講座主題：Fully decoupled and energy stable BDF schemes for a class of Keller-Segel equations
專家姓名：陳文斌
工作單位：復旦大學
講座時間：2021年12月28日 16:00-17:00
講座地點：騰訊會議，會議ID: 751-375-355
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
陳文斌，山東大學本科碩士，碩士導師梁棟教授；復旦大學博士，博士導師李立康教授。現為復旦大學數學科學學院教授。“大規模科學計算”和“高性能計算”973項目成員。對于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維問題轉化為多個一維問題快速計算，又能在每個時刻遵守物理的能量守恒性，使得計算可以長時間進行。同時在區域分解和多重網格算法、圖像處理、材料計算、量子Monte Carlo方法模擬等領域也有多項工作發表。主持多項國家自然科學基金，在計算數學頂級期刊在SIAM J. Sci. Comput.、SIAM J. Numer. Anal.、Numer. Math.、Math. Comput.發表SCI學術論文70余篇。
