演讲人Speaker：   清华大学数学科学系 黄忠亿 教授

题目Title: The direct method of lines for forward and inverse linear elasticity problems in star-shaped domains

时间Date：2023年 4 月 26 日       Time：15:00–17:00

地点Venue：腾讯会议132-561-875

链接：https://meeting.tencent.com/dm/qeTDVJS0YUVV 

内容摘要Abstract： 

In this talk, we propose the direct method of lines for linear elasticity problems in star-shaped domains and consider its application in inverse problems. We introduce the curvilinear coordinate, in which the irregular star-shaped domain is converted to a regular semi-infinite strip. The equations are discretized w.r.t. the angular variable and we solve the resulting semi-discrete approximation using a direct method. The eigenvalues of the semi-discrete approximation converge quickly to the true eigenvalues of the elliptic operator, which helps capture the singularities naturally. For the inverse problems, we determine the Lame coefficients from measurement data by minimizing a regularized energy functional. Numerical examples are presented to show the effectiveness and accuracy of our method for both forward and inverse elasticity problems.

个人简介(About the speaker):

黄忠亿，清华大学数学科学系教授、博士生导师，主要从事多尺度问题的数学建模、分析及数值模拟研究，2020年获国家杰出青年基金资助，2013年获优秀青年基金资助。