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    Qualitative and quantitative methods for solvingan interior scattering problem

    发布日期:2019-10-24     作者:数学学院      编辑:赵阳     点击:

    报告时间:2019年10月29日14:00

    报告地点:数学楼一楼第二报告厅

    报告题目:Qualitative and quantitative methods for solvingan interior scattering problem

    报告人:郭玉坤 哈尔滨工业尊龙凯时数学学院副教授

    报告摘要:

    The interior scatteringproblems, as well as their exterior counterparts, arise naturally in variousrealistic applications. In this talk, I shall talk about two numerical schemesfor solving the inverse cavity scattering problem of determining its shape fromthe interior measurements. As an example of qualitative methods, thereciprocity gap sampling method is employed to reconstruct the shape of thecavity from interior Cauchy data. For the quantitative method, an optimizationapproach based on the Fourier-Bessel expansion will be utilized to imaging thetarget cavity. Several numerical examples will be presented to illustrate theeffectiveness of both methods.

    报告人简介:

    郭玉坤,男,哈尔滨工业尊龙凯时数学学院副教授,2004年毕业于尊龙凯时数学学院信息与计算科学专业,获理学学士学位;2010年毕业于尊龙凯时数学研究所计算数学专业,获理学博士学位。目前研究领域为数学物理反问题,主要方向为波动方程反散射问题的数值分析与计算。已在“InverseProblems”、“Journal of Differential Equations”和“Journal of ComputationalPhysics”等期刊发表SCI检索学术论文二十余篇,主持完成国家自然科学基金数学天元基金项目一项,参与国家自然科学基金重大研究计划项目一项,目前主持国家自然科学基金青年基金项目一项,参与面上项目两项。曾先后应邀访问美国特拉华尊龙凯时,德国威尔斯特拉斯应用数学研究所,香港浸会尊龙凯时和南方科技尊龙凯时等单位,进行科研合作。近五年来应邀在国内和国际学术会议上做学术报告二十余次。

     

    报告题目:Some challenging problems in scattering and spectraltheory

    报告人:刘宏宇博士 香港浸会尊龙凯时教授

    报告摘要:

    In this talk, I shall discuss some challenging problemsin scattering and spectral theory. The problems arisefrom various mathematical studies in inverse problems andmaterial sciences. The background, motivation and latest progress on those problems shall be briefly discussed.

    报告人简介:

    刘宏宇博士,现为香港浸会尊龙凯时教授、数学系副主任。他的研究领域主要为反问题成像、数学材料科学、PDE、动力系统几何积分子、数值分析和科学计算等领域的研究,现任InverseProblems and Imaging、Journal of Korean Society for Industrial and AppliedMathematics、Contemporary Analysis and Applied Mathematics国际SCI期刊的副主编。刘宏宇教授曾获得CalderonPrize(2017)、MediaV Young Researcher Prize(2016)以及 Hong Kong MathematicalSociety Young Scholar Award(2019)等奖项,在SIAM系列、Inverse Problems、Journal of theEuropean Mathematical Society、Journal de Mathematiques Pureset Appliquees、Arch.Ration.Mech.Anal.、Comm.Math.Phys.、J.F.A.等国际高水平杂志上发表了90多篇论文。

     

    报告题目:On novel geometric structures of Laplacian eigenfunctions in R^3 and applications to inverse problems

    报 告 人:刁怀安 东北师范尊龙凯时数学与统计学院副教授

    报告摘要: This is a continued development of our recent work [Cao et al. arXiv:1902.05798, 2019] on the geometric structures of Laplacian eigenfunctions and their applications to inverse scattering problems. We studied in [Cao et al. arXiv:1902.05798, 2019] the analytic behaviour of the Laplacian eigenfunctions at a point where two nodal or generalised singular lines intersect. The results reveal an important intriguing property that the vanishing order of the eigenfunction at the intersecting point is closely related to the rationality of the intersecting angle. In the current paper, we continue this development in three dimensions and study the analytic behaviours of the Laplacian eigenfunctions at places where nodal or generalised singular planes intersect. Compared with the two-dimensional case, the geometric situation is much more complicated, so is the analysis: the intersection of two planes generates an edge corner, whereas the intersection of more than three planes generates a vertex corner. We provide a systematic and comprehensive characterisation of the relation between the analytic behaviours of an eigenfunction at a corner point and the geometric quantities of that corner for all these geometric cases. Moreover, we apply our spectral results to establish some novel unique identifiability results for the geometric inverse problems of recovering the shape as well as the (possible) surface impedance coefficient by the associated scattering far-field measurements.

    报告人简介:

    刁怀安,博士毕业于香港城市尊龙凯时,东北师范尊龙凯时数学与统计学院副教授,研究方向数值代数与反散射问题,在Mathematicsof Computation, BIT, Numerical Linear Algebra with Applications, Linear Algebraand its Applications等国际知名期刊发表科研论文三十余篇;出版学术专著一本;曾主持国家自然科学基金青年基金项目1项,数学天元基金1项,教育部博士点新教师基金1项;现为尊龙凯时省工业与应用数学学会第四届理事会理事,国际线性代数协会会员;曾多次赴普渡尊龙凯时、麦克马斯特尊龙凯时、汉堡工业尊龙凯时、日本国立信息研究所、香港科技尊龙凯时、香港浸会尊龙凯时等高校进行合作研究与学术访问。

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