管理员登录 / English
Efficient schemes with unconditionally energy stabilities for gradient flow models with strong anisotropy: S-IEQ and S-SAV approaches
发布时间: 2018-05-12     20:47   【返回上一页】 发布人:杨霄锋


北京师范大学数学科学学院

 

计算数学学术报告

 

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:杨霄锋教授University of South Carolina

 

时间地点: 5月28日下午3:00-4:00 教八107

 

邀请人:张辉

 

报告摘要: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.