 ;  国家自然科学基金资助项目
文献收藏号 CSCD:4181590

参考文献 共 17 共1页

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引证文献 2 篇

1 孙佳安 含次同步分量下变压器时间周期有限元的Parareal求解模型 中国电机工程学报,2020,40(13):4348-4357
被引 5 次

2 孙佳安 考虑次同步分量的变压器时间并行有限元及铁心动态损耗分析 中国电机工程学报,2023,43(6):2426-2437
被引 0 次

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