Numerical experiments to "error analysis of second-order local time integration methods for discontinuous galerkin discretizations of linear wave equations"

Abstract: 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. TechnicalRemarks: 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

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

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