In this talk, we discuss an inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The well-posedness of the forward problem and a priori bounds of the Helmholtz equation on a random periodic Lipschitz surface is shown. Moreover, a novel method is proposed by combination of the Monte Carlo technique for sampling the probability space, a continuation method with respect to the wavenumber, and the KL expansion of the random structure, which reconstructs key statistical properties of the profile for the unknown random periodic structure from boundary measurements of the scattered fields away from the structure. Numerical results are presented to demonstrate the reliability and efficiency of the proposed method.

徐翔，浙江大学数学科学学院研究员。徐翔的研究主要集中在反问题的理论与计算，共发表SCI论文30余篇，部分论文被列为ESI高引论文和Inverse Problems亮点收录。2014年入选浙江省特聘专家，2016年入选浙江省151人才工程。主持国家自然科学基金委面上项目，参与国家自然科学基金委创新群体项目、重大研究计划重点项目、国际（地区）交流合作等多项项目。现担任中国计算数学会第九届理事，浙江省数学会第十二届理事。