时变Stokes方程迭代方法的研究

Study of Iterative Methods for Time-Dependent Stokes Equations

时变Stokes方程的求解在物理学、离散动力学系统和科学计算等领域具有广泛的应用,但是时变Stokes方程是一个随时间变化的偏微分方程组,在实际中求解非常困难.针对时变Stokes方程在预处理基础上构造了一个新的双预优迭代方法,然后给出了迭代格式、收敛域以及一些相关的结论.通过改进迭代法中参数的选取和对方程组本身进行预处理等方式,提高了迭代方法的收敛速度.最后用数值算例验证了双预优迭代方法的可行性和有效性.

The solution to the time-dependent Stokes equations has broad application in physics,discrete dynamic system,scientific computing,and other fields.However,the equations are timedependent partial differential equations and very difficult to solve in practice.To solve this problem,a new dual preconditioned method was firstly constructed based on preconditioned technology.Then their iterative formats,convergence domains and the corresponding conclutions were given.The convergence rate of the iterative method was improved by modifying the parameters in the iterative method and preprocessing on the equations themselves.Finally,the feasibility and effectiveness of the dual preconditioned iterative method were verified with numerical examples.