发布时间:2019年11月04日 作者:邓又军   消息来源:    阅读次数:[]


Mini Workshop on Recent Progress in Inverse Problems and Metamaterials





报告题目: Time-domain metamaterial models and finite element simulations

报告人:   杨伟 湘潭大学

报告时间:11月7日 9:00-10:00


报告摘要:In this talk, we first introduce the development history of metamaterials and give some time-domain mathematical model in metamaterials. Then, we focus on the time-domain cloaks model. The explicit expressions of the cloak parameters without the contour curve expressions of the objects and 2d arbitrary shape cloak model are established. A new time-domain finite element scheme is developed to solve the governing equations, and it's stability is also provided. Numerical results are presented to confirm the theoretical analysis and the effectiveness of our cloak model and FETD method.

报告人简介:杨伟,党员,理学博士,副教授,于2013年7月在湘潭大学数学与计算科学学院任教,现任院党委委员、信息与计算科学系党支部书记,工作认真负责,成绩显著,2019年被评为湖南省普通高校“先锋工程”双带头人标兵。长期从事超材料中电磁波传播问题的数学建模与数值方法研究,在国际期刊发表SCI论文30余篇,SCI他引超过150次,Google学术引用430余次,h指数 12。现主持国家面上项目1项,参与国自科重大研究计划2项、面上项目1项,2016年荣获第三届中国工业与应用数学学会优秀青年学者奖;2015年获湖南省优秀博士学位论文;2013年获第九届东亚工业和应用数学学会优秀学生论文奖。

报告题目:  A space-time finite element method for solving linear Riesz space fractional partial differential equations

报告人:  赖军将 闽江学院

报告时间:11月7日 10:30-11:30


报告摘要:In this paper, the numerical solutions for linear Riesz space fractional partial differential equations with a second order time derivative are considered. A space-time finite element method is proposed to solve these equations numerically. In the time direction, the $C^0$-continuous Galerkin method is used to approximate the second order time derivative. In the space direction, the usual linear finite element method is developed to approximate the space fractional derivative. The matrix equivalent form of this numerical method is deduced. The stability of the discrete solution is established and the optimal error estimates are investigated. Some numerical tests are given to validate the theoretical results.

报告人简介:赖军将,上海交通大学计算数学博士,2008年7月到闽江学院工作。现为闽江学院数学与数据科学学院数据科学教研室教师、副教授,入选福建省高等学校新世纪优秀人才支持计划。在《中国科学》、《DCDS-B》等国内外重要学术期刊上发表论文十余篇。主持完成国家自然科学基金、福建省自然科学基金各1项。获评福州市教育系统先进工作者。《Mathematical Problems in Engineering》、《计算数学》,《数学物理学报》等期刊审稿专家。

报告题目:  An optimization method for inverse acoustic obstacle scattering with multiple incident waves

报告人:  郭玉坤 哈尔滨工业大学

报告时间:11月7日 14:30-15:30


报告摘要:The inverse problem considered in this talk is to determine the shape of a two-dimensional time-harmonic acoustic scatterer with Dirichlet boundary condition from the knowledge of some far field patterns. Based on the optimization method due to Kirsch and Kress for the inverse scattering problem, we propose a new scheme by reformulating the cost functional via a technique of piecewise integration with respect to incident directions. Convergence analysis of this method will be given. Numerical experiments will be presented to show that our method accelerates the computations without losing the accuracy of the reconstructions.

报告人简介:郭玉坤,男,哈尔滨工业大学数学学院副教授,2004年毕业于吉林大学数学学院信息与计算科学专业,获理学学士学位;2010年毕业于吉林大学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“Inverse Problems”、“Journal of Differential Equations”和“Journal of Computational Physics”等期刊发表SCI检索学术论文20余篇。曾主持完成国家自然科学基金数学天元基金项目1项,参与国家自然科学基金重大研究计划项目1项,面上项目2项,目前主持国家自然科学基金青年基金项目1项,参与面上项目1项。曾先后应邀访问美国特拉华大学,德国威尔斯特拉斯应用数学研究所,香港浸会大学和南方科技大学等单位,进行科研合作。近5年来应邀在国内和国际学术会议上做学术报告20余次。

