應(yīng)用數(shù)學(xué)短課

不可壓流體力學(xué)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(bào)告人 / Докладчик / Speaker: 蔡明超 教授

地點(diǎn) / Место / Venue: 主樓336

內(nèi)容 / Содержание / Course content: 時(shí)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(xué)時(shí)：24學(xué)時(shí)2．適用專(zhuān)業(yè)：理學(xué), 工學(xué)3．適用對(duì)象：碩士生,博士生,博士后4．先修課程：高等數(shù)學(xué)、C/C++程序設(shè)計(jì)基礎(chǔ)、計(jì)算方法5．參考書(shū)

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(gè)人簡(jiǎn)介：

蔡明超：美國(guó)摩根州立大學(xué)終身教授，博導(dǎo)。主要從事數(shù)值分析，流體,彈性和生物力學(xué)的計(jì)算，自2017年來(lái)，獲得NSF，NIH,ArmyResearch 0ffice等機(jī)構(gòu)累計(jì)超過(guò)120 萬(wàn)美元的科研項(xiàng)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(fā)表論文30多篇，出版著作2部，做大會(huì)或邀請(qǐng)報(bào)告共 70多次，NSF計(jì)算數(shù)學(xué)研究項(xiàng)目評(píng)審專(zhuān)家.