
应用数学短课
不可压流体力学模型的有限元方法与快速算法
Finite Element Methods and Fast Solvers for Incompressible Fluid Flow Models
报告人 / Докладчик / Speaker: 蔡明超 教授
地点 / Место / Venue: 主楼336
内容 / Содержание / Course content: 时间 / Время / Time:
1. Apr 2 (Wed. 9:00-10:30) Introduction of Poisson problem and its FEM approximations.
2. Apr 7 (Mon. 14:00-15:30) Fluid flow models
3. Apr 9 (Wed. 9:00-10:30) MAC finite difference approximation
4. Apr 14(Mon. 14:00-15:30) Theory of saddle point problems
5. Apr 16 (Wed. 9:00-10:30) (Preconditioners, and Multigrid solvers for Stokes Equations
6. Apr 21(Mon. 14:00-15:30) Nonlinear and linear solvers for incompressible Navier-Stokes equations.
7. Apr 23 (Wed. 9:00-10:30)Projection methods for incompressible Navier-Stokes equations.
8. Apr 28(Mon. 14:00-15:30) Domain decomposition algorithms for Poisson equations
9. Apr 30 (Wed. 9:00-10:30)Introduction of FreeFEM++
10. May 7 (Wed. 9:00-10:30)Theory of two-level overlapping Schwarz methods
11. May 12 (Mon. 14:00-15:30) Algorithms and implementation of Schwarz methods
12. May 14 (Wed. 9:00-10:30) Domain decomposition algorithms for incompressible fluid flow model
短课基本情况:
1.学时:24学时2.适用专业:理学, 工学3.适用对象:硕士生,博士生,博士后4.先修课程:高等数学、C/C++程序设计基础、计算方法5.参考书
1) Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. Elman H C, Silvester D J, Wathen A J., Numerical Mathematics and Scie, 2014.
2)Lectures by Dr. Long Chen, https://www.math.uci.edu/~chenlong/lectures.html
3) Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations. Author: Tarek Mathew.
4) An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation. Victorita Dolean, Pierre Jolivet and Frédéric Nataf; 2015
个人简介:
蔡明超:美国摩根州立大学终身教授,博导。主要从事数值分析,流体,弹性和生物力学的计算,自2017年来,获得NSF,NIH,ArmyResearch 0ffice等机构累计超过120 万美元的科研项目资助,在SIAM J Numer. Anal., SIAM J.Sci.Comput,Math. Comput. 和Biomechanics等有影响力的SCI期刊上发表论文30多篇,出版著作2部,做大会或邀请报告共 70多次,NSF计算数学研究项目评审专家.