Series of Academic Activities of School and Institute of Mathematics in 2020（the 211th）：
Associate Professor Yang Jiaqing Xi'an Jiaotong University
Report title: Convergence Analysis of the PML Method for Time-Domain Electromagnetic Scattering Problems
Reporter: Associate Professor Yang Jiaqing, Xi'an Jiaotong University
Reporting time: 8:50-09:25 am, September 10, 2020
Report location: Tencent Conference ID: 233 270 107
Conference password: 0910
School contact: Lu Junliang lvjl@jlu.edu.cn
Report summary:
In this talk, we will report our recent work on the perfectly matched layer (PML) method of the time-domain electromagnetic scattering problems in 3D. The PML problem is defined in a spherical layer and derived by using the Laplace transform and real coordinate stretching in the frequency domain. The well-posedness and the stability estimate of the PML problem are first proved based on 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.
Brief introduction of the speaker:
Yang Jiaqing, associate professor of Xi'an Jiaotong University, PhD supervisor. In 2012, he graduated from the School of Mathematics and Systems Science, Chinese Academy of Sciences; from 2012 to 2014, he was a postdoctoral fellow at the Chinese Academy of Sciences for Systems Science; from 2014 to 2015, he was a Research Fellow at the Chinese University of Hong Kong; His research interests are the mathematical theory and calculation of inverse problems, publishing more than 20 academic papers.Inverse Problems, SIAM Journal on Numerical Analysis, SIAM Journal on Applied Mathematics, SIAM Journal on Imaging Sciences, Inverse Problems and Imaging, Journal of Differential Equations.
