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Numerical experiments for "Error bounds for discrete minimizers of the Ginzburg-Landau energy in the high-κ regime" (v2)

Dörich, Benjamin ORCID iD icon 1; Henning, Patrick
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Forschungsdaten
Publikationsdatum 08.11.2023
Erstellungsdatum 15.09.2023
Identifikator DOI: 10.35097/1791
KITopen-ID: 1000163945
Lizenz Creative Commons Namensnennung – Nicht kommerziell – Weitergabe unter gleichen Bedingungen 4.0 International
Projektinformation SFB 1173/3 (DFG, DFG KOORD, SFB 1173/3)
Schlagwörter Ginzburg–Landau equation, superconductivity, error analysis, finite element method
Liesmich

This program is intended to reproduce the results from the preprint

"Error bounds for discrete minimizers of the Ginzburg–Landau energy in the high-$\kappa$ regime"
by Benjamin Dörich and Patrick Henning

The codes generates the lines in Figures2 and 3

Requirements

The program is tested with

Ubuntu 20.04.5 LTS and Python 3.8.10 and the following version of its modules:

  • numpy - 1.17.4
  • scipy - 1.3.3
  • matplotlib - 3.1.2
  • tikzplotlib - 0.9.8
  • dolfin - 2019.2.0.dev0
  • fenics - 2019.2.0.dev0

Figures

In the folder "code_23_DoerichHenning_GL" open a console and run the following commands after each other (2a+b, 4a+b can be executed in paralell).

1) Run "python3 c1_generate_rectangle.py"
2a) Run "python3 c2a_GL_FEM_comp_all_min_finest.py"
2b) Run "python3 c20_GL_FEM_comp_kappa20.py"
3) Run "python3 c2b_GL_FEM_comp_all_min.py"
4a) Run "python3 c3a_GL_FEM_comp_all_errors.py"
4b) Run "python3 c3b_GL_FEM_comp_all_eigs.py"
5) Run "python3 c4_GL_FEM_draw_error_plot.py"

After running the calculations, the files are stored as follows:

(a) the folder "plots_for_paper" contains the pdf and tikz files for the error plots in Figure 2 and 3.
(b) the folders "sol_ref_3_Mag_st_2.0kappa[KAPPA]_P1_square" contain all figures of the solutions where [KAPPA] is replaced by the respective value.

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