数学讲坛-Efficient schemes with unconditionally energy stabilities for gradient flow models with strong anisotropy: S-IEQ and S-SAV approaches
发布于:2018-05-15 10:34:00   |   作者:[学院] 数学学院   |   浏览次数:1034
时间:2018.5.17 15:30-16:30
地址:清水河主楼A1-513
主办:数学学院
承办:数学学院
范围:全校

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:Prof. Xiaofeng Yang

报告时间:2018.5.17  15:30-16:30

报告地点:清水河主楼A1-513

 

Abstract: 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.

 

Biographical Sketch:

Dr. Yang got his Ph.D from Purdue University at 2007. He finished his postdoc at University of North Carolina at Chapel Hill at 2009, and started the assistant professorship at University of South Carolina then. He is now the full professor of USC. 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/seminars in many conferences, universities and institutes around the world.