报告时间：2019年7月29日15:00

报告地点：数学院会议室（玉衡北302）

报告题目1：Immersed finite elements and their applications to the problems of charging in space

报告人简介：何晓明现为美国密苏里科学技术大学教授，博士生导师。主要研究领域为界面问题，计算流体力学，随机偏微分方程，非线性偏微分方程，反馈控制问题，计算电磁学等，主要研究有限元方法，区域分解方法等。担任计算数学领域国际期刊International Journal of Numerical Analysis & Modeling的编委，是多个著名国际学术期刊特刊的Guest editor。2014-2016年担任SIAM Central States Section第一任主席和前两届年会的组织委员会主席。在SIAM J. Sci. Comput., SIAM J. Numer. Anal., Math. Comput., Numer. Math., J. Comput. Phys.等国际知名期刊发表SCI 文章40余篇, 他将计算数学与实际工程应用问题结合起来，在科学计算和应用领域做了大量的工作。先后主持国家级或省（区）级基金项目10余项，另外参与了工程课题项目4项。

报告摘要：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.

报告题目2：Efficient schemes with unconditionally energy stabilities for anisotropic phase field models

报告人简介：杨霄锋，美国南卡莱罗纳大学教授，主要从事多相复杂流体, 软物质材料的数值计算方法与分析。至今已发表科研论文70余篇，其中10篇高引用论文(web of Science), Google学术引用2200多次。并主持多项由美国国家科学基金会(NSF)资助的科研项目。

报告摘要：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.