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Numerical experiments to "On averaged exponential integrators for semilinear wave equations with solutions of low-regularity"

Dörich, Benjamin

Abstract (englisch):
This code was used for the numerical experiments in the preprint (CRC Preprint 2021/12; URL: https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-12.pdf) and in the paper "On averaged exponential integrators for semilinear wave equations with solutions of low-regularity" by S. Buchholz, B. Dörich, and M. Hochbruck.

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Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsdaten
Publikationsdatum 25.03.2021
Erstellungsdatum 04.03.2021
Identifikator DOI (KIT): 10.5445/IR/1000130367
KITopen-ID: 1000130367
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
Schlagwörter highly oscillatory problems, error bounds, order-reduction, time-integration, second-order evolution equations, filter functions, summation-by-parts formula
Liesmich

This program is intended to reproduce the results from the paper

"On averaged exponential integrators for semilinear wave equations with solutions of low-regularity. "
by S. Buchholz, B. Dörich, and M. Hochbruck.

The codes generates Figure 2.

Requirements

The program is tested with

1) Ubuntu 16.04.7 LTS and Python 3.7.6 and the following version of its modules:

  • numpy - 1.15.4
  • scipy - 1.4.1
  • matplotlib - 3.2.1
  • tikzplotlib - 0.9.6

2) Ubuntu 18.04.5 LTS and Python 3.6.9 and the following version of its modules:

  • numpy - 1.19.2
  • scipy - 1.5.1
  • matplotlib - 3.3.2
  • tikzplotlib - 0.9.4

Figure 2

In this folder open a console and run the following commands after each other.

1) Run "python3 run_paper_Strang_N_2pw09.py"
2) Run "python3 run_paper_Strang_N_2pw10.py"
3) Run "python3 run_paper_Strang_N_2pw11.py"

After running the calculations, the errors can be found in the folder "results" as tikz-files.

Art der Forschungsdaten Dataset
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
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