题目：Numerical method and uniqueness result for phaseless inverse diffraction grating problem

内容简介：In this talk, I will introduce some results on  uniqueness and numerical methods of identifying a smooth grating profile with a mixed or transmission boundary condition from phaseless data. The existing uniqueness result requires the measured data to be in a bounded domain. To break this restriction, we design an incident system consisting of the superposition of point sources to reduce the measurement data from a bounded domain to a line above the grating profile. Based on Rayleigh's expansion and reciprocity relation of the total field, a grating profile with a mixed or transmission boundary condition can be uniquely determined from the phaseless total field data. An iterative algorithm is proposed to recover the Fourier modes of grating profiles at a fixed wavenumber. Some numerical examples are presented to the effectiveness of our numerical algorithm.

报告人：吕俊良

报告人简介：吉林大学数学学院，教授，博导。研究兴趣包括无界域散射问题的数值方法，反散射问题的数值算法与理论，偏微分方程有限体积元法等。研究成果发表在SIAM J. Numer. Anal.，Math. Comput.，Inverse Problems, J.Sci. Comput. 以及 IMA J. Numer. Anal. 等杂志上。承担国家自然科学基金项目、国防项目、吉林省自然科学基金等。

现任中国数学会计算数学分会理事、中国仿真学会仿真算法专委会委员、吉林省数学会理事。

时  间：2025年5月15日（周四）下午18:00开始

地  点：石牌校区南海楼124会议室

热烈欢迎广大师生参加!

信息科学技术学院

2025年5月6日