Project 3. (Due on 1/14)
Do Project 7.1 (CG) in
Lecture 7.
Exam 2. (On 1/7/2010)
Project 2. (Due on 12/3)
Do Project 3.1 (JM) in
Lecture 3 and Project 4.1 (GS) in Lecture 4.
Exam 1. (On 11/5)
Project 1. (Due on 10/22)
Do Project 2.1 (GE)
in Lecture 2. Submit
all files including I/O files via email.
Homework 3.
Homework 2.
Homework 1. Do Problems 2.1 and 2.2 in Lecture 2.
課程大綱
Lecture 1. 1D Poisson's
Equation and Finite Difference Method (FDM)
Lecture 2. Gaussian Elimination (GE) for Ax=b
Lecture 3. Jacobi’s Method (JM)
Templates for the
Solution of Linear Systems (pdf)
Lecture 4. Gauss-Seidel
Method (GS)
Lecture 5. Successive
Overrelaxation Method (SOR)
Lecture 6.
Symmetric
Successive Overrelaxation Method (SSOR)
Lecture 7. Conjugate Gradient Method (CG)
Lecture 8. Finite Element
Method (FEM) for 1D Poisson’s Problem
Lecture 9. 2D and 3D Poisson's Equation
Lecture 10. Convection-Diffusion-Reaction Model
教學目標
·
Learn basic
numerical methods for Partial Differential Equations (PDEs)
·
Learn basic
numerical methods for Linear Algebra
·
Learn basic
Physics behind PDEs
·
Learn programming
in Scientific Computing
授課方式
·
Regular Lecturing
評分標準
·
Programming
projects 30%
·
Homeworks 40%
·
Exams 30%
教科書
·
Jinn-Liang Liu,
Lecture Notes on Numerical Methods for Partial Differential Equations, 2009.
·
Juan Soulie, C++
Language Tutorial, 2007. 2007X C++
Programming
閱讀文獻
·
R. J. LeVeque, Finite Difference Methods for Differential Equations,
2005.
LeVeque-FDM-2005.pdf (Chapters
1-5)
·
E. Suli, Finite Element Methods for Partial Differential Equations,
2007. Suli-FEM-2007.pdf
·
G. H. Golub and C.
F. Van Loan, Matrix Computations, Johns Hopkins University
Press, 1996.
·
R. Barrett, M.
Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra , V. Eijkhout, R. Pozo, C.
Romine, and H. Van der Vorst, Templates for the
Solution of Linear Systems: Building Blocks for Iterative Methods,
2nd Edition, SIAM, 1994, Philadelphia, PA.
Templates for the
Solution of Linear Systems (pdf)
·
J. R. Shewchuk, An Introduction to the Conjugate Gradient
Method Without the Agonizing Pain, 1994.
·
A. Quarteroni and A. Valli, Numerical
Approximation of Partial Differential Equations, Springer-Verlag,
1994.