cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.35097/1404
title: Numerical experiments for "Dynamical low-rank integrators for second-order matrix differential equations"

description: Instructions: The scripts inside the subfolder are intended to reproduce the figures from the preprint Dynamical low-rank integrators for second-order matrix differential equations by Marlis Hochbruck, Markus Neher, and Stefan Schrammer Requirements The codes are tested with Ubuntu 20.04.2 LTS and Python 3.8.5 and the following version of its modules: numpy 1.19.2 scipy 1.5.2 numba 0.51.2 colorama 0.4.4 h5py 2.10.0 matplotlib 3.3.2 tikzplotlib 0.9.6 Generation of figures (tikz files containing the data are also created) In the folder homwave open a console and run the commands to create the data for Figure (1) python3 hom_planar.py to create Figure (1) python3 hom_planar_plots.py In the folder homwav open a console and run the commands to create the data for Figure (2) python3 hom_semi.py to create Figure (2) python3 hom_semi_plots.py
DOI: 10.35097/1469
title: Numerical experiments for "Error bounds for discrete minimizers of the Ginzburg--Landau energy in the high-$\kappa$ regime"

description: 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 Figure 1 #### 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 "CRC1173_Preprint_2023-11_Codes" open a console and run the following commands after each other (2a-c can be executed in paralell). 1) Run "python3 c1_generate_rectangle.py" 2a) Run "python3 c2_GL_FEM_comp_all_min.py" 2b) Run "python3 c16_GL_FEM_comp_kappa16.py" 2c) Run "python3 c20_GL_FEM_comp_kappa20.py" 3) Run "python3 c3_GL_FEM_comp_all_errors.py" 4) 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 1. (b) the folders "sol_ref_3_Mag_st_2.0_kappa_[KAPPA]_P1_square" contain all figures of the solutions where [KAPPA] is replaced by the respective value.
DOI: 10.35097/1343
title: Numerical experiments for "On dynamical low-rank integrators for matrix differential equations"

description: This code has been used for the numerical experiments in the thesis "On dynamical low-rank integrators for matrix differential equations" by Stefan Schrammer, see https://www.doi.org/10.5445/IR/1000148853.
description: #### Instructions: The scripts inside the subfolders are intended to reproduce the figures from the thesis &gt; On dynamical low-rank integrators for matrix differential equations. by Stefan Schrammer We provide two different versions of the code: - Code_Prom_wo_ref.zip provides the scripts for computing and plotting the data for all numerical experiments. - Code_Prom_incl_ref.zip addtionally provides the reference solutions to all considered problems as hdf5-files. ##### Requirements The codes are tested with Ubuntu 20.04.2 LTS and Python 3.8.5 and the following version of its modules: numpy 1.19.2 scipy 1.5.2 numba 0.51.2 colorama 0.4.4 h5py 2.10.0 matplotlib 3.3.2 tikzplotlib 0.9.6 ##### Generation of figures (tex files containing the data are also created) In the folder fracginz open a console and run the commands 1. to create the data for Figures (7.1) and (7.2) python3 fgl.py 2. to create Figures (7.1) and (7.2) python3 fgl_results.py In the folder fracschr open a console and run the commands 3. to create the data for Figure (7.3) python3 fsr.py 4. to create Figure (7.3) python3 fsr_results.py In the folder laserplasma open a console and run the commands 5. to create the data for Figure (7.4) python3 lpi_hom.py 6. to create Figure (7.4) python3 lpi_hom_plots.py 7. to create the data for Figures (7.5), (7.6), and (7.7) python3 lpi.py 8. to create Figures (7.5), (7.6), and (7.7) python3 lpi_globalerr.py python3 lpi_1d_plot python3 lpi_svals_maxint.py In the folder sinegordon open a console and run the commands 9. to create the data for Figures (7.8) and (7.9) python3 sineg.py 10. to create Figures (7.8) and (7.9) python3 sineg_globalerr_ranks.py If the reference solutions shall be recomputed, uncomment the line methods.append(...) at the beginning of the scripts fgl.py, fsr.py, lpi.py, and sineg.py, respectively.
DOI: 10.35097/1408
title: Numerical experiments for "Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations"

description: ##### Instructions: The scripts inside the subfolder are intended to reproduce the figures from the preprint ###### Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations by Marlis Hochbruck, Markus Neher, and Stefan Schrammer We provide two different versions of the code: - Code_rad_wo_ref.zip provides the scripts for computing and plotting the data for all numerical experiments. - Code_rad_incl_all.zip additionally provides the reference solutions as well as the low-rank approximations as hdf5-files. ##### Requirements The codes are tested with Ubuntu 20.04.2 LTS and Python 3.8.5 and the following version of its modules: numpy 1.19.2 scipy 1.5.2 numba 0.51.2 colorama 0.4.4 h5py 2.10.0 matplotlib 3.3.2 tikzplotlib 0.9.6 ###### Generation of figures (tikz files containing the data are also created) In the folder fracginz open a console and run the commands to create the data for Figures (1) and (2) python3 fgl.py to create Figures (1) and (2) python3 fgl_results.py In the folder fracschr open a console and run the commands to create the data for Figure (3) python3 fsr.py to create Figure (3) python3 fsr_results.py In the folder laserplasma open a console and run the commands to create the data for Figures (4) and (5) python3 lpi.py to create Figures (4) and (5) python3 lpi_globalerr.py python3 lpi_svals_maxint.py In the folder sinegordon open a console and run the commands to create the data for Figures (6) and (7) python3 sineg.py to create Figures (6) and (7) python3 sineg_globalerr_ranks.py
DOI: 10.35097/1535
title: Numerical experiments to "A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions"

