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报告承办单位: 数学与统计学院

报告题目:  An inverse acoustic-elastic interaction problem with phased or phaseless far-field data

报告内容:  This talk concerns an inverse acoustic-elastic interaction problem, which is to determine the location and shape of the elastic obstacle by using either the phased or phaseless far-field data. By introducing the Helmholtz decomposition, the model problem is reduced to a coupled boundary value problem of the Helmholtz equations. The jump relations are studied for the second derivatives of the single-layer potential to establish the corresponding boundary integral equations. The well-posedness is discussed for the coupled boundary integral equations. An efficient and high order Nyström-type discretization method is proposed for the integral system. For the phaseless inverse problem, we show that the modulus of the far-field pattern is invariant under a translation of the obstacle. To break the translation invariance, an elastic reference ball technique is introduced. We prove that the inverse problem with phaseless far-field pattern has a unique solution under certain conditions. In addition, a reference ball technique based nonlinear integral equations is also proposed for the phaseless inverse problem. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed methods. 

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: 2020年10月30日9:10－9:50

报告地点: 理科楼A-419 

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。