應用數學短課

不可壓流體力學模型的有限元方法與快速算法

Finite Element Methods and Fast Solvers for Incompressible Fluid Flow Models

報告人 / Докладчик / Speaker: 蔡明超 教授

地點 / Место / Venue: 主樓336

內容 / Содержание / Course content: 時間 / 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

短課基本情況：

1．學時：24學時2．適用專業：理學, 工學3．適用對象：碩士生,博士生,博士后4．先修課程：高等數學、C/C++程序設計基礎、計算方法5．參考書

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

個人簡介：

蔡明超：美國摩根州立大學終身教授，博導。主要從事數值分析，流體,彈性和生物力學的計算，自2017年來，獲得NSF，NIH,ArmyResearch 0ffice等機構累計超過120 萬美元的科研項目資助，在SIAM J Numer. Anal., SIAM J.Sci.Comput，Math. Comput. 和Biomechanics等有影響力的SCI期刊上發表論文30多篇，出版著作2部，做大會或邀請報告共 70多次，NSF計算數學研究項目評審專家.