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
This introduction focuses primarily on the "classical" AMG of Brandt, McCormick, and Ruge. An understanding of the principles of multigrid is assumed, but the tutorial introduces algebraic multigrid in a simple, practical manner.
- "Classical" AMG
- Hammers and Wrenches: the Required AMG Toolkit
- The Ardent Quest: Seeking Algebraic Smoothness
- Get to the Point: Coarse Grid Selection
- Building a Better Mousetrap: Prolongation
- Other Algebraic Approaches: an Overview
- Smoothed Aggregation
- Multigraph methods
- Energy-Minimizing Basis methods
This presentation focuses on the issues involved in parallelizing a multigrid algorithm. Assuming no experience with parallel computing, but an understanding of the principles of multigrid, the tutorial introduces some of the standard and efficient techniques for developing a parallel multigrid solver.
- Algorithmic and implementation scalability.
- Parallelization of multigrid by domain partitioning.
- Performance models and metrics for parallel multigrid solvers.
- Novel parallel multigrid algorithms: multiple coarse grids and concurrent multigrid.
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.