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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 (at) math.montana.edu
- Office Hours: 9:00-9:50 MWF
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No Required Textbook. Notes will be posted on-line.
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Additional On-Line Resources
- Professor Uri Asher's Web Notes have been made available with
permission ONLY to students in this class. Please Do NOT
distribute.
- chapter 1
- chapter 2
- chapter 3
- chapter 4
- chapter 5
- chapter 6
- chapter 7
- chapter 8
- chapter 9
- chapter 10
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Optional Textbook
- A Multigrid Tutorial, 2nd Edition,
by W.L. Briggs, V.E. Henson, and S.F. McCormick
- Published by SIAM
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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
- Finite Volume Methods
- Automatic Mesh Generation
- Numerical Methods for Large, Sparse Linear Systems
The final exam is scheduled for 8:00-9:50 pm, Tuesday, Dec. 15, 2006.
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 Sept. 1.
- Click here for Review of Vector Calculus
in PDF format. Hand in solutions to exercises at the end of the Review.
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Click here for notes on Steady-State
Diffusion Equations and Boundary Conditions.
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Click here for notes on Well-Posedness
and Analytic Solution to Poisson's Equation.
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Homework Assignment 2: Due Sept. 8.
- Exercises 1-3 at the end of Steady-State Diffusion Equations and
Boundary Conditions.
- Exercises 1-4 at the end of Well-Posedness and Analytic Solution
to Poisson's Equation.
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Click here for notes on Finite Difference Methods
in 1-D.
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Click here for notes on Finite Difference Methods
in 2-D.
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Click here for notes on Boundary Conditions.
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Click here for notes on Finite Volume Methods.
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Homework Assignment 3: Due Sept. 15.
- 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.
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Click here for notes on Introduction to
Ritz-Galerkin Discretization.
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Click here for notes on Convergence Analysis
for Finite Difference Methods.
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Click here for notes on Stability Analysis for
Finite Difference Methods.
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Click here for notes on Review of Calculus of Variations.
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Click here for notes on Minimization in Vector Spaces.
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Click here for notes on Basic Functional Analysis.
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Click here for More Notes on Functional Analysis.
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Click here for Notes on Theory of Boundary Value Problems.
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Click here for Notes on Best Linear Approximation and Galerkin's Method.
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Click here for Notes on Natural Bounary Conditions.
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Sample Finite Element Codes.
- Click here for a sample MATLAB 1-D finite
element code for 2nd order BVPs.
- Click here for a sample MATLAB 1-D finite
element code for 4th order BVPs.
- Click here for a sample MATLAB 2-D finite
element code.
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Click here for Notes on Hermite interpolation
and Gaussian quadrature.
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Click here for Notes on 4th Order Boundary Value
Problems.
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Click here for M581 FEM miniproject.
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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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Click here for Notes on Nonlinear Boundary Value
Problems.
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Click here for Notes on Nonlinear Systems and
Unconstrained Optimization.
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Click here for Notes on Stationary Iterative
Methods for Linear Systems.
- Click here for a sample MATLAB stationary
iterative codes for Poisson's equation in 1-d.
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Click here for Notes on the Conjugate Gradient
Method.
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Click here for Notes on the Convergence Analysis
for the Conjugate Gradient Method.
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Click here for Notes on Multigrid Basics.
- Click here for MATLAB codes which
implement multigrid for a 1-d Poisson equation.