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

Schrammer, Stefan ORCID iD icon 1; Hochbruck, Marlis [Beteiligte*r] 1; Neher, Markus [Beteiligte*r] 1
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsdaten
Publikationsdatum 28.12.2022
Erstellungsdatum 06.12.2022
Identifikator DOI: 10.5445/IR/1000153539
KITopen-ID: 1000153539
Lizenz Creative Commons Namensnennung – Nicht kommerziell – Weitergabe unter gleichen Bedingungen 4.0 International
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Liesmich
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
Art der Forschungsdaten Dataset
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