报告题目：Numerical method and uniqueness result for phaseless inverse diffraction grating problem
报告人：吕俊良 教授（吉林大学）
邀请人：郑光辉
时间：2025年10月24日（周五）15:30--16:10
地点：数学院203报告厅
报告摘要：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. We derive reciprocity relations for point sources, diffracted fields, and total fields, respectively. 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 verify the correctness of theoretical results and to show the effectiveness of our numerical algorithm.
报告人简介：吕俊良，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、机器学习算法与应用等。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。
