报告题目： A novel quantitative inverse scattering scheme using interior resonant mode

报 告 人： 汪贤超 副教授 单位: 哈尔滨工业大学数学系  

报告时间：2025年7月14日 下午14:00-15:00

报告地点：腾讯会议：225409567

校内联系人：卜柯文 [email protected]

报告摘要：In this talk, we introduce a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we determine the interior eigenvalues of the underlying unknown

obstacle from the far-field data via the indicating behavior of the linear sampling method. Then we further determine the associated interior eigenfunctions by solving a constrained optimization problem, again only involving the far-field data. In the second phase, we propose a novel iteration scheme

of Newton’s type to identify the boundary surface of the obstacle. By using the interior eigenfunctions determined in the first phase, we can avoid computing any direct scattering problem at each Newton’s iteration. The proposed method is particularly valuable for recovering a sound-hard obstacle, where the

Newton’s formula involves the geometric quantities of the unknown boundary surface in a natural way. We provide rigorous theoretical justifications of the proposed method. Numerical experiments in both 2D and 3D are conducted, which confirm the promising features of the proposed imaging scheme.

报告人简介：汪贤超，哈尔滨工业大学副教授。2019年毕业于哈尔滨工业大学，获理学博士学位。目前研究领域为数学物理反问题，主要集中于反散射问题的数值分析与计算，涵盖波源反演、目标追踪、超声测温、超分辨率成像以及共振隐形等方向。迄今为止，已在SCI期刊上发表论文20余篇。主持国家自然科学基金2项，并于2019年入选香江学者，2023年入选洪堡学者。