Numerical Linear Algebra
數值線性代數

Fall 2009


Jinn-Liang Liu

個人網頁: http://www.nhcue.edu.tw/~jinnliu/

新竹教育大學應數系

 

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.