题目: A novel reconstruction method for multilayered elastic gratings from one-sided measurements

主讲人：杨家青 教授

时间：2026年7月13日（星期一）11：00 - 12：00

地点：理学院308会议室

主办单位：理学院

主讲人简介：

杨家青，西安交通大学数学与统计学院教授，研究方向为反问题的数学理论与计算方法，在SIAM J.Numer. Anal.、SIAM J. Sci. Comput.、SIAM J. Appl. Math.、SIAM J. Imaging Sci.、SIAM Multiscale Model. Simul.、Inverse Problems、J. Comput. Phys.、J. Differential Equations等国际权威期刊发表学术论文50篇。曾或现主持国家自然科学基金青年科学基金项目（B类）、国家重点研发计划课题、天元基金重点专项、面上项目等；曾获CSIAM应用数学青年科技奖、陕西省百人计划（青年）、山东省自然科学二等奖等。

摘要：

This talk is associated with the inverse scattering problem of reconstructing multilayered elastic periodic media using only one-sided near-field measurements. A novel Lippmann-Schwinger-type integral equation is established by introducing a two-layer quasiperiodic Green's tensor for the Navier equation, providing a foundation for the well-posedness analysis of the direct problem. Building on this formulation, we propose an innovative inversion algorithm that reconstructs the whole periodic structure using one-sided measurements generated by only a small number of compressional waves. The method combines a Newton-type iterative scheme with total variation (TV) regularization for sharp interface recovery, and incorporates a segmentation-based postprocessing step to improve the accuracy and enforce piecewise constancy. Numerical experiments show that the algorithm accurately reconstructs complex multilayer structures with sharp corners, which are beyond the reach of existing methods even in the simpler Helmholtz case. Notably, even when the measured data contain little to no evanescent wave information, leading to a highly ill-posed inverse problem,experiments demonstrate that our algorithm still provides accurate reconstructions.

科研团队：