Numerical Differential Equations
數值微分方程

Fall 2010

http://www.math.nuk.edu.tw/jinnliu/teaching/cs97/J01.gif
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 1/5) Do Project 8.1 in Lecture 8.
Project 2. (Due 12/1) Do Project 7.1 in Lecture 7.
Project 1. (Due 11/3) Do Project 3.2 in Lecture 3. (Example: JM1.cpp)

Report 2. (Due 1/12)
Report 1. (Due 11/10)

Homework 2. (Due 11/17) Do HW 2.1 and HW2.2 in Lecture 2. Do Example 7.1 in Lecture 7.
Homework 1. (Due 11/3) Do HW 1.2 in Lecture 1.
Submit all Reports and Projects via email. 

課程大綱

Course Topics:

Lecture Order: 1, 2, …, 15.

 

I.            Overview
  1.  Semiconductor Transistors  
       A. Transistor / MOSFET tutorial
     B. Silicon Wafer Processing Animation
       C. Making a computer processor (AMD)
       D. Quantum Computer
        E. Quantum Mechanics
  2.  Life’s Transistors

II.         Numerical Methods
  3.  1D Poisson’s Problem and Finite Difference Method 
  4.  Jacobi Method (Read Lecture 2.)
  5.  Conjugate Gradient Method
  6.  1D Finite Element Method 
10.  Newton and Monotone Iterative Methods
11.  Scharfetter-Gummel (Exponential Fitting) Method

I.                  Mathematical Models with Fundamental Physics
  7.  Poisson’s Equation in Electrostatics 
  8.  Convection-Diffusion-Reaction Model
  9.  A Drift Diffusion Model for Ion Channel
12.  Schrödinger’s Equation
13.  Bohm’s Quantum Potential
14.  A Quantum-Corrected Drift Diffusion Model for Ion Channel
15.  A Quantum-Corrected Energy Transport Model for Semiconductor Device


Links:  2009F數值線代   

         The Mathematics Genealogy Project

 

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

·        Projects 50%

·        Reports and Homeworks 50%

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

·      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.