Numerical Methods and Analysis
數值方法分析

Spring 2010


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 6/15)
Project 2. (Due 5/18)  
Project 1. (Due 4/20)

Report 3. (Due 6/8)
Report 2. (Due 5/11)
Report 1. (Due 4/13)
Submit all Reports and Projects via email.

課程大綱  


Course Topics:

Lecture Order: 1, 2, …, 16.

 

I.            Overview
  1.   Semiconductor Transistors
  2.   Life’s Transistors

II.         Mathematical Models with Fundamental Physics
  6.  Poisson’s Equation in Electrostatics  
  7.  Convection-Diffusion-Reaction Model  
  9.  1D Ion Channel Model
11.  Schrödinger’s Equation 
12.  Bohm’s Quantum Potential
13.  A Quantum Corrected Energy Transport Model  
14.  Scaling Analysis of the QCET Model  
15.  Boltzmann’s Equation and Classical Hydrodynamic Models
       Based on Maximum Entropy Principle 
16.  Quantum Hydrodynamic Models Based on Maximum Entropy Principle   

I.                    Numerical Methods
  3.  1D Poisson’s Problem and Finite Difference Method  
  4.  Jacobi and Conjugate Gradient Methods  
  5.  Newton and Monotone Iterative Methods
  8.  Scharfetter-Gummel (Exponential Fitting) Method   
10.  1D Finite Element Method 

 

 教學目標

·        Learn Fundamental Physics in Mathematical Models

·        Learn Basic Numerical methods for Linear Algebra and PDEs

·        Learn C++ Programming in Scientific Computing

授課方式

·         Regular Lecturing

評分標準

·        Reports 45%

·        Projects 45%

·        In class performance 10%

教科書

·        Jinn-Liang Liu, Lecture Notes on Numerical Methods for Partial Differential Equations, 2010.

·        Jinn-Liang Liu, 量子流體之數學建模、數值方法、與應用Quantum Hydrodynamic Modeling, Numerical Methods, and Applications, 2010.

·        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

·      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.