Numerical experiments for "On dynamical low-rank integrators for matrix differential equations"

Instructions:

The scripts inside the subfolders are intended to reproduce the figures from the
thesis
> On dynamical low-rank integrators for matrix differential equations.

by Stefan Schrammer

We provide two different versions of the code:

• Code_Prom_wo_ref.zip provides the scripts for computing and plotting the data
  for all numerical experiments.
• Code_Prom_incl_ref.zip addtionally provides the reference solutions to all
  considered problems as hdf5-files.

Requirements

The codes are tested with

Ubuntu 20.04.2 LTS and Python 3.8.5 and the following version of its modules:

    numpy       1.19.2
    scipy       1.5.2
    numba       0.51.2
    colorama    0.4.4
    h5py        2.10.0
    matplotlib  3.3.2
    tikzplotlib 0.9.6

Generation of figures (tex files containing the data are also created)

In the folder fracginz open a console and run the commands

1. to create the data for Figures (7.1) and (7.2)
   python3 fgl.py
2. to create Figures (7.1) and (7.2)
   python3 fgl_results.py

In the folder fracschr open a console and run the commands

3. to create the data for Figure (7.3)
   python3 fsr.py
4. to create Figure (7.3)
   python3 fsr_results.py

In the folder laserplasma open a console and run the commands

5. to create the data for Figure (7.4)
   python3 lpi_hom.py
6. to create Figure (7.4)
   python3 lpi_hom_plots.py
7. to create the data for Figures (7.5), (7.6), and (7.7)
   python3 lpi.py
8. to create Figures (7.5), (7.6), and (7.7)
   python3 lpi_globalerr.py
   python3 lpi_1d_plot
   python3 lpi_svals_maxint.py

In the folder sinegordon open a console and run the commands

9. to create the data for Figures (7.8) and (7.9)
   python3 sineg.py
10. to create Figures (7.8) and (7.9)
    python3 sineg_globalerr_ranks.py

If the reference solutions shall be recomputed, uncomment the line

methods.append(...)

at the beginning of the scripts fgl.py, fsr.py, lpi.py, and sineg.py, respectively.