This presentation is an updated reincarnation of the tutorials Bill gave at Copper Mountain in 1987 and 1989. The 1987 tutorial led to the publication of the popular book, A Multigrid Tutorial (SIAM books), which has served as the introduction to multigrid for a good many workers in the field. Assuming no familiarity with multigrid, the tutorial introduces multigrid from first principles, examining basic iterative methods, coarse-grid correction, two-level approaches, and extending to multigrid methods.
- Model Problems
- Basic Iterative Methods
- Elements of Multigrid
- Some Theory
In this section we will take up some "complications" that arise commonly in practice, and illustrate some of the techniques used to deal with them. These will be presented in simple, model-problem form. Typical solution methods will be outlined. Time constraints may prohibit coverage of all topics.
- Neumann boundary conditions
- Anisotropic operators
- Variable mesh problems
- Variable coefficients
- Multigrid for Nonlinear problems: introduction to FAS
- Grid refinement: introduction to FAC
- Overview of algebraic multigrid (AMG)
An introduction to methods for improving locality of data usage in iterative
methods will be presented. The emphasis will be for problems related
to solving PDE's. Separate methods for structured, unstructured,
and quasi-unstructured grids will be given. In some cases, but not
all, bitwise identical results are achieved with respect to standard implementations
of the algorithms considered. The methods are applicable to almost
any compiled language. No background in machine architectures will
be assumed or needed.
Morning and afternoon sessions will consist of individual
talks of approximately 25 minutes each. Workshop
and Circus sessions will be held in the evenings.
WORKSHOPS AND CIRCUS SESSIONS
The program will include special time set aside for
Workshops and Circuses. The Workshop Chair will encourage and
support informal workshops on special topics of interest. The
Circus Chair, for each of the three planned circus sessions,
will encourage participation and contributions and will organize,
set the schedule, and oversee its progress.
We encourage special sessions on focus topics of interest. Anyone
wishing to organizing such a session should contact
Anyone interested in contributing to a special
session should contact the session chair. Current planned sessions