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

报告人：张汝明教授 柏林工业大学

报告时间：6月14日(周三) 16：00-17：00

#腾讯会议：779-957-551 (无密码)

报告摘要：The main task is to prove that the perfectly matched layers (PML) method has high order converge 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. 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 for almost all 2D cases and 3D cases with small wavenumbers, and high order convergence is proved for 3D cases with larger wavenumbers .

报告人简介：张汝明博士2014年获中国科学院数学与系统科学研究院博士学位，现今在柏林工业大学担任教授，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26篇。她于2023年获得国际应用数学与力学学会(GAMM)颁发的Richard-von-Mises Prize。