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Talk of Prof. Xinfeng Liu

Xinfeng Liu


刘新峰教授1997年毕业于复旦大学数学系获数学学士学位, 1999年在东南大学应用数学系获得硕士学位,2006年在美国纽约州立大学石溪分校应用数学与统计系获得计算数学博士学位。2006-2009年在美国加州大学尔湾分校从事生物数学博士后研究。随后进入美国南卡莱罗纳大学工作,历任数学系助理教授 (2009年8月-2013年8月),终身副教授 (2013年8月-2017年12月),及终身教授 (2018年1月-至今)。 主要从事计算流体,数值计算方法与分析, 系统生物数学模型及计算等科研研究,主持了多项由美国国家科学基金会 (NSF) 资助的科研项目,并多次受邀担任美国国家科学基金会生物数学领域基金会审评议组成员。现任国际重要期刊Mathematical Biosciences and Engineering和Cogent Mathematics的编委。


Integration factor method for a class of high order differential equations with moving free boundaries


The systems of reaction-diffusion equations coupled with moving boundaries defined by Stefan condition have been widely used to describe the dynamics of spreading population. There are several numerical difficulties to efficiently handle such systems. Firstly extremely small time steps are usually demanded due to the stiffness of the system. Secondly it is always difficult to efficiently and accurately handle the moving boundaries. In this talk, to overcome these difficulties, we first transform the one-dimensional problem with a moving boundary into a system with a fixed computational domain, and then introduce four different temporal schemes: Runge-Kutta, Crank-Nicolson, implicit integration factor (IIF) and Krylov IIF for handling such stiff systems. Numerical examples are examined to illustrate the efficiency, accuracy and consistency for different approaches, and it can be shown that Krylov IIF is superior to other three approaches in terms of stability and efficiency by direct comparison. I will also briefly review the integration factor methods and their applications in viscous fluid flows with moving interfaces.