基于形状优化框架下的Steklov特征值问题研究

<正>1引言特征值问题在应用数学分支和工程中,尤其是在最优设计问题中,有很多的应用,所以特征值问题的最优化已经有了较为深入的研究,见在我们的研究当中,最优设计问题常常以一种指定载荷的设计下、能量的极小化问题的形式出现.在大多数关于最优设计的文章里面,我们更重视在一个固定载荷下条件下结构的最

STEKLOV EIGENVALUE PROBLEM BASED ON SHAPE OPTIMIZATION

This paper investigates the first Steklov eigenvalue problem by the method of shape optimization.This first Steklov eigenvalue problem is established in the domain which contains a smooth open subset with its functions vanishing in and the subset is optimized in order to get the first eigenvalue of the Steklov eigenvalue problem.The first order optimality conditions of the corresponding shape optimization problem are established by using the function space parametrization techniques,the continuous conjugated method and the velocity method to describe the perturbation of the domain.Then an appropriate gradient type algorithm is proposed.Finally numerical examples are applied to validate the theory and the efficiency of this proposed algorithm.