受公司国际项目管理中心资助，应6163银河线路检测中心宋明辉教授的邀请，美国密歇根理工大学孙继广教授将于近日在公司做两场线上学术讲座，报告内容为特征值问题的有限元方法。以下是报告信息，欢迎感兴趣的师生参加。

报告一

时间：2020年7月22日上午10:00-11:30

平台：腾讯会议，会议ID：627 471 385，可点击链接直接加入会议：

https://meeting.tencent.com/s/qNXjnIYJXulq

题目：A New Finite Element Approach for the Dirichlet Eigenvalue Problem

摘要：We propose a new finite element approach, which is different than the classic Babu\v{s}ka-Osborn theory, to approximate Dirichlet eigenvalues. The problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for conforming finite elements is proved using the abstract approximation theory for holomorphic operator functions. The spectral indicator method is employed to compute the eigenvalues. A numerical example is presented to validate the theory.

报告二

时间：2020年7月23日上午10:00-11:30

平台：腾讯会议，会议ID：793 580 495，可点击链接直接加入会议：https://meeting.tencent.com/s/jSowYzchhdrC

题目：A New Finite Element Approach for the Transmission Eigenvalue Problem

摘要：The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media. The problem plays a key role in the proof of the unique determination of an inhomogeneous media. Furthermore, transmission eigenvalues can be reconstructed from the scattering data and used to estimate the material properties of the unknown object. The problem is posted as a system of two second order partial differential equations and is nonlinear and non-selfadjoint. It is challenging to develop effective numerical methods and prove the convergence. We formulate the transmission eigenvalue problem for anisotropic media as an eigenvalue problem of a holomorphic Fredholm operator function of index zero. The Lagrange finite elements are used for the discretization and the convergence is proved using the abstract approximation theory for holomorphic operator functions. A spectral indicator method is developed to compute the eigenvalues. Numerical examples are presented for validation.

报告人简介：孙继广1996年毕业于清华大学应用数学系。在University of Delaware师从于麦克斯韦有限元方法的专家Peter Monk，获得计算机科学硕士和应用数学博士。之后在University of North Carolina, Charlotte从事博士后研究。现在任Michigan Technological University终身正教授（tenured full professor）。孙继广的研究方向包括特征值问题有限元方法和逆散射理论。近年来从事传输特征值计算的研究。从2004年至今在Inverse Problems, SIAM Journal of Numerical Analysis, Numerische Mathematik, SIAM Journal on Imaging Sciences, Journal of Computational Physics等杂志上发表60余篇文章。与中科院计算所的周爱辉教授合作的专著Finite Element Methods for Eigenvalue Problems由Taylor & Francis公司于2016年出版。