Shape derivatives — new perspective and applications in scattering

发布时间：2018-04-02 作者：浏览次数：

Speaker:	Professor Jingzhi Li (李景治)	DateTime:	2018年04月02日（星期一）上午9:50—10:40
Brief Introduction to Speaker: Professor Jingzhi Li (李景治)，南方科技大学		Place:	六号楼二楼报告厅
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.