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

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.

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.