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学术预告:Yang Xiaofeng 教授谈“Efficient schemes with unconditionally energy stabilities for anisotropic phase field models”

来源 : 理学院     编辑 : 理学院     时间 : 2019-12-19  访问量 : 157

时间:12月19日(周四)13:30-14:30

地点:勤园21号楼306学术报告厅

主讲人概况:

美国南卡罗莱纳大学数学系,教授。自从2006年以来,在国际一流应用以及计算数学杂志发表SCI论文约 100余篇,其中以第一编辑或通讯编辑发表的论文共计约50篇,其中ESI 高引用论文12篇, 总引用次数约2700余次。自 2007 以来,受邀在国际,国内国际会议,以及美国和亚洲著名大学做学术报告共 100 余次。

内容概况:

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.


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