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学术报告五十七:Efficient schemes with unconditionally energy stabilities for gradient flow models

来源:数学与统计学院     作者:     时间:2018/6/25 9:59:11  0次

数学与统计学院学术报告[2018] 057

(高水平大学建设系列报告176)

报告题目: Efficient schemes with unconditionally energy stabilities for gradient flow models with strong anisotropy: S-IEQ and S-SAV approaches.

报告人:   Yang Xiaofeng    教授  南卡罗莱纳大学, 美国

报告时间:62910:00-11:00

报告地点: 科技楼514

报告邀请人:  龚华均                           

报告内容:

We consider numerical approximations for gradient flow models with strong anisotropy 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 linear stabilization approach, where some linear stabilization terms are added. These terms 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.

报告人简历:

Dr. Yang is now the full professor of University of South Carolina (USC). He got his Ph.D from Purdue University at 2007 and finished his postdoc at University of North Carolina at Chapel Hill at 2009. After that, he started the assistant/associate/full professorship at University of South Carolina. His research is about the modeling, numerical analysis and simulations for nonlinear system, in particular the Complex fluids system. He published more than 60 peer reviewed journal papers. Among that, 8 papers are ESI highly cited papers. He had been invited to give more than 90 talks, colloquims, and seminars in many conferences, universities and institutes around the world. His research had bee continuously supported by federal agents including NSF and AFOSR.

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