应数学系郭玉坤副教授的邀请，吉林大学数学学院张德悦教授将于近日来访我校，并做两场学术讲座，报告内容涉及声波反散射问题、无相位数据问题的参考球技术、以及基函数展开法求解反问题的算法框架及其应用等课题。以下是报告信息，欢迎感兴趣的师生参加。

报告1：Basis function expansion method for solving some inverse problems

时间：2018年11月18日（周日）下午14:00-15:00

地点：格物楼503报告厅

摘要：In this talk, I will present some recent studies on the basis function expansion methods for inverse problems. The basis functions may include the fundamental solutions to the wave equations, the harmonic polynomials, the Fourier-Bessel functions and the Fourier basis functions. Based on the expansion of these basis functions, we would be able to find the numerical solutions of the inverse problem easily. Two typical applications of the expansion methods, namely, the Cauchy problem and the inverse source problem, will be discussed in details.

报告2：Reference object techniques for phaseless inverse scattering problems

时间：2018年11月20日（周二）上午9:00-10:00

地点：格物楼503报告厅

摘要：This talk is concerned with the recent progresses on the phaseless inverse scattering problems with auxiliary reference objects. By incorporating an additional reference ball to the scattering system and using the superposition of different incident waves, we rigorously prove that the location and shape of the obstacle as well as its boundary condition or the refractive index can be uniquely determined by the modulus of acoustic far-field patterns. A reference ball based iterative method is also developed to numerically reconstruct the location and shape of a sound-soft obstacle from phaseless far-field data. For phaseless inverse acoustic source scattering problem, we first propose a phase retrieval formula based on the reference point sources, and then reconstruct the source function using the Fourier method. Several numerical examples will be provided to demonstrate the effectiveness and robustness of these methods.

报告人简介：张德悦，男，吉林大学数学学院教授、博士生导师，1998年毕业于吉林大学数学学院信息与计算科学专业，获学士学位，2004年毕业于吉林大学数学研究所计算数学专业，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。已在“Inverse Problems”、“Advances in Computational Mathematics”等期刊发表多篇SCI检索学术论文，其中一篇论文入选反问题领域国际著名期刊“Inverse Problems”的2017年度“亮点论文”（Editorial Highlights）。主持国家自然科学基金面上项目两项，参与国家自然科学基金项目三项。