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

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.