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    學術預告:Yang Xiaofeng 教授談“Efficient schemes with unconditionally energy stabilities for anisotropic phase field models”

    來源 : 理學院     作者 : 理學院     時間 : 2019-12-19  訪問量 : 295

    時間:12月19日(周四)13:30-14:30

    地點:勤園21號樓306學術報告廳

    主講人簡介:

    美國南卡羅萊納大學數學系,教授。自從2006年以來,在國際一流應用以及計算數學雜志發表SCI論文約 100余篇,其中以第一作者或通訊作者發表的論文共計約50篇,其中ESI 高引用論文12篇, 總引用次數約2700余次。自 2007 以來,受邀在國際,國內國際會議,以及美國和亞洲著名大學做學術報告共 100 余次。

    內容簡介:

    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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