Navier-Stokes方程的有限元边界元耦合方法

主要研究了三维外部区域上具有Dirichlet边界条件的非定常Navier-Stokes方程的有限元边界元耦合方法,并分析了这一数值解的收敛速度.     

非线性算子方程的泰勒展式算法

本文的目的是给出一种解Ｈｉｌｂｅｒｔ空间中非线性方程的ｋ阶泰勒展式算法（ｋ１）．标准Ｇａｌｅｒｋｉｎ方法可以看作１阶泰勒展式算法，而最优非线性Ｇａｌｅｒｋｉｎ方法可视为２阶泰勒展式算法．我们应用这种算法于定常的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的数值逼近．在一定情景下，最优非线性Ｇａｌｅｒｋｉｎ方法提供比标准Ｇａｌｅｒｋｉｎ方法和非线性Ｇａｌｅｒｋｉｎ方法更高阶的收敛速度．     

Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.     

定常Stokes方程一种基于完全区域分解的有限元并行算法

基于完全区域分解技巧,提出了一种求解定常Stokes方程的有限元并行算法．该算法中,所有子问题都是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,通信需求少．数值结果验证了算法的高效性．