非定常Stokes方程一种基于完全重叠型区域分解的有限元并行算法  

A Parallel Finite Element Algorithm Based on Fully Overlapping Domain Decomposition for the Time-dependent Stokes Equations

作　　者：尚月强[1,2] 何银年[2] 

机构地区：[1]贵州师范大学数学与计算机科学学院,贵阳550001 [2]西安交通大学理学院,西安710049

出　　处：《工程数学学报》2010年第2期233-241,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10971166);国家重大基础研究项目(973计划)(2005CB321703);贵州省科学技术基金([2008]2123)~~

摘　　要：基于完全重叠型区域分解技巧,本文提出了一种求解非定常Stokes方程的有限元并行算法。该算法的基本思想是首先对空间施行完全重叠型区域分解,然后各个处理器使用向后Euler格式独立并行求解关于时间t的常微分方程;在整个关于时间的迭代过程中,无需处理器间的通信,具有良好的并行性能。该算法中每个处理器所负责的子问题是一个全局问题,它定义在整个求解区域上,但绝大部分自由度来自其所负责的子区域,从而使得该算法稍加修改现有的串行程序即可实现相应的并行计算,实现简单,具有重要的使用价值。同时通过数值算例,在曙光集群并行机上编程实现了上述算法,验证了其有效性。Based on the fully overlapping domain decomposition, a parallel finite element algorithm for the time-dependent Stokes equations is proposed. The basic idea of the algorithm is to first discretize the spatial space by using the fully overlapping domain decomposition technique, then independently solve a system of ordinary differential equations with respect to time by the backward Euler scheme in overlapped subdomains. During the time-iterations, there is no communication between processors and hence a good parallel performance can be obtained. In this algorithm, each subproblem is a global problem with the vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for, and hence can be solved with other subprobtems in parallel by using an existing sequential solver without extensive recoding. Numerical tests on a Dawning parallel cluster illustrated the efficiency of the algorithm.

关 键 词：STOKES方程 有限元方法 重叠型区域分解 并行算法 

分 类 号：O241.82[理学—计算数学]