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長沙理工大學學術活動預告

報告承辦單位: 數學與統計學院

報告題目:  An inverse acoustic-elastic interaction problem with phased or phaseless far-field data

報告內容:  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 Nystr?m-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. 

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: 2020年10月30日9:10－9:50

報告地點: 理科樓A-419 

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。