The 40th Anniversary of Shenzhen University and the 40th Anniversary of Mathematics Department
Liyuan scholar Colloquiumsixty
Lecture Title:The direct method of lines for forward and inverse linear elasticity problems in star-shaped domains
Speaker：Prof. Zhongyi Huang (Tsinghua University)
Lecture time: December 10, 2023 (Sunday) 9:30-10:30pm
Lecture location:Classroom No. 1, 1/F, Hui Xing Building, Yuehai Campus, Shenzhen University, China
Overview：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.
Speaker Introduction：Huang Zhongyi is a long term professor and doctoral supervisor in the Department of Mathematical Sciences, Tsinghua University. He has been engaged in research in computational mathematics and scientific engineering computation, and has achieved a series of innovative results in modeling, analysis and numerical simulation of multi-scale problems. He was awarded the National Distinguished Young Persons' Fund (NDYPF) in 2020, and the Outstanding Young Persons' Fund (OYPF) in 2013.
Teachers and students are welcome to participate!
Invited by: School of Mathematical Sciences
School of Mathematical Sciences
December 06, 2023
