Efficient positivity/bound/length preserving schemes for complex nonlinear systems

发布时间:2023年07月01日 作者:潘克家   阅读次数:[]

报告题目:Efficient positivity/bound/length preserving schemes for complex nonlinear systems

报 告 人:沈捷 教授(东方理工大学、普渡大学)



报告摘要:Solutions of a large class of partial differential equations (PDEs) arising from sciences and engineering applications are required to preserve positivity/bound or length, and also energy dissipative. It is of critical importance that their numerical approximations preserve these structures at the discrete level, as violation of these structures may render the discrete problems ill posed or inaccurate.

I will review the existing approaches for constructing positivity/bound preserving schemes, and then present several efficient and accurate approaches: (i) through reformulation as Wasserstein gradient flows; (ii) through a suitable functional transform; and (iii) through a Lagrange multiplier, which can also be used to construct length preserving schemes. These approaches have different advantages and limitations, are all relatively easy to implement and can be combined with most spatial discretizations.

个人简历:沈捷,美国普渡大学数学系教授、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,随后赴法国巴黎十一大学研究数值分析,师从国际著名数学大师ROGER TEMAN1991年起在宾夕法尼亚州立大学任教,2002年起任美国普度大学数学系教授,2012年起任普度大学计算与应用数学中心主任。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,同时在海洋和大气动力系统以及材料科学计算方面也有很深的造诣。2008年沈捷教授因在微分方程研究中的卓越贡献获得富布赖特奖,2009年度被授予教育部“长江学者”讲座教授,2017年当选美国数学会会士,2020年当选国际工业与应用数学协会(SIAMFellow。目前已在SIAM Review, SIAM J. Numer. Anal.SIAM J. Sci. Comput.Numer. Math.Math. Comp. 等著名期刊上发表学术论文200余篇,研究结果被国际同行广泛引用,在Google Scholar上被引用逾两万次。

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