| Schwarz 算法的 Lions 框架与异步并行算法的收敛性证明 |
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| 引用本文： | 吕涛.Schwarz 算法的 Lions 框架与异步并行算法的收敛性证明[J].系统科学与数学,1989,9(2):128-132. |
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| 作者姓名： | 吕涛 |
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| 作者单位： | 中国科学院成都分院数理室 |
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| 摘 要： | 经典的Schwarz算法,早在1870年就提出了,是求解不规则椭圆型方程的交替法.本世纪苏联学者等又在变分框架下论证了收敛性.近年来以 Schwarrz算法为基础的区域分解算法,发展十分活跃,当前该方法正与并行算法,预处理,快速直接解,多水平及多层网格技术结合,成为计算数学领域内最有前途一个分支.虽然表面看 Schwarz 算法不是并行的,但康立山等打破了分解区域为两子域的
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LIONS FORMWORK FOR SCHWARS ALGORITHM AND THE CONVERGENCE FOR THE ASYNCHRONOUS PARALLEL ALGORITHM |
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| LU TIO.LIONS FORMWORK FOR SCHWARS ALGORITHM AND THE CONVERGENCE FOR THE ASYNCHRONOUS PARALLEL ALGORITHM[J].Journal of Systems Science and Mathematical Sciences,1989,9(2):128-132. |
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| Authors: | LU TIO |
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| Institution: | Chengdu Branch,Academia Sinica |
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| Abstract: | In this paper,we consider the Schwarz algorithm for the Dirichlet problem of the secondorder linear elliptic equation.The convergence of the Schwars algorithm with m overlappingsubbdomains is shown by using the Lions formwork and the Von Neumann theorem.Moreover,we give a convergence proof for an asynchronous parallel algorithm advanced by Kang Li-Shan. |
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