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報告承辦單位: 數學與統計學院

報告題目:  Exponential convergence of the PML method for periodic surface scattering problems

報告內容:  

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.

報告人姓名:  張汝明

報告人所在單位: Karlsruhe Institute of Technology

報告人職稱/職務及學術頭銜:   Junior Group Leader

報告時間:  2021年11月26日16:00-16:40

報告方式: 騰訊會議ID: 838 2530 8952

報告人簡介:  張汝明博士2014年獲中國科學院大學博士學位，現今在卡爾斯魯厄理工學院擔任Junior Group Leader，研究興趣為聲波與電磁波在周期結構中的正，反散射問題的理論分析和數值模擬。目前正承擔1項德國科學基金會(DFG)項目，已發表SCI論文22篇。