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(fù)旦大學(xué)
講座時(shí)間：2021年12月28日 16:00-17:00
講座地點(diǎn)：騰訊會(huì)議,，會(huì)議ID: 751-375-355
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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(xué)本科碩士,，碩士導(dǎo)師梁棟教授,；復(fù)旦大學(xué)博士,，博士導(dǎo)師李立康教授?，F(xiàn)為復(fù)旦大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授,?！按笠?guī)?？茖W(xué)計(jì)算”和“高性能計(jì)算”973項(xiàng)目成員,。對(duì)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(zhuǎn)化為多個(gè)一維問題快速計(jì)算,，又能在每個(gè)時(shí)刻遵守物理的能量守恒性，使得計(jì)算可以長(zhǎng)時(shí)間進(jìn)行,。同時(shí)在區(qū)域分解和多重網(wǎng)格算法,、圖像處理、材料計(jì)算,、量子Monte Carlo方法模擬等領(lǐng)域也有多項(xiàng)工作發(fā)表,。主持多項(xiàng)國(guó)家自然科學(xué)基金，在計(jì)算數(shù)學(xué)頂級(jí)期刊在SIAM J. Sci. Comput.,、SIAM J. Numer. Anal.,、Numer. Math.,、Math. Comput.發(fā)表SCI學(xué)術(shù)論文70余篇。
