Numerical Analysis (II)
數值分析(II)

Spring 2011

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 2. (Due 6/9)
Project 1. (Due 3/31) Do Project 9.1 in Lecture 9.
Submit  Projects via email to TA蔡炘澤 at g9824204@mail.nhcue.edu.tw
(Email標題: NameP1 etc. )

Report 2. (Due 6/16)
Report 1. (Due 4/21)
Submit  Reports via email to me.
(Email標題: NameR1 etc. )

 

課程大綱

Course Topics: (Lecture Order: 1, 2, …, 15.)

I.            Overview
  1.  Semiconductor Transistors  
  2.  Life’s Transistors
      (Nervous system (0:50), Action Potentials (3:24), Potassium Channel (1:42))

II.          Numerical Methods
  3.  1D Poisson’s Problem and Finite Difference Method 
  4.  Jacobi Method (Read 2010F數值分析(I))
  5.  Conjugate Gradient Method
  6.  1D Finite Element Method 
  7.  Newton and Monotone Iterative Methods
11.  Scharfetter-Gummel (Exponential Fitting) Method
12.  Object-Oriented Programming of Adaptive Computation

III.       Mathematical Models with Fundamental Physics
  8.  Poisson’s Equation in Electrostatics 
  9.  Convection-Diffusion-Reaction Model
10.  A Quantum Corrected Drift-Diffusion Model for Ion Channels
       (吳信宏Thesis-ppt, Thesis-pdf, Program-zip, QCPNP)
13.  Schrödinger’s Equation
14.  Bohm’s Quantum Potential

 

IV.           Report


研究計畫名稱：

Numerical Simulation of Biological Ion Channel by Quantum Hydrodynamic Model

 

研究計畫內容：

(一)摘要

(二)研究動機

(三)研究問題與文獻回顧

(四)研究方法與步驟

(五)需要學習與請教之內容

(六)預期結果

(七)參考文獻


Links:   2007X C++ Programming
             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

·        Project 50% Report 50%

教科書

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