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.