板振动特征值问题基于混合格式的二网格方法研究
Two-Grid Method Based on Hybrid Scheme for Plate Vibration Eigenvalue Problem
摘要: 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πh上的板振动特征值问题可以简化为求粗网格πH上的板振动问题和细网格上πh线性方程组的解。我们证明了当H>h≥O(H2)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。
Abstract: 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 πh grid can be simplified to the solution of plate vibration on πH grid and the solution of system of linear equations on πh grid. In this paper, it is proved that when H>h≥O(H2), the solution still keeps asymptotically worst-case accuracy. Finally, the numerical results show the high efficiency of the proposed scheme.
文章引用：张云飞, 段丽梅, 徐良坤. 板振动特征值问题基于混合格式的二网格方法研究[J]. 声学与振动, 2022, 10(4): 45-58. https://doi.org/10.12677/OJAV.2022.104006

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