2026-10-14T01:01:12Zhttps://www.radar-service.eu/oai/OAIHandler10.35097/14562026-10-09T10:59:08Zradar4kit
https://dx.doi.org/10.35097/1456
Carle, Constantin
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
Mathematics
dataset
Dataset
info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
Hochbruck, Marlis
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
time integration
wave equation
leapfrog method
discontinuous Galerkin method
error analysis
CFL condition
Chebyshev polynomials
local time-stepping
locally implicit
Hochbruck, Marlis
10.5445/IR/1000158573
KITopen-DOI
application/x-tar