Series of Academic Activities of School and Institute of Mathematics in 2020（the 210th）：
Professor Jiang Xue Beijing University of Technology
Report title: UPML Method for Electromagnetic Scattering Problems in a Two-Layer Medium
Reporter: Professor Jiang Xue, Beijing University of Technology
Reporting time: 10:10-10:45 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:
The perfectly matched layer (PML) method is extensively studied for scattering problems in homogeneous background media. However, rigorous studies on the PML method in layered media are very rare in the literature, particularly, for three-dimensional electromagnetic scattering problems. Cartesian PML method is favorable in numerical solutions since it is apt to deal with anisotropic scatterers and to construct finite element meshes. Its theories are more difficult than circular PML method due to anisotropic wave-absorbing materials. This work presents a systematic study on the Cartesian PML method for three-dimensional electromagnetic scattering problem in a two-layer medium. We prove the well-posedness of the PML truncated problem and that the PML solution converges exponentially to the exact solution as either the material parameter or the thickness of PML increases. We propose an edge finite element approximation to the scattering problem, and prove the optimal error estimates for the finite element solution.
Brief introduction of the speaker:
Jiang Xue, professor of Beijing University of Technology, graduating from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2013. In 2019, she was selected as the "High-end Talent Team Construction Plan-Excellent Talents" of Beijing University of Technology, and won the second prize of the 14th Beijing Youth Outstanding Science and Technology Thesis in 2018, the 2014 Excellent Doctoral Dissertation of the Chinese Academy of Sciences, and the 2013 Chinese Academy of Sciences Dean's Excellence Award. She was funded by the China Scholarship Council and visited Purdue University in 2016 for one year. The main research content includes the high-efficiency numerical method of the three-dimensional electromagnetic field eddy current problem, and the adaptive finite element method of the unbounded scattering problem. Currently, he has published more than 10 SCI papers, including SIAM Journal on Scientific Computing, SIAM Journal on Applied Mathematics, SIAM: Multiscale Modeling and Simulation, Inverse Problems, etc. He presided over the National Natural Science Foundation of China Youth Fund and General Fund.
