报告时间：2024年9月26日（星期四）9:00

报告地点：翡翠湖校区科教楼B座1710室

报 告 人：沈捷 教授

工作单位：宁波东方理工大学

举办单位：数学学院

报告简介：

In this talk I will present some recent advances on using the scalar auxiliary variable (SAV) approach and Lagrange multiplier approach to develop highly efficient and accurate structure preserving schemes for a large class of complex nonlinear systems. These schemes can preserve energy  dissipation/conservation as well as other global constraints and/or are positivity/bound preserving, only require solving decoupled linear equations with constant coefficients at each time step, and can achieve higher-order accuracy.

However, a direct application of the SAV approach will not preserve positivity or maximum principle. In the second lecture, I will then present two strategies, one based on convex splitting and the other based on SAV with transformation, to construct efficient energy stable and positivity preserving schemes for certain nonlinear evolution systems, such as the Poisson-Nernst-Planck (PNP) equation and Keller-Segel equation, whose solutions remain to be positive.

报告人简介：

沈捷，教授，现为宁波东方理工大学讲席教授和数学科学学院院长。1982年毕业于北京大学计算数学专业, 1987年获法国巴黎十一大学博士学位，2009年入选海外高层次人才项目，2017年当选 AMS fellow，2020当选 SIAM fellow，2023年全职回国前为普渡大学杰出教授。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2万八千余次。