長沙理工大學(xué)學(xué)術(shù)活動(dòng)預(yù)告
報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告題目: An inverse acoustic-elastic interaction problem with phased or phaseless far-field data
報(bào)告內(nèi)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(bào)告人姓名: 董和平
報(bào)告人所在單位: 吉林大學(xué)數(shù)學(xué)學(xué)院
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 副教授
報(bào)告時(shí)間: 2020年10月30日9:10－9:50
報(bào)告地點(diǎn): 理科樓A-419
報(bào)告人簡介: 董和平副教授，2008年獲吉林大學(xué)博士學(xué)位。主要研究方向是散射與反散射問題的數(shù)值方法與理論分析，近兩年針對(duì)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(guān)研究結(jié)果發(fā)表在《Inverse Problems》，《SIAM. J. Imaging Sci.》，《Inverse Problems and Imaging》等學(xué)術(shù)期刊上。目前，正在主持國家自然科學(xué)基金青年科學(xué)基金項(xiàng)目1項(xiàng)。2020年，獲得“天元東北中心優(yōu)秀青年學(xué)者獎(jiǎng)勵(lì)計(jì)劃”資助。