Numerical Computation
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Spring 2011

http://www.math.nuk.edu.tw/jinnliu/teaching/cs97/J01.gif
Jinn-Liang Liu

­Ó¤Hºô­¶: http://www.nhcue.edu.tw/~jinnliu/

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Project 2. (Due 6/9)
Project 1. (Due 3/31) Do Project 9.1 in Lecture 9.
Submit  Projects
via email to TA½²ÍQ¿A at g9824204@mail.nhcue.edu.tw
(Email¼ÐÃD: NameP1 etc. )

Report 2. (Due 6/16)
Report 1. (Due 4/21)
Submit  Reports via email to
me.
(Email¼ÐÃD: NameR1 etc. )

 

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Course Topics: (Lecture Order: 1, 2, ¡K, 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 2010F¼Æ­È¤ÀªR(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
       (
§d«H§»Thesis-ppt, Thesis-pdf, Program-zip, QCPNP)
13.  Schrödinger¡¦s Equation
14.  Bohm¡¦s Quantum Potential

 

IV.           Report


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Numerical Simulation of Biological Ion Channel by Quantum Hydrodynamic Model

 

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Links:  2007X C++ Programming
            
The Mathematics Genealogy Project  

 

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¡P        Learn basic Numerical Methods for Partial Differential Equations (PDEs)

¡P        Learn basic Numerical Methods for Linear Algebra

¡P        Learn basic Physics behind PDEs

¡P        Learn Programming in Scientific Computing

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¡P        Regular Lecturing

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¡P        Project 50% Report 50%

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

¡P        Juan Soulie, C++ Language Tutorial, 2007. 2007X C++ Programming    

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¡P        R. J. LeVeque, Finite Difference Methods for Differential Equations, 2005.  LeVeque-FDM-2005.pdf (Chapters 1-5)

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

¡P      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

¡P      J. R. Shewchuk, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, 1994.