讲座主题：Fully decoupled and energy stable BDF schemes for a class of Keller-Segel equations

专家姓名：陈文斌

工作单位：复旦大学

讲座时间：2021年12月28日 16:00-17:00

讲座地点：腾讯会议，会议ID: 751-375-355

主办单位：9728太阳集团数学与信息科学学院

内容摘要：

The Keller-Segel equations are widely used for describing chemotaxis in biology. Recently, first-order and second-order approximations for a class of Keller-Segel equations based on the gradient flow structure were proposed by Shen and Xu. Mass conservation, positivity and energy stability were proved for the first-order scheme, whereas for the second-order scheme the energy stability was not provided. Besides, an explicit-implicit treatment is performed to a non-convex and non-concave term $-\chi\rho\phi$, making their decoupled system could only be solved in sequence. In this talk, we propose new BDF schemes of first-order (BDF1) and second-order accuracy(BDF2 and EsBDF2): the coupled term $-\chi\rho\phi$ involved in two equations of $\rho$ and $\phi$ is fully explicitly treated, thus the discrete schemes could be computed in parallel. Several numerical examples are presented to verify the theoretical results.

主讲人介绍：

陈文斌，山东大学本科硕士，硕士导师梁栋教授；复旦大学博士，博士导师李立康教授。现为复旦大学数学科学学院教授。“大规模科学计算”和“高性能计算”973项目成员。对于Maxwell方程，首次提出了能量守恒的交替方向算法，提出的交替方向既能把三维问题转化为多个一维问题快速计算，又能在每个时刻遵守物理的能量守恒性，使得计算可以长时间进行。同时在区域分解和多重网格算法、图像处理、材料计算、量子Monte Carlo方法模拟等领域也有多项工作发表。主持多项国家自然科学基金，在计算数学顶级期刊在SIAM J. Sci. Comput.、SIAM J. Numer. Anal.、Numer. Math.、Math. Comput.发表SCI学术论文70余篇。