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Numerical experiments to "Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations"

Dörich, Benjamin

Abstract:
This code has been used for the numerical experiments in the thesis "Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations" by Benjamin Dörich, see https://www.doi.org/10.5445/IR/1000130187.

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Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsdaten
Publikationsdatum 09.03.2021
Erstellungsdatum 01.03.2021
Identifikator DOI (KIT): 10.5445/IR/1000130189
KITopen-ID: 1000130189
Lizenz Creative Commons Namensnennung – Nicht kommerziell – Weitergabe unter gleichen Bedingungen 4.0 International
Liesmich

Readme

This program is intended to reproduce the results from the thesis "Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations" by Benjamin Dörich

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
    (quasilinear only:)
  • dolfin - 2018.1.0
  • fenics - 2018.1.0

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
    (quasilinear only:)
  • dolfin - 2019.2.0.dev0
  • fenics - 2019.2.0.dev0

Figure 4.2

In the folder "semilinear_low_reg/Fig_convergence" open a console and run the following commands after each other.

1) Run "python3 run_diss_Strang_N_2pw09.py"
2) Run "python3 run_diss_Strang_N_2pw10.py"
3) Run "python3 run_diss_Strang_N_2pw11.py"

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

Figure 4.3

In the folder "semilinear_low_reg/Fig_inner_filter" open a console and run the following commands after each other.

1) Run "python3 run_diss_Strang_N_2pw09.py"
2) Run "python3 run_diss_Strang_N_2pw10.py"
3) Run "python3 run_diss_Strang_N_2pw11.py"

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

Figure 7.1

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

1) Run "python3 1_generate_initial_matrices.py"
2) Run "python3 2_diss_run_reference_solution.py"
3) Run "python3 3_diss_run_Euler_X.py"
4) Run "python3 4_diss_run_Euler_Y.py"
5) Run "python3 5_diss_run_midpoint.py"

After running the calculations, the errors can be found in the folder "quasilinear_expo/extracteddata/".
(a) settings
contains the information of the config file
(b) infos_
contains the computed errors
(c) plot_* contains a tikz-file which gives the plot for the Euler and the midpoint rule separately.

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