Documentation: Moving grid finite element method for reaction-diffusion systems

1-d: Moving grid finite element method for reaction-diffusion systems

We present the software package for one-dimensional growing interval. The software is selfcontained and produces results that can be readily visualised. We use Matlab for graphic visualisation. Included with the package are Matlab files to plot results on either a fixed interval or a continuously deforming interval.

Download the documentation for the 1-d software here

The Fortran files for the software package are all in an archive file, myoned.tar file. To open the archive type the following:

tar xf myoned.tar

Download the software package for 1-d here

Turing diffusion-driven instability

Download some .eps files which illustrate Turing diffusion-driven instability:

2-d: Moving grid finite element method for reaction-diffusion systems

This documentation contains the details of how to use the numerical software package developed in Fortran 77. The key components are mesh generation and the numerical solver. I illustrate how to generate an unstructured triangular mesh by using delaunay mesh generation package (Muller et al., 1993). I have simplified the way data input is handled. The user inputs the boundary data and connectivity through a data file. Calling delaundo, which is the executable file automatically generates the mesh as specified in the input data file. This is a lot easier than the original format provided by the original authors.

Once the mesh has been generated, the user is in a position to call the numerical solver package. The specific details of how to use the solver are detailed in this documentation. Also, I illustrate graphically typical results obtained from various model equations. This is to help the user to understand and appreciate the complexity and generality of the numerical solver.

Download the documentation file below:

This is a numerical software package for both mesh generation and numerical solution developed in Fortran 77. Any system with suitable Fortran compilers will be sufficient to run the software. The Fortran files for the software package are all in an archive file, mysoftware.tar file. To open the archive type the following:

tar xf mysoftware.tar

This will create a folder mysoftware which contains two subdirectories containing the Fortran files together with the executable files. These subdirectories are meshgenerator and mfem. The file delaundo is in the subdirectory meshgenerator while the software package mgfem is in the subdirectory mfem. The software reads the mesh connectivity from the subdirectory meshgenerator and therefore once created, there is no need to move the data file with the mesh connectivity. Although the author uses MATLAB for graphic representation, any graphic package can be used. However, such packages should be able to read the format of the output files. For those who have Matlab at their disposal, we have included two Matlab files, one to plot solutions only on a fixed domain and the other to plot transient solutions on continuously deforming domains. These files are fxduvplot.m and papmovie.m. The last file can also be used to create a movie of the transient solutions. There are also choices to print out encapsulated postcript (.eps) files.

Fortran 90 and 95 compilers can compile Fortran 77 codes, and can therefore be used to compile this software. Also, by converting the Fortran codes into C, one can use C/C++ to compile the software although this has not been tested by the author.

Download the software package below: