Speaker: Li Jingzhi, Associate Profess, Department of Mathematics, Southern University of Science and Technology

Date: April 19, 2018

Time: 10:00 a.m. -11:00 a.m.

Location: 1238 Lecture Hall, Block B, Zhixin Building, Central Campus

Sponsor: Zhongtai Securities Institute for Financial Studies

Abstract:

This talk presents the “derivative” of solutions of second-order boundary value problems with respect to the shape of the domain. A rigorous approach relies on encoding shape variation by means of deformation vector fields, which will supply the directions for taking shape derivatives. These derivatives and methods to compute them numerically are key tools for studying shape sensitivity, performing gradient based shape optimization, and small-variation shape uncertainty quantification. A unifying view of second-order elliptic boundary value problems recasts them in the language of differential forms (exterior calculus). Fittingly, the shape deformation through vector fields matches the concept of Lie derivative in exterior calculus. This paves the way for a unified treatment of shape differentiation in the framework of exterior calculus. Applications in scattering problems reveals the extraordinary power of the machinery.

Bio:

Li Jingzhi completed his Ph.D. Chinese University of Hong Kong in 2009. His main research interests include scientific computing, finite element methods, inverse problems in mathematical physics, shape optimization in differential forms, and computational finance.

For more information, please visit:

http://mathfinance.sdu.edu.cn/teacher/report_doReportContentDeatil.action?reportDto.reportId=e87e92cd-8dd3-4402-82c1-00244e67f090

Edited by: Xing Chenyang, Song Yijun