| 报告题目： | 反散射问题理论、计算及应用最新进展 |
| 报 告 人： | 包刚 教授 |
| 浙江大学数学系， Michigen State University | |
| 报告时间： | 11月4号(星期一)下午2:00 |
| 报告地点： | 九龙湖数学系第一报告厅 |
| 相关介绍： | 报告摘要：The inverse scattering problem arises in diverse areas of industrial and military applications, such as nondestructive testing, seismic imaging, submarine detections, near-field or subsurface imaging, near-field and nano optical imaging, and medical imaging. A model problem is concerned with a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain. Given the incident field, the direct problem is to determine the scattered field for the known scatterer. The inverse scattering problem is to determine the scatterer from the boundary measurements of near field currents densities. Although this is a classical problem in mathematical physics, mathematical issues and numerical solution of the inverse problems remain to be challenging since the problems are nonlinear, large-scale, and most of all ill-posed! The severe ill-posedness has thus far limited in many ways the scope of inverse problem methods in practical applications. Our progress over the past ten years in mathematical analysis and computational studies of the inverse boundary value problems for the Helmholtz and Maxwell equations will be reported. Several classes of inverse scattering problems will be studied, namely inverse medium problems, inverse source problems, inverse obstacle problems, and inverse waveguide problems. A novel stable continuation approach based on the uncertainty principle will be presented. By using multi-frequency or multi-spatial frequency boundary data, our approach is shown to overcome the ill-posedness for the inverse scattering problems. Convergence issues for the continuation algorithm will be examined. New stability and uniqueness results for the inverse problem will be presented. In particular, our most recent stability result on inverse problems for the related time-domain wave equation with possible caustics will be highlighted. The speaker will also discuss our recent efforts in multi-scale/multi-physics nano optics modeling and inverse problems in nano science. 报告人介绍：包刚教授现任浙江大学数学系主任。1985年毕业于吉林大学，1991年5月在美国莱斯大学（Rice University）获得应用数学博士学位。1992年起他先后在美国明尼苏达大学数学应用研究所、佛罗里达大学和密歇根州立大学工作，是密歇根工业与应用数学中心创始人、主任，曾任吉林大学长江特聘教授。2003年获得冯康奖，2004年获得国家自然科学基金委海外杰青，2007年获密歇根州立大学杰出教职奖。包刚教授同时还担任包括SIAM J. on Applied Math. 等10多个国际著名期刊的编委。 包刚教授的工作主要涉及衍射光学、非线性光学、近场光学、纳米光学及其它波传播问题的数学建模，理论分析和科学计算。他最早开始对光栅衍射问题的数学模型进行系统研究；第一个获得间断系数有源Maxwell方程的Lp估计这一非常重要和深刻的成果；分析和发展了一系列Maxwell方程组应用问题的基于有限元方法，最小二乘有限元方法，杂交边界有限元方法的算法；发展了一系列新的技巧，为光学和电磁学中的反问题和最优设计问题提供了原创性的结果，是光学和Maxwell方程组这一重要应用领域的国际学科带头人。 |
