Steklov特征值问题的一类基于固定位移反迭代的多网格方法

发布时间：2019-05-14 07:29

【摘要】：Steklov特征值问题的特征值参数在边界条件上,有很强的物理背景.因此,其数值方法逐步成为学者们关注的焦点.在偏微分方程的数值逼近中,基于后验误差估计的自适应算法因具有计算量小、计算时间短的特点,成为有限元方法的主流方向,得到极大的重视.结合有限元方法及固定位移反迭代,本文提出了Steklov特征值问题的一种基于固定位移反迭代的多网格离散方案.通过该方案,将Steklov特征值问题的解归结为首先在粗网格V_H上求特征值问题的解,然后在越来越细的网格V_(h_i)上求一系列线性代数方程组的解.本文进一步研究了先验误差估计和残差型后验误差估计,并证明了后验误差指示子的全局可靠性和局部有效性.此外,基于后验误差估计,我们设计了一种新的固定位移反迭代型的自适应算法.这种算法不仅计算量小而且避免了求解几乎奇异代数方程的困难,是一种更为有效的算法.最后,对比三种不同类型的自适应算法,用MATLAB编程分别在方形区域、L-型区域和菱形裂缝区域上给出数值结果来验证我们方法的有效性.
[Abstract]:The eigenvalue parameters of Steklov eigenvalue problem have a strong physical background on the boundary conditions. Therefore, its numerical method has gradually become the focus of attention of scholars. In the numerical approximation of partial differential equations, the adaptive algorithm based on posterior error estimation has become the mainstream direction of finite element method because of its small amount of calculation and short calculation time, and has been paid great attention to. Based on the finite element method and the inverse iteration of fixed displacement, a multi-grid discretization scheme based on fixed displacement inverse iteration for Steklov eigenvalue problem is proposed in this paper. Through this scheme, the solution of the Steklov eigenvalue problem is reduced to the solution of the eigenvalue problem on the rough grid V 鈮，

本文编号：2476533