The multigrid and adaptive grid refinement communities have developed some very nice web based tutorials. There used to be more tutorials, but people moved or retired and their tutorials were lost. Most of the ones here have been on MGNet itself. If you have a tutorial that you want to contribute, please contact me.
You need either a good browser, presentation software (e.g., Adobe Acrobat Reader, Microsoft PowerPoint, or Google Docs), or a PostScript viewer (e.g., ghostview) to see the tutorials. It depends what the file format is for a given tutorial. There seems to be a little of everything here. Try one of the tutorials and see if you have the software already loaded on your computer.
Christian Wagner's Introduction to Algebraic Multigrid
Christian's tutorial is a course handout (100+ pages) that explains how algebraic multigrid works. The original can be found at the author's home page.
Uli Ruede's Multigrid Workbench
This is a modified version for MGNet. I modified Ruede's tutorial to greatly reduce data transmissions of LaTeX to HTML inspired GIF files. It is a basic tutorial covering linear multigrid methods with an emphasis on elliptic problems in two dimensions.
Jim Jones' Parallel Multigrid Tutorial
Jim's tutorial was given at the 1999 Copper Mountain Conference on Multigrid 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.
Topics covered in this tutorial include
- 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.
Gundolf Haase's Short Course on Parallelization and Multigrid
Gundolf's online notes for his course based on his parallel methods for solving elliptic PDEs book with Craig Douglas and Ulrich Langer.
Van Emden Henson's An Algebraic Multigrid Tutorial
Van's tutorial was given at the 1999 Copper Mountain Conference on Multigrid Methods. The original Powerpoint presentation is also available. The Powerpoint file is much nicer to look at than the HTML files thatPowerpoint2000 produced and retains all of the animations
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.
Topics covered in this tutorial include
- Classical AMG
- The Required AMG Toolkit
- Seeking Algebraic Smoothness
- Coarse Grid Selection
- Other Algebraic Approaches: An Overview
- Smoothed Aggregation
- Multigraph methods
- Energy-Minimizing Basis methods
Stephen Kirkup's Boundary Element Method
Manish Parashar and James C. Browne's DAGH Tutorial
Manish and Jim's tutorial is on parallel adaptive grid refinement techniques. The goals for the tutorial are
- To acquaint you with the adaptive mesh refinement (AMR) technique for the solution of partial differential equations.
- To familiarize you with the conceptual frame work of DAGH (Distributed Adaptive Grid Hierarchy) and how it is implemented.
- To provide you with a working knowledge of DAGH interfaces through annotated examples.
After you have gone through this tutorial you will be able to write a driver for DAGH and run it in either sequential or parallel mode.
Marcus Speh's Multigrid Tutorial
A long, long time ago, Marcus Speh worked at CERN in the field of high energy physics. Then the web came along and he moved to London to work for one of the first web companies. Uli Ruede took this tutorial over and reworked it a bit. It moved to MGNet, where I updated the links where possible. While quite dated, it still has interesting things to say about object oriented multigrid in C++ and high energy physics.
Of course, Wikipedia has a multigrid page.