简支边界条件下的重调和特征值问题基于混合格式的二网格方案.pdfVIP

目录

摘要··················································································I

ABSTRACT········································································II

1绪论·······················································································1

2预备知识················································································4

3基于移位反迭代的二网格离散化方案······································9

4基于子空间迭代的二网格离散化方案······································19

5基于移位反迭代的多网格离散化方案······································22

6数值实验················································································25

7总结与展望············································································32

参考文献···················································································33

致谢··················································································37

攻读硕士学位期间主要研究成果················································39

贵州师范大学学位论文原创性声明············································40

摘要

重调和特征值问题在机械制造、结构工程等领域中有广泛的应

用，其处理方法受到了学术界的高度关注。本文给出了基于移位反

迭代的二网格和多网格离散化方案以及子空间上的二网格迭代方案，

基于移位反迭代的二网格方法是当今特征值问题计算的有效方法之

一，它可以有效地处理求解特征值问题时计算量大、耗时长的问题，

是计算特征值的一个强有力的工具。本文主要研究的是简支边界条

件下的重调和特征值问题的基于Ciarlet-Raviart混合格式的移位反迭

代二网格有限元方法。采用我们的方案，求解细网格上的特征值

ℎ

问题可以简化为在粗网格上求解一个特征值问题和在细网格上

ℎ

2

求解一个线性方程组。随后证明了当ℎ≥()时，结果解仍然保持

渐近最优精度，并在正方形和L形以及正六边形区域上进行了数值实

验。数值结果表明了该方法在计算方面的高效性和准确性，对于简

化计算具有重要价值。