Summer School on Computational Materials Science
2001
University of Illinois, Urbana-Champaign

 

Iterative methods for linear, non-linear and eigenvalue problems
Eric de Sturler - sturler@uiuc.edu - University of Illinois, Urbana-Champaign, Computational Science and Engineering Program

Outline of Lecture

  1. Krylov subspace methods for solving large sparse linear systems of
    equations
    1. intro iterative methods
    2. GMRES, MINRES, CG
    3. Convergence bounds and how to use them
    4. BiCG and related methods
    5. Preconditioning
  2. Krylov subspace methods for large sparse eigenvalue problems
    1. Arnoldi / Lanczos
    2. Davidson / Jacobi-Davidson
  3. Multigrid methods
    1. Basic iterative methods and smoothing
    2. Smoothing analysis for Fourier modes
    3. Grid transfer operators and multigrid
    4. Local mode analysis
  4. Fast Multipole Methods

Lecture 1
Krylov subspace methods
  Introduction - Adobe PDF Slides (653 KB) - crcd_01a.pdf
  Hermitian Problems - Adobe PDF Slides (539 KB) - crcd_01c.pdf

Lecture 2
Krylov subspace methods (contd.)
  Convergence of CG, MINRES, and GMRES - Adobe PDF Slides (466 KB) - crcd_02a.pdf
  Preconditioning - Adobe PDF Slides (249 KB) - crcd_02b.pdf

Lecture 3
Krylov subspace methods (contd.)
  Short Recurrence Methods for Non-Hermitian Problems (347 KB) - crcd_03a.pdf

Lecture 4
Krylov subspace methods (contd.)
  Introduction to Multigrid - Adobe PDF Slides (459 KB) - crcd_04a.pdf
  Introduction to Multigrid (contd.) - Adobe PDF Slides (569 KB) - crcd_04b.pdf
Mike Parks
parks@uiuc.edu

 

Lab 1
  Handout - PDF File (21 KB) - lab1_handout.pdf
  Readme - PDF File (8 KB) - lab1_README.pdf
  Slides - PDF File (802 KB) - lab1_slides.pdf
  Numerical Lab Software - TAR.GZ File (1.3 MB) - numerical_lab1.tar.gz

Lab 2
  Readme - PDF File (6 KB) - lab2_README.pdf
  Slides - PDF File (2.5 MB) - lab2_slides.pdf
  Numerical Lab Software - TAR.GZ File (1.3 MB) - numerical_lab2.tar.gz

 

Last Updated July 19, 2001
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