講座主題：Efficient schemes with unconditionally energy stabilities for anisotropic phase field models
主講人：楊霄鋒
工作單位：University of South Carolina
講座時間：2019年6月4日下午4:00（周二）
講座地點：數(shù)學(xué)院會議室341
主辦單位：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)技術(shù)學(xué)院
內(nèi)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.
主講人介紹：
楊霄鋒,，美國南卡萊羅納大學(xué)教授，1998年以及2001年于中國科學(xué)技術(shù)大學(xué)數(shù)學(xué)系獲數(shù)學(xué)學(xué)士以及碩士學(xué)位,。2007年在美國普度大學(xué)獲得應(yīng)用數(shù)學(xué)博士學(xué)位。2007-2009年在美國北卡羅來納大學(xué)教堂山分校從事博士后研究,。隨后進入美國南卡萊羅納大學(xué)工作，歷任數(shù)學(xué)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-現(xiàn)在)。主要從事多相復(fù)雜流體, 軟物質(zhì)材料的數(shù)值計算方法與分析,。至今已發(fā)表科研論文70余篇,，其中10篇高引用論文(web of Science), Google學(xué)術(shù)引用2200多次。主持了多項由美國國家科學(xué)基金會(NSF)資助的科研項目,。
