报告题目:On effective numerical methods for phase-field models

报告时间:2018年12月25日上午10:30-11:30

报告地点:数学院会议室(玉衡北302)

报告人概况:乔中华教授,香港理工大学应用数学系博士生导师。乔中华教授博士毕业于香港浸会大学,博士导师为世界著名计算数学家,教育家汤涛院士。乔中华教授主要从事非线性偏微分方程的高效数值算法和相场方程的大时间步长数值方法研究;申报获批政府及科研机构研究课题10余项,发表顶级期刊的学术论文四十余篇;并获得2013年香港政府研究资助委员会青年成就奖和2018年香港数学会杰出青年学者奖。

In this talk, we overview our recent works on modern computational methods for the approximate solution of phase-field problems. The main difficulty for developing a numerical method for phase field equations is a severe stability restriction on the time step due to nonlinearity and high order differential terms. It is known that the phase field models satisfy a nonlinear stability relationship called gradient stability,usually expressed as a time-decreasing free-energy functional. This property has been used recently to derive numerical schemes that inherit the gradient stability.We will discuss implicit-explicit time discretization methods which satisfy the energy stability. A time-adaptive strategy will be presented for solving the phase-field problems. Several numerical results will be given to demonstrate the efficiency and reliability of the proposed numerical methods.