腾讯会议：452140856
线下地点：行健楼学术活动室526
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.
This talk is based on the following joint work with Changkun Wei and Jiaqing Yang.
1. C Wei, J Yang & Bo Zhang, Convergence Analysis of the PML Method for Time-Domain Electromagnetic Scattering Problems, SIAM Journal on Numerical Analysis 58(3) (2020), 1918-1940.
2. C Wei, J Yang & Bo Zhang, Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems, ESAIM: Mathematical Modelling and Numerical Analysis 55 (2021), 2421-2443.
报告人简介：
张波，1983年毕业于山东大学数学系，1985年在西安交通大学获硕士学位，1992年在英国Strathclyde大学获博士学位。现任中科院数学与系统科学研究院“百人计划”研究员，应用数学研究所副所长，反问题国际联合会东亚分会副主席，中国数学会常务理事，中国工业与应用数学学会秘书长、大数据与人工智能专委会副主任。2003-2007任Coventry大学应用数学教授，2004年通过中科院“百人计划”回国，在波传播与散射、反问题与成像、机器学习与智能数据分析的理论和算法方面进行了深入系统研究，在国际重要学术期刊发表论文130余篇。曾任2019年反问题国际联合会Calderon奖委员会成员，国际著名SCI期刊《IEEE Transactions on Cybernetics》编委（2012-2018），应邀在2012年第6届和2018年第9届反问题国际会议做1小时大会特邀报告，三次获得中科院优秀导师奖（2013, 2019, 2020），荣获2021年度中国科学院大学领雁奖。
