## Tutorials

The multigrid and adaptive grid refinement communities have developed some very nice web based tutorials.  You need either a good browser (e.g., Netscape Navigator or Microsoft Internet Explorer), presentation software (e.g., Adobe Acrobat Reader,  Microsoft PowerPoint, or StarOffice), or a PostScript viewer (e.g., ghostview) to see the tutorials.  It depends what the file format is for a given tutorial.  There seem to be a little of everything here.

Try one of the tutorials and see if you have the software already loaded on your computer.

Stephen Kirkup's Boundary Element Method

This is the introduction to his book that he published within 2000 with revisions in 2002 and 2004.  It contains a BEM tutorial applied to the Laplace operator.

Oliver Ruebenkoenig's Mathematica Tutorial

The advantage of a Mathematica tutorial are in the way Mathematica allows to do documentation.  It is possible to explain the principals of multigrid and immediately show the code leading to a multigrid algorithm. Thus, the Mathematica tutorial can be used to cross-check an implementation in another language.

Uli Rüde's Multigrid Workbench

This is a modified version for MGNet. I modified Rüde'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

This 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.

Van Emden Henson's An Algebraic Multigrid Tutorial

This 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 that Powerpoint2000 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
• Prolongation
• Other Algebraic Approaches: An Overview
• Smoothed Aggregation
• Multigraph methods
• AMGe
• Energy-Minimizing Basis methods

Christian Wagner's Algebraic Multigrid Tutorial

This is a course handout (100+ pages) that explains how algebraic multigrid works. The original can be found at the author's home page.

A tutorial for the computer program Kaskade 3.x that has a nice introduction to multigrid methods. This is located at the Konrad-Zuse-Zentrum für Informationstechnik (ZIB) in Berlin.

The DAGH Tutorial

A tutorial on parallel adaptive grid refinement techniques, written by M. Parashar and James C. Browne of the University of Texas. 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 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 a web company.  Uli Rüde took this tutorial over and reworked it a bit.  It has moved to MGNet, where I am updating the links, where possible.  While somewhat dated, it still has interesting things to say about object oriented multigrid in C++ and high energy physics.

Cheers,
Craig C. Douglas