報告承辦單位: 數學與統計學院
報告題目: A high order spectral Galerkin method for the elastic 3D-obstacle scattering problem
報告內容: 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.
報告人姓名: 董和平
報告人所在單位: 吉林大學數學學院
報告人職稱/職務及學術頭銜: 副教授
報告時間: 2021年12月4日9:40－10:20
報告地點: 卡斯迪漫享酒店二樓VIP會議廳
報告人簡介: 董和平副教授，2008年獲吉林大學博士學位。主要研究方向是散射與反散射問題的數值方法與理論分析，近兩年針對聲波和彈性波的phaseless反散射問題提出了基于參考球的非線性積分方程方法，相關研究結果發表在《Inverse Problems》，《SIAM. J. Imaging Sci.》，《Inverse Problems and Imaging》等學術期刊上。目前，正在主持國家自然科學基金青年科學基金項目1項。2020年，獲得“天元東北中心優秀青年學者獎勵計劃”資助。