| Parareal算法的均方稳定性分析 |
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| 引用本文： | 吴树林,王志勇,黄乘明. Parareal算法的均方稳定性分析[J]. 计算数学, 2011, 33(2): 113-124 |
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| 作者姓名： | 吴树林 王志勇 黄乘明 |
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| 作者单位： | 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 |
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| 基金项目： | 四川理工学院人才引进项目资助，国家自然科学基金 |
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| 摘 要： | 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-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Turinici等人首次提出至今,在短短...
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| 关 键 词： | Parareal算法 并行计算 稳定性 超线性收敛 线性收敛 |
| 收稿时间： | 2009-06-20; |
ANALYSIS OF MEAN-SQUARE STABILITY OF THE PARAREAL ALGORITHM |
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| Wu Shulin,Wang Zhiyong,Huang Chengming. ANALYSIS OF MEAN-SQUARE STABILITY OF THE PARAREAL ALGORITHM[J]. Mathematica Numerica Sinica, 2011, 33(2): 113-124 |
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| Authors: | Wu Shulin Wang Zhiyong Huang Chengming |
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| Affiliation: | 1. School of Science, Sichuan University of Science and Engineering, Zigong 643000, Sichuan, China;2. School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China;3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China |
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| Abstract: | 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. |
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| Keywords: | Parareal algorithm parallel computation stability superlinear convergence linear convergence |
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