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 东北师范大学

报告时间: 11月7日 16:00-17:00

报告地点: 数学院145报告厅

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 behavior of the Laplacian eigenfunctions at a point where two nodal or generalized 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 behaviors of the Laplacian eigenfunctions at places where nodal or generalized 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 characterization of the relation between the analytic behaviors 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,数学哲学博士,副教授,于2007年11月在东北师范大学数学与统计学院任教,研究方向为数值代数与反问题,曾经在《 MATH COMPUT》、《NUMER LINEAR ALGEBR.》、《J COMPUT APPL MATH》、《 LINEAR ALGEBRA APPL.》、《 J COMPUT MATH.》以及《SCI. CHINA MATH.》等杂志发表多篇论文,出版学术专著一本。主持国家自然科学基金青年基金1项,国家自然科学基金天元基金1项,教育部博士点新教师基金1项,东北师范大学培育基金1项,参加国家自然科学基金委项目2项。 曾多次访问Purdue University,Technical University of Hamburg,McMaster University,National Institute of Informatics, Japan,以及Hongkong Baptist University等国(境)外高校。曾为《Applied Numerical Mathematics》《BIT Numerical Mathematics》、《Calcolo》、《Computers & Mathematics with Applications》、《Journal of Computational and Applied Mathematics》、《International Journal of Computer Mathematics》、《Journal of Applied Mathematics and Computing》、《Linear Algebra and its Applications》、《Linear and Multilinear Algebra》、《Numerical Algorithms》、《SIAM Journal on Matrix Analysis and Applications》等杂志审稿。

报告题目:  Mathematical study on plasmon resonance beyond quasi-static approximation

报告人:  李宏杰 香港中文大学

报告时间:11月7日 17:00-18:00


报告摘要:This talk discusses the mathematical progress made by our study on the plasmon resonances and their application to invisibility cloaking for optics and linear elasticity. First, I shall briefly discuss the major results obtained in the quasi-static regime. Then I shall focus on talking about our recent study beyond the quasi-static approximation for the Lame system.

报告人简介:李宏杰, 2019年毕业与香港浸会大学(导师:刘宏宇),目前在香港中文大学做博士后,已在顶级杂志发表多篇论文.

报告题目:  Some challenging problems in scattering and spectral theory

报告人:  刘宏宇 香港浸会大学

报告时间:11月8日 9:00-10:00


报告摘要:In this talk, I shall discuss some challenging problems in scattering and spectral theory. The problems arise from various mathematical studies in inverse problems and material sciences. The background, motivation and latest progress on those problems shall be briefly discussed.

报告人简介:刘宏宇现任香港浸会大学数学系系副主任, 教授。刘宏宇教授于2007年在香港中文大学数学系取得博士学位,曾任职于美国北卡罗来纳大学(2011-2014),英国雷丁大学(2010/2011),美国华盛顿大学(2007--2010)。刘宏宇教授于2019年获香港数学会颁发的“Young Scholar Award”; 2017年获国际反问题协会(Inverse Problems International Association)颁发的“Calderon Prize”;2016年国际会议ICIP16上获颁“MediaV Prize”。刘宏宇教授现担任“Inverse Problems and Imaging”等4个国际期刊的编委,国际反问题协会东亚分会秘书,香港研究资助局会评专家等。

刘宏宇教授的研究领域为应用数学和计算数学,包括数学物理中的反问题,偏微分方程,超材料和隐形,散射理论和谱理论。在上述领域取得了一系列创新性的研究成果, 在国际高水平学术期刊发表论文100余篇,其中9篇论文被相关杂志评为年度亮点论文、特色论文或高被引论文。

报告题目:  Identifying multipolar acoustic sources by the direct sampling method

报告人:  汪贤超 哈尔滨工业大学&香港浸会大学

报告时间:11月8日 10:30-11:30


报告摘要:This paper concerns the direct sampling method for solving the inverse problem of identifying point sources for the Helmholtz equation from far-field data. We develop some novel indicator functions which could determine the locations and intensities of the target multipolar sources with a single wavenumber. Theoretically, the indicating behaviors are rigorously analyzed. Two and three dimensional numerical experiments are conducted to illustrate the effectiveness and robustness of the proposed approach.





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