报告题目：An Alternating Direction Implicit Method for Mean Curvature Flows

报告时间：2021年7月21日，星期三，上午10:00－12:00

报告地点：数学楼2-2会议室

报告人：应文俊教授，上海交通大学

报告摘要：

In this talk, I will present an alternating direction implicit method for mean curvature flows. Unlike explicit time integration method such as the forward Euler method for the problems, the method does not have severe timestep restriction due to the stiffness of the motion. The timestep by the method can be linearly proportional to the spacing parameter of the curve or surface. Alternating direction implicit treatment for the curve/surface motion avoids solving a globally coupled system. This is especially good for the mean curvature flows in three space dimensions. The method is a Cartesian grid-based method. The curve or surface is represented by its intersection with an underlying Cartesian grid, which has several advantages in efficiency, accuracy as well as stability. In this talk, I will present numerical examples by the method for mean curvature flows in both two and three space dimensions.

报告人简介：

    应文俊, 上海交通大学数学科学学院及自然科学研究院教授。美国杜克大学计算数学博士, 生物医学工程系博士后，曾任美国密歇根理工大学助理教授。应文俊教授的研究主要包括求解非线性双曲守恒律方程和奇异扰动反应扩散方程的时间空间自适应网格加密算法，求解刚性系统的大步长稳定时间积分方法,求解椭圆型偏微分方程的边界积分方法，以及一类基于位势理论的求解复杂区域上椭圆型，抛物型偏微分方程的笛卡尔直角网格法。研究涉及的领域包括计算空气动力学,计算生物物理学,计算电生理学和计算流体力学等。应文俊教授目前是杂志Applied Numerical Mathematics的编委。