学术报告

沈捷学术报告

阅读次数:2536

 题目:The Scalar Auxiliary Variable (SAV) Approach for Gradient Flows

报告人:沈捷 教授(长江学者、千人计划,普渡大学、厦门大学)

地点:致远楼101室

时间:2018年3月15日(周四)16:00-17:00

Abstract:Many dynamical physical processes can be described by gradient flows. In this talk, I shall start by reviewing existing approaches for constructing energy stable schemes for gradient flows, then I'll introduce the new scalar auxiliary variable (SAV) approach which will allow us to construct linear, decoupled, energy stable schemes for a large class of gradient flows. The new class of schemes constructed by using the SAV approach enjoy the following advantages: (i) at each time step, one only has to solve decoupled, linear positive definite systems with constant coefficients; (ii) it is proved to be unconditionally energy stable and appears to be quantitatively more accurate than existing schemes of the same order; (iii) it applies to a wider class of problems. As examples of application, I shall use the SAV approach to construct efficient and accurate energy stable schemes for several challenging gradient flows that can not be easily handled by the existing approaches.

简历:

沈捷,美国普渡大学数学系和厦门大学数学科学学院教授,国际著名数值计算和分析专家。1982年毕业于北京大学计算数学专业,1987年获得法国巴黎十一大学博士学位,之后在印第安纳大学从事博士后研究。1991年起在宾夕法尼亚州立大学任教,2002年转至普渡大学任教。2008年沈捷教授获得富布赖特奖,2009年被授予教育部“长江学者”讲座教授,2010年入选国家“千人计划”,2017年当选美国数学会会士。沈捷教授主要从事偏微分方程数值解研究,特别在谱方法数值分析理论和科学计算方面有杰出贡献,目前已在Numer. Math., Math. Comp. , SIAM J. Numer. Anal., SIAM J. Sci. Comput.等国际著名期刊上发表学术论文200余篇。

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