Well commented 1-D, 2-D, and 3-D multigrid matlab code

The biggest advantage provided on this site is the thoroughly commented 1-D and 2-D finite difference geometric multigrid matlab code.

• The 1-D matlab code includes plots at each step of the process and is intended to help you thoroughly understand the basics of the multigrid process.

1D Finite Difference Matlab Multigrid Code

• The 2D matlab multigrid code is well commented and provides a more realistic level of complication while still being understandable. This code is ideal to understand how to write fast, modular multigrid code for 2D and 3D problems. It includes code to do V-cycles and Full Multigrid (FMG) where nested iteration is used.

2D Finite Difference Matlab Multigrid Code

I've included 3D matlab multigrid code as well. This code offers a selection of finite difference stencils and is mostly a generalization of the better commented 2D multigrid code. There is no nested iteration in this code; it is V or W-cycles only. 3D Finite Difference Matlab Multigrid Code

A simple explanation of multigrid methods for the undergraduate math, science, or engineering student

Explanation of solving differential equations numerically

In the linked 3 page pdf I provide an overview of how solving a differential equation on a computer amounts to solving a linear algebra problem. I then go on to explain how iterative methods offer a fast approximation to the solution of the linear algebra problem, but slow down once the approximation error is smooth. Multigrid is explained as the solution to this slowing.

Useful references

Very good introductory book on multigrid. Classroom slides covering the basics.