報告時間:2019年7月29日15:00

報告地點:數學院會議室(玉衡北302)

報告題目1:Immersed finite elements and their applications to the problems of charging in space

報告人簡介:何曉明現為美國密蘇里科學技術大學教授,博士生導師。主要研究領域為界面問題真人平台炸金花单机版下载页面,計算流體力學,隨機偏微分方程,非線性偏微分方程真人平台炸金花单机版下载页面,反饋控制問題,計算電磁學等,主要研究有限元方法真人平台炸金花单机版下载页面,區域分解方法等真人平台炸金花单机版下载页面。擔任計算數學領域國際期刊International Journal of Numerical Analysis & Modeling的編委,是多個著名國際學術期刊特刊的Guest editor。2014-2016年擔任SIAM Central States Section第一任主席和前兩屆年會的組織委員會主席。在SIAM J. Sci. Comput., SIAM J. Numer. Anal., Math. Comput., Numer. Math., J. Comput. Phys.等國際知名期刊發表SCI 文章40余篇, 他將計算數學與實際工程應用問題結合起來,在科學計算和應用領域做了大量的工作。先后主持國家級或?。▍^)級基金項目10余項,另外參與了工程課題項目4項真人平台炸金花单机版下载页面。

報告摘要:In this presentation we will first introduce the immersed finite elements to efficiently solve elliptic interface PDEs on structured meshes. Then two applications to the problems of charging in space will be discussed: the ion thruster and the electrostatic levitation of lunar dust. The later one is one of the greatest inhibitors to a nominal operation on the moon. Finally, the immersed finite elements will be extended to a moving interface PDE for more applications.


報告題目2:Efficient schemes with unconditionally energy stabilities for anisotropic phase field models

報告人簡介:楊霄鋒,美國南卡萊羅納大學教授真人平台炸金花单机版下载页面真人平台炸金花单机版下载页面,主要從事多相復雜流體, 軟物質材料的數值計算方法與分析。至今已發表科研論文70余篇,其中10篇高引用論文(web of Science), Google學術引用2200多次真人平台炸金花单机版下载页面。并主持多項由美國國家科學基金會(NSF)資助的科研項目。

報告摘要: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.



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