A Software Package for High Accuracy Multigrid Computation of Three Dimensional Convection Diffusion Equations

Jun Zhang

Department of Computer Science
University of Kentucky
Lexington, KY 40506-0047, USA

Introduction to MG3DCV

MG3DCV is a standard implementation of multigrid technique with a fourth compact finite difference discretization of the three dimensional convection-diffusion equation.

The advantages of MG3DCV compared to other more standard implementations of multigrid techniques:

Fast Convergence
For moderate convection dominated problems, MG3DCV can deliver text book multigrid convergence. This high efficiency is achieved by using the fourth order compact discretization scheme which ensures convergence of the Gauss-Seidel relaxation.

Inherited Parallelism
A four color decomposition of the three dimensional grid is used to decouple the grid points so that the Gauss-Seidel relaxation can be run independently as four sweeps. This strategy is similar to what you can expect in the two dimensional case with red black Gauss-Seidel relaxation for the five point stencil.

Please see my publication list.

Authorship and Acknowledgment
MG3DCV was written by Jun Zhang. The project was partially funded by a grant of supercomputer CPU time from National Science Foundation through the Pittsburgh Supercomputing Center.

Obtaining MG3DCV

You can download the current version of MG3DCV by pointing your web browser to MG3DCV and click it.

The software package of MG3DCV contains a number of files written entirely in Fortran 77 and is portable on most Unix systems that have a Fortran 77 compiler. It has been extensively tested on SGI and SUN workstations.

After downloading MG3DCV you need to uncompress it. This is achieved by executing the following command:

  gunzip mg3dcv.f.gz

This should give you a file named mg3dcv.f.

Version Update

We keep updating and improving MG3DCV. This web page will keep the up-to-date version. For major modifications and the relation to the old version, please check the update file.

Contact Information

Even though MG3DCV contains no known bugs, it does not mean that all of its bugs have been found and fixed. If you find any problems, please send an e-mail to, with a brief description of the problem you have found.

Also if you have any comments regarding MG3DCV or any suggestions for additional functionality that you want to see being incorporated in future releases of MG3DCV, send them to If you want to keep tracking of the continuous development of GM3DCV, please put the URL address: in your collection of bookmarks.


For technical details, please see the paper:

Murli M. Gupta and Jun Zhang, High accuracy multigrid solution of the 3D convection-diffusion equations, Applied Mathematics and Computation, Vol. 113, No. 2-3, pp. 249-274, (2000).

Your citation of this paper in your work will be highly appreciated.


This is a preliminary version of MG3DCV. Permission is granted for using the software for the purpose of examination. Users are not permitted to distribute the software. This software package comes with no warranty. The authors are not liable for any loss/damage or inconvenience caused in the use of this software package or any modification thereof. You use it at your own risk.

This page is created by Jun Zhang
originally created: Friday, November 17, 1998.
Last modified: Monday, May 6, 2003.