Speaker

Title

Time

2023年11月20日16:00

Venue

N219

Abstract

   In the first part, I shall present a new way to construct highly stiff stable schemes. Traditional time discretization schemes are usually based on Taylor expansions at $t_{n+\beta}$ with $\beta\in [0,1]$. However, their ability to deal with very stiff problems are limited by their stability regions. Furthermore, their stability regions decrease as their order of accuracy increase. We show that by using Taylor expansion at $t_{n+\beta}$ with $\beta>1$ as a parameter, we can construct a new class of schemes whose stability region increases with $\beta$, thus allowing us to choose $\beta$ according to the stability and accuracy requirement. In addition, this approach enabled us to solve a long standing problem in the numerical approximation of Navier-Stokes equations: namely, construction and analysis of decoupled schemes with second- or higher-order pressure extrapolations.

  In the second part, I shall briefly present several efficient algorithms based on the SAV approach for solving unconstrained minimization problems. These algorithms are usually more effective than GD based methods as they can be energy diminishing and can be used with arbitrarily large time steps/learning rates.  

Affiliation  

   沈捷教授1982年毕业于北京大学计算数学专业，1983年公派赴法国巴黎十一大学留学，于1987年获得博士学位后赴美国印第安纳从事博士后研究。1991年至2001年先后任美国宾州州立大学数学系助理教授，副教授，教授。 2002年后任美国普渡数学系教授，2017年当选 AMS fellow， 2020当选 SIAM fellow, 2012-2022年任普渡大学计算与应用数学中心主任，2023年被聘为普渡大学杰出教授。 2023年5月起，任宁波东方理工大学讲席教授和数学科学学院院长。沈捷教授主要从事偏微分方程数值解研究工作，具体研究方向包括谱方法数值分析理论，计算流体，以及计算材料科学。在国际杂志上发表了两百多篇论文，两本专著，在谷歌学术的引用逾25000余次，2009年入选国家重要人才计划。