MA 798k, Spring 2008
Domain Decomposition and Multigrid
House Rules

• Instructor: C. T. Kelley
  Office: HA 331, (919) 515-7163 (office), (919) 515-3798 (FAX)
  Office Hours: TBA
  Electronic Mail: Tim_Kelley@ncsu.edu
• Course web page: http://www4.ncsu.edu/~ctk/ma798k.html
  Pointers to on line help live here!
• Books
  • Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , B. Smith, P. Bjorstad, W. Gropp, Cambridge, 1996.
  • A Multigrid Tutorial, 2nd edition , W. L. Briggs, V. E. Henson, S. McCormick, SIAM, 2000
• Objectives: Introduce multilevel methods: multigrid and domain decomposition
  • Multigrid: The students will
    • implement multigrid on two-dimensional problems.
    • implement multigrid as both a solver and a preconditioner
    • learn convergence theory, other applications, and nonlinear multigrid methods
  • Domain Decomposition: The students will
    • implement one and two level additive Schwarz preconditioners with varying degrees of overlap
    • learn theory
• Prerequisites:
  • MA580
  • Knowledge of numerical methods for PDEs
  • Knowledge of Fortran, C, or Matlab
    Good programming skills
    Matlab required for most programming work. Easy to learn if you can program well.
  • Knowledge of eos/unity environment
    ftp, editors, WWW, email, ...
    I will send homework, announcements, ...via email.
• Grade:
  • Homework: two assignments (1 MG, 1 DD), 100 points each, mostly programming. If you don't actually implement this stuff, you won't understand it. I provide lots of software in MATLAB to help.
  • Project: 100 points, oral presentation on a topic of interest to you. I can suggest some or you can come up with your own.
  • It's a REAL GOOD idea to do the homework and projects in teams.
• Computing: NCSU UNIX Workstations in your college or department.
  University charge applies.
• Language: MATLAB

It's optimal if you do all of your computing in MATLAB. This environment is very convenient for this kind of course and allows you to get things running quickly. I will provide software in MATLAB. A good introduction to MATLAB is the MATLAB Primer. We will put this on the course web page soon. The latest edition is available commerically ( MATLAB Primer: 4th Edition, K. Sigmon, CRC Press, 1994).

The computing environment for this course is EOS-UNITY environment at the university. It is your responsibility to learn to use this environment. We have consultants who can help if if you have problems. You must also learn how to use electronic mail, an editor, and technical word processing package, and ftp.

I expect the homework and project work to be typeset (12pt font, single-sided). Word or L^ATEX is fine for this and I'll be happy to take almost anything else. You must sign all documents you turn in.

I encourage you to collaborate on the homework. You may turn in assignments jointly, putting each participant's name on the paper. By doing this you are telling me that each participant contributed to the assignment. You are responsibile for understanding and following the university policy on academic integrity:
http://www.ncsu.edu/provost/academic_policies/integrity/reg.htm.

If you have a disability, the university and I can provide some help. I need to know about this today, so that I can make arrangements and put you in touch with the right people in the university. For more information, please look at
http://www2.ncsu.edu/ncsu/provost/affirm_action/ada/.

MA 798k Schedule

The course is new, so the schedule of events is approximate. Check the course web page:
http://www4.ncsu.edu/~ctk/ma798k.html frequently for changes in dates. Please read the text before the lecture.

• Background (2 wks: BHM00 ch 1, 2)
• Multigrid basics and implementation (3 wks: BHM00 ch 3, 4)
• Multigrid theory, other applications (2 wks: BHM00 ch 5, 7 + literature)
• Parallel computing/Iterative methods workshop (1 wk)
• Domain decomposition basics and implementation (SBG96 ch 1, 2 wks)
• Domain decomposition theory (2 wks, SBG96, ch 5)
• Student projects (2 wks)

We will not cover every section and the sections we omit are good topics for projects.

1.

Learn to use ftp and your printers. ftp the MATLAB primer and print this postscript file.

2.

Learn how to use MATLAB on the workstations.

3.

Make sure you can typeset the homework using Word, L^ATEX, or something else.

4.

Brush up on the prerequisites.

5.

Start reading Chapters 1 and 2 of BHM00

References

• A Multigrid Tutorial, 2nd edition , W. L. Briggs, V. E. Henson, S. McCormick, SIAM, 2000

• G. H. GOLUB AND C. G. VANLOAN , Matrix Computations, Johns Hopkins University Press, Baltimore, 1983.

• A. GREENBAUM, Iterative Methods for Solving Linear Systems, no. 17 n SIAM Frontiers in Applied Mathematics, SIAM, Philadelphia, 1997.

• E. ISAACSON AND H. B. KELLER , Analysis of numerical methods, Wiley, New York, 1966.

• C. T. KELLEY , Iterative Methods f or Linear and Nonlinear Equations, no. 16 in SIAM Frontiers in Applied Mathematics, SIAM, Philadelphia, 1995.

• J. M. ORTEGA AND W. C. RHEINBOLDT, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.

• K. SIGMON, MATLAB Primer, Fourth Edition, CRC Press, Boca Raton, FL, 1994.

• G. W. STEWART , Introduction to matrix computations, Academic Press, New York, 1973.

• L. N. TREFETHEN and D. BAU, Numerical Linear Algebra , SIAM, Philadelphia, 1996.

• Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , B. Smith, P. Bjorstad, W. Gropp, Cambridge, 1996.