Stokes外问题的一种重叠型区域分解法  

AN OVERLAPPING DOMAIN DECOMPOSITION METHOD FOR EXTERIOR STOKES PROBLEMS

作　　者：郑权[1] 赵鹏[1] 

机构地区：[1]北方工业大学理学院,北京100144

出　　处：《数值计算与计算机应用》2010年第4期271-278,共8页Journal on Numerical Methods and Computer Applications

基　　金：北京市自然科学基金资助(No.1072009).

摘　　要：本文讨论了平面无界区域上Stokes问题的重叠型区域分解法.利用混合元方法求解内子区域问题得到速度和压力,再用Poisson积分公式解出外子区域的速度和压力,如此交替迭代克服区域无界性并按原始变量求出原问题的数值解.根据投影理论证明重叠型区域分解法的几何收敛性.最后给出数值例子.An overlapping domain decomposition method for the Stokes problems on planar unbounded domains is investigated. Mixed element for solving the problem in the inner sub- domain is used and the velocity and pressure are obtained, then the velocity and pressure in the exterior subdomain can be figured out by the Poisson＇s integral formula, and so on alternatively. This alternating method can conquer the infinity of the domain and give the numerical solution for the original problem by using the primitive variables. The geometric convergence of the overlapping domain decomposition method is proved basing on the projection theorem. Numerical examples are given at last.

关 键 词：STOKES问题 无界区域 SCHWARZ交替法 几何收敛 Mini元 

分 类 号：O241.82[理学—计算数学]