报告题目：Shapederivatives-new perspective and applications in scattering
报 告 人： 李景治（南方科技大学数学系副教授，博士生导师）
Thistalk presents the “derivative” of solutions of second-order boundary valueproblems with respect to the shape of the domain. A rigorous approach relies onencoding shape variation by means of deformation vector fields, which willsupply the directions for taking shape derivatives. These derivatives andmethods to compute them numerically are key tools for studying shapesensitivity, performing gradient based shape optimization, and small-variationshape uncertainty quantification. A unifying view of second-order ellipticboundary value problems recasts them in the language of differential forms(exterior calculus). Fittingly, the shape deformation through vector fieldsmatches the concept of Lie derivative in exterior calculus. This paves the wayfor a unified treatment of shape differentiation in the framework of exteriorcalculus. Applications in scattering problems reveals the extraordinary powerof the machinery.