TUTORIAL DAY AT COPPER MOUNTAIN

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.

Contents

• Model Problems
• Basic Iterative Methods
• Elements of Multigrid
• Performance
• 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.

Contents

• "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
  • AMGe
  • 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.

Contents

• 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.

WORKSHOPS AND CIRCUS SESSIONS