具有滑动边界条件Stokes问题的自适应Uzawa块松弛算法

A Self-Adaptive Uzawa Block Relaxation Method for Stokes Problems With Slip Boundary Conditions

对一类具有非线性滑动边界条件的Stokes问题,得到了求其数值解的自适应Uzawa块松弛算法(SUBRM).通过该问题导出的变分问题,引入辅助变量将原问题转化为一个基于增广Lagrange函数表示的鞍点问题,并采用Uzawa块松弛算法(UBRM)求解.为了提高算法性能,提出利用迭代函数自动选取合适罚参数的自适应法则.该算法的优点是每次迭代只需计算一个线性问题,同时显式计算辅助变量.对算法的收敛性进行了理论分析,最后用数值结果验证了该算法的可行性和有效性.

A self-adaptive Uzawa block relaxation method was designed for Stokes problems under nonlinear slip boundary conditions.For the variational formulation of the problem,an auxiliary unknown was introduced to transform the problem into a saddle-point one based on an augmented Lagrangian function,which can be solved with the Uzawa block relaxation method.To improve the performance of the method,a self-adaptive rule was proposed with the proper penalty parameter chosen automatically.The main advantage of this method is that each iterative step consists of a linear problem while the auxiliary unknown can be computed explicitly.The convergence of the algorithm was analyzed.The numerical results show the feasibility and effectiveness of the proposed method.