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 with
science-books.net in
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.
Kaskade 3.X's Multigrid
Tutorial
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.
