Software Engineering in Mathematics

數學軟體工程

Spring 2009


Jinn-Liang Liu

高雄大學應數系

Goal

     

Write a course report on “A Mathematical Software for Semiconductor Device Simulation”

Format:

Title, Abstract, 1. Introduction,  2. Mathematical Model, 3. Gummel’s Iteration, 4. Finite Element Method, 5. Scharfetter-Gummel Method, 6. Monotone Iterative Method, 7. Numerical Algorithms, 8. Software Description, 9. Numerical Experiments, 10. Conclusions, Appendix, Acknowledgements, References.

 

Prerequisite

1.     2008S C++ Programming

2.     2008F數值微分方程

 

How to do

1.     Self-Study

·        (2/24) First Self-Evaluation (Form)

·        (4/14) Second Self-Evaluation

·        (6/9) Final Self-Evaluation

2.     Set your own agenda and schedule

3.     Review your progress in this course week-by-week 

 

Assignments

  1. Send biweekly (on Mondays starting 2/23) email to jinnliu@nuk.edu.tw in the following format:
    標題:姓名E#-Topic Title
    Dear Professor Liu,
      
    … (Except
    姓名 above in Chinese, write emails strictly in English)

    Best regards,
    Your name
  2. Send biweekly (on Mondays starting 3/3) your report to jinnliu@nuk.edu.tw in the following format:
    標題:姓名R#-Report Title
     

    Briefly say some thing about the report.
    Write your report in Tex by using
    Scientific WorkPlace 4.0.rar
    Attach your report in pdf format.

     
     
  3. Send 3 C++ programming projects (on 3/10, 4/7, 5/5) to jinnliu@nuk.edu.tw in the following format:
    標題:姓名P#-Project Title

    Define your own projects and describe the project at the beginning of the main program.
    Attach your C++ codes and I/O files.
    Briefly say something about your project in the email.


  4. Two 15-minitute presentations about the report on 4/14 and 6/9 in PowerPoint format written in English. The order of presentations will be drown randomly.
     

 

課程大綱

1. Introduction  

1.   Classical Computer Device.ppt

2.   台積電45奈米製程 全球前三強.pdf

3.   台積電28奈米製程

 

2. Mathematical Models

1.     1D Example: EE656: Fundamentals of Carrier Transport

2.     1D Algorithm:  陳婉伶 Report.pdf

3.      Convection-Diffusion-Reaction Model   

4.      3D Poisson’s Equation.pdf 

5.      Semiconductor Models.pdf

6.     Quantum-Corrected Energy Transport Model (QCET):
2003jcp-semi.pdf,  2005jcp-semi.pdf (Read these two papers very thoroughly.)


3. Numerical Methods for PDEs

1.     Gummel’s Iteration:  2005jcp-semi.pdf

2.     1D Finite Element Method (FEM): Lecture 8.

3.     Scharfetter-Gummel (SG) Method: SGMethod.pdf

4.     Newton’s Method and Monotone Iterative Methods: 2003jcam-semi.pdf

5.     Adaptive FEM:   1998Adaptive.pdf,  1996OOP.pdf


4. Implementations  (Computer Programming)

1.     1D C++ Code:  program1D.zip, result1D.zip

2.     2D C++ Code:  program2D.zip, matlab2D.zip

 

教學目標 

l           Learn Programming in Scientific Computing

l           Learn Software Development for Semiconductor Device Simulation

l           Learn Numerical Methods for Semiconductor Device Simulation

l           Learn Basic Physics of Semiconductor Devices

授課方式

l           Regular Lecturing, Discussions, Presentations, Demos

評分標準

l           Assignments 50%  

l           Final Report 50%   

教科書

None

參考文獻

l         Jinn-Liang Liu, Lecture Notes on Numerical Methods for Partial Differential Equations, 2008. 
2008F數值微分方程  

l          Mark Miller, Lectures on Semiconductor Materials, 2006. 
Lecture01.pdf  Lecture02.pdf  Lecture03.pdf  Lecture04.pdf  Lecture05.pdf Lecture06.pdf

l         E. Suli, Finite Element Methods for Partial Differential Equations, 2007.
Suli-FEM-2007.pdf

l         An Introduction to Software Engineering