报告题目：A novel integral equation for scattering by locally rough surfaces and application to the inverse problem: the Neumann case
报 告 人：张海文 助理教授 (中科院 应用数学研究所)
摘要：This talk is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface) with Neumann boundary condition. We propose a novel integral equation formulation for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containing the local perturbation and the lower part of a circle) with two corners. This novel integral equation can be solved efficiently by using the RCIP method introduced previously by Johan Helsing and is capable of dealing with large wave number cases. For the inverse problem, we propose a Newton iteration method to reconstruct the local perturbation of the plane from multiple frequency far-field data, based on the novel integral equation formulation. Numerical examples are carried out to demonstrate that our reconstruction method is stable and accurate even for the case of multiple-scale profiles.
张海文助理教授，主要研究兴趣为：粗糙曲面中的逆散射问题 (inverse scattering problems in rough surfaces),相关工作发表在 Inverse Problems，SIAM Journal on Applied Mathematics，Journal of Computational Physics等期刊上。