長(zhǎng)沙理工大學(xué)學(xué)術(shù)活動(dòng)預(yù)告
報(bào)告承辦單位: 數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告題目: On well-posedness and convergence of UPML method for analyzing wave scattering in layered media
報(bào)告內(nèi)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.
報(bào)告人姓名: 魯汪濤
報(bào)告人所在單位: 浙江大學(xué)數(shù)學(xué)科學(xué)學(xué)院
報(bào)告人職稱/職務(wù)及學(xué)術(shù)頭銜: 百人計(jì)劃研究員
報(bào)告時(shí)間: 2020年10月30日15:10-15:50
報(bào)告地點(diǎn):理科樓A-419
報(bào)告人簡(jiǎn)介: 魯汪濤教授于2007年和2012年分別獲中國科學(xué)技術(shù)大學(xué)理學(xué)學(xué)士和理學(xué)博士學(xué)位，2012年同年獲得香港城市大學(xué)聯(lián)合培養(yǎng)博士學(xué)位。2013-2017年，赴密歇根州立大學(xué)開展博士后研究。研究興趣為計(jì)算光學(xué)和波散射問題的數(shù)學(xué)建模和數(shù)值算法。目前已在SISC、SIAP、MMS、JCP等雜志上發(fā)表多篇論文。