报告题目：The PML method for 3D time-domain electromagnetic scattering problems

报 告 人：张波研究员（中国科学院）

报告时间：2021年3月10日  9:00-10:00

报告地点：数统院5楼数学研究中心多功能研讨室（线上报告）

报告摘要：

In this talk, we introduce a perfectly matched layer (PML) method to solve the 3D time-domain electromagnetic scattering problems. The PML problem is defined in a spherical layer and derived by using the Laplace transform and the real coordinate stretching in the transformed domain. The well-posedness and the stability estimate of the PML problem are first proved by using the Laplace transform and the energy method. The exponential convergence of the PML method is then established in terms of the thickness of the layer and the PML absorbing parameter. As far as we know, this is the first convergence result for the time-domain PML method for the three-dimensional Maxwell equations. Our proof is mainly based on the stability estimates of solutions of the truncated PML problem and the exponential decay estimates of the stretched dyadic Green's function for the Maxwell equations in the free space.

The uniaxial PML method is also studied for the 3D time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The convergence in both L^2 and L^\infty norms has also been established for the PML method, based on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem.

报告人简介：

张波，中国科学院数学与系统科学研究院“百人计划”研究员，博士生导师。张波教授在反问题、机器学习以及电磁散射问题上取得了重要研究成果。他相继主持了2项国家自然科学基金项目，1项国家自然科学基金重大研究项目，1项863计划课题，并发表论文被SCI收录80多篇。