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A novel inverse scattering scheme using interior resonant modes

  • 演讲者:汪贤超(哈尔滨工业大学)

  • 时间:2022-07-18 14:00-15:00

  • 地点:腾讯会议 ID 220-979-877,密码 220718

讲座摘要

In this talk, we discuss 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 behaviour 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. 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. 


个人简介
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数学学院计算数学专业,获理学博士学位。目前研究领域为数学物理反问题,主要方向为波动方程反散射问题的数值分析与计算。目前已在“Inverse Problems”、“Journal of Computational Physics”和“SIAM Journal on Imaging Sciences”等期刊发表 SCI 检索学术论文 10 余篇,主持国家自然青年基金项目 1 项和“香江学者计划”项目 1项。