报告题目:Multiscale methods and analysis for the highlyoscillatory nonlinear Klein-Gordon equation
报告人:包维柱教授 新加坡国立大学
会议时间:2025年6月6日下午4点
会议地点:色情网
113报告厅
摘要:In this talk, I will review our recent works on numerical methods and analysis for solving the highloscillatory nonlinear Kein-Gordon equation (NKGE) including the nonrelativistic regime, involving asmall dimensionless parameter which is inversely proportional to the speed of light. In this regime, thesolution is highly oscillating in time and the energy becomes unbounded, which bring significantdificulty in analysis and heavy burden in numerical computation. We begin with four frequently usedFDTD methods and obtain their rigorous error estimates in the nonrelativistic regime by payingDarticularly attention to how error bounds depend explicitly on mesh size and time step as well as thesmall parameter. Then we consider a numerical method by using spectral method for spatial derivativescombined with an exponential wave integrator (EWl) in the Gautsch-type for temporal derivatives todiscretize the NKGE. Based on a large-small amplitude wave decompostion to the solution of the NKGEMTI is presented for discretizing the NKGE in the nonrelativistic regime. Extension to the long-timedynamics of the NkGE with weak nonlinearity is discussed andimproved uniform error bounds on timesplitting spectral method are presented based ona, new technique -- regularity compensation oscillation.Finally, applications to several high oscillatory dispersive partial differential equations will bediscussed.This is based on joint works with Yongyong Cai, Yue Feng, Yong Lu, Chunmei Su, Wenfan YiJia Yin, Zhifei Zhang and Xiaofei Zhao.
报告人简介:包维柱教授现为新加坡国立大学(NUS)理学院副院长，新加坡科学院院士，美国工业与应用数学学会会士(SIAMFellow)，美国数学会会士(AMS Fellow)。1987-1995就读于清华大学数学系，先后获学士、硕士和博士学位。曾先后在清华大学、英国帝国理工学院及美国佐治亚理工学院任教、做博士后或访问学者。2001年起在新加坡国立大学工作，并于2009年晋升为教授。现为该校数学系provost’s讲座教授。2013年获冯康科学计算奖，2014年应邀在第26届国际数学家大会(ICM)上作45分钟邀请报告，2024年被选为国际工业与应用数学联盟(ICIAM)的0fficer-at-Large，担任包括SlAM Journal on Scientific Computing等多个国际期刊杂志编委包维柱教授长期从事科学与工程计算研究，主要工作涉及偏微分方程数值方法及其在量子物理、流体和材料中的应用。特别是在Bose-Einstein 凝聚的数值方法及应用、高震荡色散类偏微分方程的多尺度算法和分析、无界区域上科学和工程问题的计算等方面取得了多个重要进展。
