题 目:

1.A decoupled, linear, and unconditionally energy stable finite element method for a two-phase ferrohydrodynamics model；

2.An Introduction for Writing a Computational Science Paper

主讲人：何晓明 教授 （美国密苏里科技大学）

时 间：2024年06月21日（星期五）10:00 —11:00、11:00 —12:00

地 点：理学院306会议室

主办单位：理学院

主讲人简介:

何晓明,美国密苏里科技大学教授。2002年与2005年在四川大学数学学院分别获学士与硕士学位, 2009年在弗吉尼亚理工大学数学系获博士学位, 2009年至 2010年在佛罗里达州立大学作博士后。2010年至今在美国密苏里科技大学任授，2021年晋升为正教授。何晓明教授主要的研究领域是计算科学与工程。研究问题主要包括界面问题, 计算流体力学, 计算电磁学, 有限元方法, 各类解耦算法, 数据同化, 随机偏微分方程, 控制问题等。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, 在SIAM Journal on Scientific Computing, SIAM Journal on Numerical Analysis, Mathematics of Computation, Numerische Mathematik, Journal of Computational Physics, Computer Methods in Applied Mechanics and Engineering, IEEE Transactions on Plasma Science, Lab on a Chip, Langmuir, Energy \& Fue1s, Computational Materials Science 等杂志发表论文 100 余篇。
摘要：

1.In this talk, we present numerical approximations of a phase-field model for two-phase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equations, as well as the magnetic field equation. By combining the projection method for the Navier-Stokes equations and some subtle implicit-explicit treatments for coupled nonlinear terms, we construct a decoupled, linear, fully discrete finite element scheme to solve the highly nonlinear and coupled multi-physics system efficiently. The scheme is provably unconditionally energy stable and leads to a series of decoupled linear equations to solve at each time step. Through numerous numerical examples in simulating benchmark problems such as the Rosensweig instability and droplet deformation, we demonstrate the stability and accuracy of the numerical scheme.

2.When students in computational mathematics start their research work, they usually encounter a critical issue, i.e., how to write a good paper which is clear about the novelty, major difficulties, key ideas, and description in details. We will discuss about four keys: (1) how to highlight and justify the selling points of a paper; (2) how to explain the major difficulties and contributions of the paper; (3) how to provide a clear description for the logic framework of the paper; (4) how to efficiently find and correct the mistakes and typos of a paper.