深圳大学四十周年校庆暨数学学科四十周年庆

荔园学者Colloquium第六十期

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

主讲人：黄忠亿 教授(清华大学)

讲座时间：2023年12月10日（周日）9:30-10:30

讲座地点：深圳大学粤海校区汇星楼一楼一号教室

内容概述：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 and the linear elasticity problem is reduced to a variational-differential problem. 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.

主讲人简介：报告人简介：黄忠亿，清华大学数学科学系长聘教授、博士生导师，一直从事计算数学与科学工程计算方面的研究，在多尺度问题的建模、分析和数值模拟等方面取得了一系列创新性成果。2020年获国家杰出青年基金资助，2013年获优秀青年基金资助。

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2023年12月06日