Math 581

Numerical Solution to Differential Equations I

Fall Semester 2006

• Class Meets: 8:00-8:50 am, MWF, in Wilson 1-139
• Instructor:
  Curt Vogel
  2-210 Wilson Hall
  ph. 994-5332
  e-mail: vogel (at) math.montana.edu
  Office Hours: 9:00-9:50 MWF
• No Required Textbook. Notes will be posted on-line.
• 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
• Optional Textbook
  A Multigrid Tutorial, 2nd Edition, by W.L. Briggs, V.E. Henson, and S.F. McCormick
  Published by SIAM
• MATLAB Software
  For more information, check out the following links.
  Mathworks home page
  MATLAB Tutorials
• Other Resources
  A Matlab object oriented finite element toolkit SOFEA
  Another oriented finite element toolkit freeFEM
• 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.

• 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.
• Click here for notes on Steady-State Diffusion Equations and Boundary Conditions.
• Click here for notes on Well-Posedness and Analytic Solution to Poisson's Equation.
• 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.
• Click here for notes on Finite Difference Methods in 1-D.
• Click here for notes on Finite Difference Methods in 2-D.
• Click here for notes on Boundary Conditions.
• Click here for notes on Finite Volume Methods.
• 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.
• Click here for notes on Introduction to Ritz-Galerkin Discretization.
• Click here for notes on Convergence Analysis for Finite Difference Methods.
• Click here for notes on Stability Analysis for Finite Difference Methods.
• Click here for notes on Review of Calculus of Variations.
• Click here for notes on Minimization in Vector Spaces.
• Click here for notes on Basic Functional Analysis.
• Click here for More Notes on Functional Analysis.
• Click here for Notes on Theory of Boundary Value Problems.
• Click here for Notes on Best Linear Approximation and Galerkin's Method.
• Click here for Notes on Natural Bounary Conditions.
• 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.
• Click here for Notes on Hermite interpolation and Gaussian quadrature.
• Click here for Notes on 4th Order Boundary Value Problems.
• Click here for M581 FEM miniproject.
• 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.
• Click here for Notes on Nonlinear Boundary Value Problems.
• Click here for Notes on Nonlinear Systems and Unconstrained Optimization.
• 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.
• Click here for Notes on the Conjugate Gradient Method.
• Click here for Notes on the Convergence Analysis for the Conjugate Gradient Method.
• Click here for Notes on Multigrid Basics.
  Click here for MATLAB codes which implement multigrid for a 1-d Poisson equation.