Numerical experiments for "Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations"

Instructions:

The scripts inside the subfolder are intended to reproduce the figures from the
preprint

Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations

by Marlis Hochbruck, Markus Neher, and Stefan Schrammer

We provide two different versions of the code:

- Code_rad_wo_ref.zip provides the scripts for computing and plotting the data for all numerical
  experiments.
- Code_rad_incl_all.zip additionally provides the reference solutions as well as the low-rank
  approximations 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 (tikz files containing the data are also created)

In the folder fracginz open a console and run the commands

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

In the folder fracschr open a console and run the commands

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

In the folder laserplasma open a console and run the commands

to create the data for Figures (4) and (5)
python3 lpi.py
to create Figures (4) and (5)
python3 lpi_globalerr.py
python3 lpi_svals_maxint.py

In the folder sinegordon open a console and run the commands

to create the data for Figures (6) and (7)
python3 sineg.py
to create Figures (6) and (7)
python3 sineg_globalerr_ranks.py