杨霄锋教授学术报告

报告题目：Efficient schemes with unconditionally energy stabilities for anisotropic phase field models

报告人: 杨霄锋 教授 （University of South Carolina）

报告时间: 2019年6月4日下午4:00（周二）

报告地点: 数学院大会议室341

内容摘要：We consider numerical approximations for anisotropic phase field models, by taking the anisotropic Cahn-Hilliard/Allen-Cahn equations with their applications to the faceted pyramids on nanoscale crystal surfaces and the dendritic crystal growth problems, as special examples. The main challenge of constructing numerical schemes with unconditional energy stabilities for these type of models is how to design proper temporal discretizations for the nonlinear terms with the strong anisotropy. We combine the recently developed IEQ/SAV approach with the stabilization technique, where some linear stabilization terms are added, which are shown to be crucial to remove the oscillations caused by the anisotropic coefficients, numerically. The novelty of the proposed schemes is that all nonlinear terms can be treated semi-explicitly, and one only needs to solve some coupled/decoupled, but linear equations at each time step. We further prove the unconditional energy stabilities rigorously, and present various 2D and 3D numerical simulations to demonstrate the stability and accuracy.

报告人简介: 杨霄锋，美国南卡莱罗纳大学教授，1998年以及2001年于中国科学技术大学数学系获数学学士以及硕士学位。2007年在美国普度大学获得应用数学博士学位。2007-2009年在美国北卡罗来纳大学教堂山分校从事博士后研究。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-20013年8月)，副教授(2013年8月-2017年12月)，及教授(2018年1月-现在)。主要从事多相复杂流体, 软物质材料的数值计算方法与分析。至今已发表科研论文70余篇，其中10篇高引用论文(web of Science), Google学术引用2200多次。主持了多项由美国国家科学基金会(NSF)资助的科研项目。