Exam 2. (On 1/6/09)
Projects. (Final due on 12/30)
No projects will be accepted after this day.
Project 2. (Due on 12/23)
Do Project
7.1 (CG) in Lecture 7.
Homework 3. (Due on 12/16)
Do Problems
7.5 and 8.1~8.2.
Homework 2. (Due on 11/25)
Do Problems
6.1~6.4 and 7.1~7.4.
Exam 1. (On 11/11)
Project 1. (Due on 10/28)
Do Project
3.1 (JM) in Lecture 3.
Homework 1. (Due on 10/14)
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 in Numerical 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,
2008.
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.
· A.
Quarteroni and A. Valli, Numerical Approximation of Partial
Differential Equations, Springer-Verlag,
1994.
· 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.