沈捷教授受邀进行讲座
发布时间: 2023-12-14 15:44:00
题目:Positivity/Bound/Length Preserving Schemes for Complex Nonlinear Svstems
报告人:沈捷
时间:2023-12-12 15:00-16:00
地点:腾讯会议:656-4902-4546
报告人简介:
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,1987年获得博士学位后赴美国Indiana University从事博士后研究。1991年至2001年先后任美国Pennsylvania State University数学系助理教授,副教授,教授。2002年后任美国Purdue University数学系教授,2012至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2万五于次。他于2009年入选海外高层次人才项目,2017年当选AMS fellow,2020当选SIAM fellow。
讲座摘要:
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 yiolation 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 refor-mulation 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.
主办单位:华南师范大学数学科学学院,机器学习与最优化计算实验室
协办单位:广东省青年科学家协会,广东省计算数学学会