This talk is concerned with the direct and inverse scattering problems of time-harmonic elastic waves by an unbounded rigid rough surface. A Nyström method is proposed for the direct scattering problem based on the integral equation method. Convergence of the Nyström method is established with convergence rate depending on the smoothness of the rough surfaces. In doing so, a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators. Moreover, a direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered-field data. A Helmholtz-Kirchhoff-type identity is derived and then used to provide a theoretical analysis of the direct imaging algorithm.

张海文，中国科学院数学与系统科学研究院副研究员。2013年博士毕业于中国科学院数学与系统科学研究院。研究方向为声波、弹性波与电磁波反散射问题。2018年获全国反问题年会青年学术奖。2019年入选中国科学院数学与系统科学研究院“陈景润未来之星”计划。2021年入选中国科学院“青年创新促进会”会员。在 SIAM J. Appl. Math.、SIAM J. Imaging Sci.、SIAM J. Sci. Comput.、Inverse Problems、J. Comput. Phys. 等学术期刊上发表论文20余篇。