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報告承辦單位: 數學與統計學院

報告題目:  An accelerated level-set method for inverse scattering problems.

報告內容:  In this talk, we propose a rapid and robust iterative algorithm to solve inverse acoustic scattering problems formulated as a PDE constrained shape optimization problem. We use a level-set method to represent the obstacle geometry and propose a new scheme for updating the geometry based on an adaptation of  accelerated gradient descent methods. The resulting algorithm aims at reducing the number of iterations and improving the accuracy of reconstructions.  To cope with regularization issues, we propose the use of a smoothing to the shape gradient using a single layer potential associated with ik where k is the wave number. Numerical experiments are given for several data types (full aperture, backscattering, phaseless, multiple frequencies) and show that our method outperforms a non accelerated approach in terms of convergence speed, accuracy and sensitivity to initial guesses.

報告人姓名:  劉曉莉

報告人所在單位: 巴黎綜合理工大學

報告人職稱/職務及學術頭銜:    博士后

報告時間:  2021年11月25日16:20－17:00

報告方式: 騰訊會議ID: 838 2530 8952

報告人簡介:  劉曉莉，巴黎綜合理工大學，博士后。主要研究領域為波傳播及其反問題的數值算法，在SIAM J. Appl. Math.、SIAM J. Imaging Sci.、Inverse Problems等雜志發表多篇學術論文。