Abstract: This code has been used for the numerical experiments in the thesis "On dynamical low-rank integrators for matrix differential equations" by Stefan Schrammer, see https://www.doi.org/10.5445/IR/1000148853.
TechnicalRemarks: #### 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.
