报告承办单位: 数学与统计学院

报告题目:  Exponential convergence of the PML method for periodic surface scattering problems

报告内容:  

The main task is to prove that the perfectly matched layers (PML) method converges exponentially with respect to the PML parameter, for scattering problems with periodic surfaces. A linear convergence has already been proved for the PML method for scattering problems with rough surfaces in a paper by S.N. Chandler-Wilder and P. Monk in 2009. At the end of that paper, three important questions are asked, and the third question is if exponential convergence holds locally. In this talk, we answer this question for a special case, which is scattering problems with periodic surfaces. The result can also be easily extended to locally perturbed periodic surfaces or periodic layers. Due to technical reasons, we have to exclude all the half integer valued wavenumbers. The main idea of the proof is to apply the Floquet-Bloch transform to write the problem into an equivalent family of quasi-periodic problems, and then study the analytic extension of the quasi-periodic problems with respect to the Floquet-Bloch parameters. Then the Cauchy integral formula is applied for piecewise analytic functions to avoid linear convergent points. Finally the exponential convergence is proved from the inverse Floquet-Bloch transform.

报告人姓名:  张汝明

报告人所在单位: Karlsruhe Institute of Technology

报告人职称/职务及学术头衔:   Junior Group Leader

报告时间:  2021年11月26日16:00-16:40

报告方式: 腾讯会议ID: 838 2530 8952

报告人简介:  张汝明博士2014年获中国科学院大学博士学位，现今在卡尔斯鲁厄理工学院担任Junior Group Leader，研究兴趣为声波与电磁波在周期结构中的正，反散射问题的理论分析和数值模拟。目前正承担1项德国科学基金会(DFG)项目，已发表SCI论文22篇。