报告承办单位: 数学与统计学院

报告题目:  A high order spectral Galerkin method for the elastic 3D-obstacle scattering problem

报告内容:  This talk concerns the time-harmonic scattering by a rigid obstacle embedded in the homogeneous and isotropic elastic medium in three dimensions. A novel boundary integral formulation is proposed and its high order spectral Galerkin algorithm is developed for the obstacle scattering problem. More specifically, based on the Helmholtz decomposition, the model problem is reduced to a coupled boundary value problem, and the uniqueness of the coupled boundary value problem is proved. Then we establish coupled boundary integral equations with weakly and strongly singular operators. The uniqueness of the coupled boundary integral equations is discussed. With the help of surface differential operator and integration by parts formula, we reduce the strongly singular operators to a weakly singular operator in form of the exterior integral of the Galerkin method, which leads to a simple full-discrete scheme, since the density of the interior integral dose not involve derivative. It should be emphasized that all operations in the full discretization are scalar, which also make the numerical implementation much easier. Numerical experiments are provided to demonstrate the outstanding performance of the proposed method.

报告人姓名:  董和平

报告人所在单位: 吉林大学数学学院

报告人职称/职务及学术头衔: 副教授

报告时间: 2021年12月4日9:40－10:20

报告地点: 卡斯迪漫享酒店二楼VIP会议厅

报告人简介:  董和平副教授，2008年获吉林大学博士学位。主要研究方向是散射与反散射问题的数值方法与理论分析，近两年针对声波和弹性波的phaseless反散射问题提出了基于参考球的非线性积分方程方法，相关研究结果发表在《Inverse Problems》，《SIAM. J. Imaging Sci.》，《Inverse Problems and Imaging》等学术期刊上。目前，正在主持国家自然科学基金青年科学基金项目1项。2020年，获得“天元东北中心优秀青年学者奖励计划”资助。