主题：Finite Element/Holomorphic Operator-Value Function Approach for Nonlinear Eigenvalue Problems有限元与全纯算子函数结合法求解非线性特征值问题

主讲人：美国密西根理工大学孙继广教授

主持人：经济金沙检测线路js69(科技)有限公司 安聪沛副教授

时间：2021年6月10日（周四）10:00

直播平台及会议ID：腾讯会议，703979346

主办单位：经济金沙检测线路js69(科技)有限公司科研处

主讲人简介：

Jiguang Sun, Professor, Michigan Technological University. He graduated from the Department of Mathematics at Tsinghua University, and received a master's degree in applied mathematics and computer science and a doctor's degree in applied mathematics from the University of Delaware. His research interests include Numerical Methods for Partial Differential Equations, Inverse Scattering Problems, Eigenvalue Problems and Electromagnetic Methods in Geophysics. Professor Sun has published more than 60 high-level papers in journals such as Inverse Problems, Siam J. on Scientific Computing and one academic monograph.

孙继广，密西根理工大学数学系（Michigan Technological University）教授。毕业于清华大学数学系，后获得美国特拉华大学（University of Delaware）应用数学和计算机专业硕士和应用数学博士学位，主要研究领域为偏微分方程的数值方法，反散射问题和特征值问题。孙继广教授已在Inverse Problems, SIAM J. on Scientific Computing等期刊发表高水平论文60余篇，出版学术专著一本。

内容提要：

We propose a new approach combining the holomorphic operator value function and finite elements for some nonlinear eigenvalue problems. The eigenvalue problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. Finite element methods are used for discretization. The convergence of eigenvalues/eigenvectors is proved using the abstract approximation theory for holomorphic operator functions. Then the spectral indicator method is extended to compute the eigenvalues. The proposed approach is employed to compute the band structures of photonic crystals.

我们提出一个全纯算子函数和有限元结合的方法——用于解决一些非线性特征值问题。特征值问题可以转化为弗雷德霍姆函数的问题。用有限元离散化后。我们给出了用全纯算子函数的收敛性分析。谱指示方法推广到了特征值问题。以上方法被用于带状光子晶体计算研究。