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报告承办单位: 数学与统计学院

报告题目:  On well-posedness and convergence of UPML method for analyzing wave scattering in layered media

报告内容:  

In this talk, we propose a novel method to establish the well-posedness and convergence theory of uniaxial perfectly matched layer (UPML) method for a two-dimensional acoustic scattering problem by a compactly supported source in a two-layered medium. In particular, we solve a long standing problem by showing that the truncated layered

medium scattering problem is always resonance free regardless of the thickness and absorbing strength of UPML. The main idea is by considering an auxiliary waveguide problem, which is obtained by truncating the layered medium scattering problem through PML in the vertical direction only. The Green function due to a point source for this waveguide problem can be constructed explicitly based on separation of variables and Fourier transformation. We prove that such a construction is always well-defined regardless of the absorbing strength. The well-posedness of the fully UPML truncated scattering problem is therefore obtained by assembling the waveguide Green function through periodic extension. For the convergence part, we show that the UPML Green function converges to the exact layered Green function exponentially fast as the absorbing strength of UPML increases. This is a joint work with Jun Lai and Haijun Wu.

报告人姓名:  鲁汪涛

报告人所在单位: 浙江大学数学科学学院

报告人职称/职务及学术头衔:    百人计划研究员

报告时间:  2020年10月30日15:10-15:50

报告地点:理科楼A-419 

报告人简介:  鲁汪涛教授于2007年和2012年分别获中国科学技术大学理学学士和理学博士学位，2012年同年获得香港城市大学联合培养博士学位。2013-2017年，赴密歇根州立大学开展博士后研究。研究兴趣为计算光学和波散射问题的数学建模和数值算法。目前已在SISC、SIAP、MMS、JCP等杂志上发表多篇论文。