2026-08-05T09:48:38Zhttps://www.radar-service.eu/oai/OAIHandler10.35097/14562023-11-15T14:45:24Zradar4kit
10.35097/1456
Carle, Constantin
Constantin
Carle
Institut für Angewandte und Numerische Mathematik
Numerical experiments to "Error analysis of second-order local time integration methods for discontinuous Galerkin discretizations of linear wave equations"
Karlsruhe Institute of Technology
2023
2023
Mathematics
time integration
wave equation
leapfrog method
discontinuous Galerkin method
error analysis
CFL condition
Chebyshev polynomials
local time-stepping
locally implicit
Open Access
Creative Commons Attribution Non Commercial Share Alike 4.0 International
Carle, Constantin
Hochbruck, Marlis
Institut für Angewandte und Numerische Mathematik
This code was used for the numerical experiments in the CRC 1173 Preprint 2023/2 (URL: https://www.waves.kit.edu/downloads/CRC1173_Preprint_2023-2.pdf) by C. Carle and M. Hochbruck.
The scripts are intended to reproduce the figures from the preprint
"Error analysis of second-order local time integration methods
for discontinuous Galerkin discretizations of linear wave equations"
by Constantin Carle and Marlis Hochbruck
################################################################################
#### Requirements
The codes are tested with
Ubuntu 20.04.2 LTS and Python 3.8.10 and the following version of its modules:
numpy - 1.17.4
scipy
dolfin (fenics) - 2019.2.0.dev0 (including mshr)
matplotlib - 3.1.2
tikzplotlib - 0.9.6
pandas - 0.25.3
################################################################################
#### Generation of figures
For the generation of Figure Y, Y=1,2,3, either execute the Python script 'script_figY.py'
in a suitable integrated development environment or run the command
python3 script_figY.py
in a terminal session.
For the generation of Figure 4 first execute the Python script 'script_fig4_data.py'
(via a suitable integrated development environment or in a terminal session)
which generates and saves the data for the figure.
To obtain the figure execute the script 'script_fig4_plot.py'
(the script 'script_fig4_plot_single.py' generates a different view of the data).
Additionally to the plots you can get the tikz-files which were used for
generating the figures in the preprint by setting the Boolean variable 'write_tikz'
from 'False' to 'True' at the beginning of the scripts.
The scripts for Figure 1, 2, 4 run in parallel on all available processors.
The number of used processors can be specified with the
variable 'num_processors_max' (integer). - 1.3.3
10.5445/IR/1000158573
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