关于举行南方科技大学李景治教授学术报告会的通知

报告题目：Shape Derivatives in Differential Forms: Theory and Applications
报 告 人：李景治  教授（南方科技大学）
报告时间：2017年06月09日（星期五）上午08:30-09:30
报告地点: 4号楼4318室

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                                                                      数学学院
                                                                   2017年06月08日

报告摘要：
    In this talk, we present an intrinsic perspective in differential forms of shape derivatives of the solutions to PDEs, which is of immense significance in the field of PDE-constrained shape design, optimization and sensitivity analysis. We first depict two fundamental Hadamard structure theorems for shape derivatives of boundary and domain integrals by the exterior calculus of differential forms, whereby the Lie derivative plays a pivotal role in deriving the structure results. Higher order shape derivatives can be systematically derived in a recursive way. It is revealed that the symmetry of the shape Hessian of domain and boundary integrals depends only on the Lie bracket of the two velocity fields associated with the transformations. With resort to such an approach,one can express the abstract framework for variational formulations of concrete PDEs and incarnate the differential forms in terms of avatars like scalar functions and vector fields to derive explicit formulae by straightforward calculus for shape derivatives of solutions to certain PDE under concern. As a model problem, we illustrate the power of the theory by deriving the shape derivatives of solutions to acoustic and electromagnetic scattering problems.