報告題目：Periodic surface identification with phase or phaseless near-field data
中文標題：相場數據的周期表面識別
報告時間：2019年4月7日9:30-10:30
報告地點：必一体育平台二樓會議室
報告人：程晉，復旦大學數學科學必一教授，上海財經大學數學必一院長，國際著名計算數學專家，主要研究方向為數學物理反問題。現任中國數學會副理事長，中國工業應用與數學學會常務理事，國家基金委重大研究計劃“高性能計算的基礎算法和可計算建模”專家組成員，國家基金委數理學部會評專家，英國物理學會會士，國際反問題學會執行委員，日本九州大學工業數學研究所國際專家組成員，日本東京大學等國際著名高校客座教授。《Inverse Problems》等多個國際SCI核心刊物編委。
報告摘要：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.