多夹杂体中的本征值问题：渐近分析
Eigenvalue problem in a solid with many inclusions: asymptotic analysis
摘要：
我们构造了一个包含小刚性夹杂云的区域内的拉普拉斯算子的第一特征值和相应的本征解的渐近逼近。小夹杂物的分离的特征在于与夹杂物的标称尺寸相比大得多的小参数。给出了第一本征值和相关本征场近似的余项估计。数值例子来证明效率的渐近方法相比，传统的数值方法，如有限元法，三维固体包含集群的小夹杂物。
英文摘要：
We construct the asymptotic approximation to the first eigenvalue and corresponding eigensolution of Laplace's operator inside a domain containing a cloud of small rigid inclusions. The separation of the small inclusions is characterised by a small parameter which is much larger compared with the nominal size of inclusions. Remainder estimates for the approximations to the first eigenvalue and associated eigenfield are presented. Numerical illustrations are given to demonstrate the efficiency of the asymptotic approach compared to conventional numerical techniques, such as the finite element method, for three-dimensional solids containing clusters of small inclusions.
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