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Class Meets: 8:00-8:50 am, MWF, in Wilson 1-139
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Instructor:
- Curt Vogel
- 2-210 Wilson Hall
- ph. 994-5332
- e-mail: vogel@math.montana.edu
- Office Hours: 8:00-8:50 MWF
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Textbook
- Numerical Solution to Differential Equations, 2nd Edition,
by K.W. Morton and D.F. Mayers
- published by Cambridge University Press
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MATLAB Software
- For more information, check out the following links.
- Mathworks home page
- MATLAB Tutorials
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Other Resources
- A Matlab object oriented finite element toolkit
SOFEA
- Another oriented finite element toolkit
freeFEM
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Course Outline:
- Applications and Basic Theory of Elliptic PDEs
- Finite Difference Methods
- Finite Element Methods
- Automatic Mesh Generation
- Numerical Methods for Large, Sparse Linear Systems
The final exam is scheduled for 12:00-1:50 pm, Tuesday, Dec. 13, 2005.
Students are strongly encouraged to work together on homework assignments.
Late homework will be accepted only with the advanced permission of the
instructor.
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Homework Assignment 1: Due Friday, Sept. 9.
- Click here for homework assignment in PDF
format.
- Click here for a sample MATLAB 1-D finite
difference code.
- Click here for a sample MATLAB 2-D finite
difference code.
- To download notes on Local Accuracy of Finite Difference
Approximations, click here.
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Homework Assignment 2: Due Wednesday, Sept. 21.
- Click here for homework assignment in PDF
format.
- Click here for a MATLAB code
to get timing results for the solution of tridiagonal systems.
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Homework Assignment 3: Due Monday, Oct. 3.
- Click here for homework assignment in PDF
format.
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Homework Assignment 4: Due Friday, Oct. 7.
- Click here for homework assignment in PDF
format.
- To download notes on Hermite Interpolating Polynomials
and Gauss-Legendre Quadrature, click here.
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Homework Assignment 5: Due Friday, Oct. 14.
- Click here for homework assignment in PDF
- To download notes on Basic Functional Analysis,
click here.
- To download notes on Best Approximation in Hilbert Space,
click here.
- To download notes on Abstract Boundary Value Problems,
click here.
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Homework Assignment 6: Due Friday, Oct. 21.
- Click here for homework assignment in PDF
format.
- Click here for a sample MATLAB 1-D finite
element code for diffusion equation.
- Click here for a sample MATLAB 1-D finite
element code for biharmonic equation.
- To download notes on Natural Boundary Conditions,
click here.
- To download notes on 1-D Finite Element Error Analysis,
click here.
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Homework Assignment 7: Due Friday, Oct. 28.
- Click here for homework assignment in PDF
format.
- Click here for a sample MATLAB 2-D finite
element code for a diffusion equation.
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Automatic Mesh Generation
- Click here for article "A Simple Mesh
Generator in MATLAB", by Per-Olof Persson and Gilbert Strang,
SIAM Review, 46 (2004), pp. 329-345.
- Click here for a unix tar file
containing mesh generation codes described in the article.
- Click here
for Persson's web page devoted to mesh generation.
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Homework Assignment 8: Due Monday, Nov. 14.
- Click here for homework assignment in PDF
format.
- Click here for a sample Newton's method
code.
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Homework Assignment 9: Due Monday, Nov. 28.
- Click here for homework assignment in PDF
format.
- To download notes on the Conjugate Gradient (CG) method,
click here.
- To download notes on CG convergence analysis,
click here.
- To download Jacobi and Gauss-Seidel iteration demo code,
click here.
- To download notes on Multigrid basics,
click here.
- To download 1-D multigrid demo codes, click
here.
- To download a sample final exam, click here.