TUTORIAL DAY AT COPPER MOUNTAIN

This presentation is an updated reincarnation of the tutorials Bill Briggs 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

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.

Contents

• 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.
 
 

FORMAT