Solving fractional PDEs by rank-structured matrices

This repository contains the MATLAB code required to reproduce the numerical experiments contained in the paper "Fast solvers for 2D fractional diffusion equations using rank structured matrices", S. Massei, M. Mazza, L. Robol, 2018.

Code structure

To reproduce the tests, you will need to download and add to your MATLAB path the hm-toolbox and the rktoolbox packages. Installation of those is as simple as unpacking them somewhere, and adding them to your MATLAB path by:

>> addpath /path/to/hm-toolbox;
>> addpath /path/to/rktoolbox; addpath /path/to/rktoolbox/utils;

Once those are loaded, you can run the various tests by running the scripts listed below:

1. Experiment1D.m replicates the 1D tests that compare the HODLR solver with the preconditioned GMRES. Two files e1.dat and e2.dat will be generated containing the data included in the table in the paper.
2. FD_Example.m and FD_Example_vc.m contain the examples of the 2D solver for the finite difference formulation, discretized using implicit Euler in time. The files implement the constant and variable coefficients case, respectively.
3. FE_Example.m contains the finite element case, and is completely analogous to FD_Example.m.

You might want to inspect the file RunAllExperiments.m for further information.

Contact

Did you find bugs, or have any kind of feedback? Let us know!

stefano.massei@epfl.ch, mariarosa.mazza@ipp.mpg.de, leonardo.robol@isti.cnr.it