%0 Journal Article
%T 板振动特征值问题基于混合格式的二网格方法研究<br>Two-Grid Method Based on Hybrid Scheme for Plate Vibration Eigenvalue Problem
%A 张云飞
%A 段丽梅
%A 徐良坤
%J Open Journal of Acoustics and Vibration
%P 45-58
%@ 2328-0522
%D 2022
%I Hans Publishing
%R 10.12677/OJAV.2022.104006
%X <span style=\"font-size:14px;\">本文对于求解板振动特征值问题，给出了基于Cialet-Raviart (C-R)混合方法移位反迭代的二网格离散化方法。利用我们的方案可知，求解细网格<i>π<sub>h</sub></i>上的板振动特征值问题可以简化为求粗网格<i>π<sub>H</sub></i>上的板振动问题和细网格上<i>π<sub>h</sub></i>线性方程组的解。我们证明了当<i>H&gt;h≥O(H<sup>2</sup>)</i>时，求得的解仍然保持渐近最优精度。最后，我们用得到的数值结果表明了该方案的高效性。</span><br />
<span style=\"font-size:14px;\">In this paper, for plate vibration eigenvalue problem, we primarily give the two-grid discretization based on the shifted-inverse iteration of Ciarlet-Raviart mixed method. According to this scheme, the eigenvalue problem of plate vibration on <i>π<sub>h</sub></i> grid can be simplified to the solution of plate vibration on <i>π<sub>H</sub></i> grid and the solution of system of linear equations on <i>π<sub>h</sub></i> grid. In this paper, it is proved that when <i>H&gt;h≥O(H<sup>2</sup>)</i>, the solution still keeps asymptotically worst-case accuracy. Finally, the numerical results show the high efficiency of the proposed scheme.</span>
%K 二网格离散化，Ciarlet-Raviart混合方法，板振动特征值问题，移位反迭代<br>Two-Grid Dispersion
%K Ciarlet-Raviart Mixed Method
%K Plate Vibration Eigenvalue Problem
%K Shifted-Inverse Iteration
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=59560