报告题目：Periodic surface identification with phase or phaseless near-field data
中文标题：相场数据的周期表面识别
报告时间：2019年4月7日9:30-10:30
报告地点：理学院二楼会议室
报告人：程晋，复旦大学数学科学学院教授，上海财经大学数学学院院长，国际著名计算数学专家，主要研究方向为数学物理反问题。现任中国数学会副理事长，中国工业应用与数学学会常务理事，国家基金委重大研究计划“高性能计算的基础算法和可计算建模”专家组成员，国家基金委数理学部会评专家，英国物理学会会士，国际反问题学会执行委员，日本九州大学工业数学研究所国际专家组成员，日本东京大学等国际著名高校客座教授。《Inverse Problems》等多个国际SCI核心刊物编委。
报告摘要：We investigate the inverse diffraction grating problem which is to reconstruct the periodic surface from the diffracted field. The surface is assumed to be a sufficiently smooth and small perturbation of the flat surface. A novel computational method is developed to solve the inverse problem with super-resolution by using phase or phaseless near-field data. The method utilizes Rayleigh's coefficients of the near field data and updates iteratively the approximated surface function by solving a truncated linearized system. Monotonicity of the error estimate is proved under the small perturbation assumption of the surface. Numerical examples are shown to verify the theoretical findings and illustrate the effectiveness of the proposed method.