description: This code is used for the numerical experiment in Section 6 of the preprint "A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions" by Jan Leibold. The computations are done in C++ using the Finite Element library deal.II; the plots then are generated with Matlab. To use this code, deal.II (release 9.3.2) has to be installed, cf. https://www.dealii.org/9.3.0 In order to compile the program, open a terminal session in this folder and call "cmake -DDEAL_II_DIR=/path/to/deal.II .". Next, call "make release" and then "make" to compile the files. Finally, run the program with "make run". This performs the computations and generates the file "results" containing the results of the numerical experiments. After that, the plots can be generated with the Matlab Script 'plot_figures.m'.
DOI: 10.35097/1557
title: Numerical experiments to "A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions" (Version 2)

description: This code is used for the numerical experiment in Section 6 of the paper "A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions" by Jan Leibold. The computations are done in C++ using the Finite Element library deal.II; the plots then are generated with Matlab. To use this code, deal.II (release 9.3.2) has to be installed, cf. https://www.dealii.org/9.3.0 In order to compile the program, open a terminal session in this folder and call "cmake -DDEAL_II_DIR=/path/to/deal.II .". Next, call "make release" and then "make" to compile the files. Finally, run the program with "make run". This performs the computations and generates the file "results" containing the results of the numerical experiments. After that, the plots can be generated with the Matlab Script 'plot_figures.m'.
DOI: 10.35097/1352
title: Numerical experiments to "A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions" (Version 3)

description: This code is used for the numerical experiment in Section 6 of the paper "A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions" by Jan Leibold. The computations are done in C++ using the Finite Element library deal.II; the plots then are generated with Matlab. To use this code, deal.II (release 9.3.2) has to be installed, cf. https://www.dealii.org/9.3.0 In order to compile the program, open a terminal session in this folder and call "cmake -DDEAL_II_DIR=/path/to/deal.II .". Next, call "make release" and then "make" to compile the files. Finally, run the program with "make run". This performs the computations and generates the file "results" containing the results of the numerical experiments. After that, the plots can be generated with the Matlab Script 'plot_figures.m'.
DOI: 10.35097/1255
title: Numerical experiments to "An implicit-explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions"

description: This code was used for the numerical experiments in the preprint (CRC Preprint 2020/20; URL: http://www.waves.kit.edu/downloads/CRC1173_Preprint_2020-20.pdf) and in the paper "An implicit-explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions" by M. Hochbruck and J. Leibold (cf. Section 4.5)
description: The computations are done in C++ using the Finite Element library deal.II; the plots then are generated with Matlab. To use this code, deal.II (release 9.2.0) has to be installed, cf. https://www.dealii.org/9.2.0 In order to run the program, open a terminal session in this folder and call "cmake -DDEAL_II_DIR=/path/to/deal.II .". Next, call "make release" to compile the files. Finally, run the program with "make run". This performs the computations and generates files in the "output" folder containing the results of the numerical experiments. After that, the plots can be generated with the Matlab Skript plot_figures.m. Note that running the C++ Code will take quite long, since it runs all calculations for all figures.
DOI: 10.35097/1284
title: Numerical experiments to "Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations"

description: 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.
description: ## 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/extracted_data/". (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.
DOI: 10.35097/1270
title: Numerical experiments to "Error analysis for space discretizations of quasilinear wave-type equations"

description: This code was used for the numerical experiments in the preprint (CRC Preprint 2021/2; URL: https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-2.pdf) and in the paper "Error analysis for space discretizations of quasilinear wave-type equations" by M. Hochbruck and B. Maier.
description: This program is intended to reproduce the results from the paper "Error analysis for space discretizations of quasilinear wave-type equations" It is an implementation of the full discretization of quasilinear wave equations, e.g., the Westervelt equation, following the method of lines.For the discretization in space, we apply a continuous Galerkin approach withisoparametric finite elements. For the subsequent discretization in time, two variants of the implicit midpoint rule as well as the leapfrog scheme areimplemented. The code is based on the open source finite element library MFEM (version 4.2). Further information can be found at https://mfem.org/ . -------------------------------------------------------------------------------- To use this code, MFEM (release 4.2) has to be installed supporting MPI, using Open MPI (release 4.1), Hypre (release 2.16.0), and Metis (release 5.1.0), cf. https://mfem.org/building/ . In order to run the program, change the makefile such that MFEM_DIR and MFEM_BUILD_DIR point to the source and build directory of MFEM on your system. Then, open a terminal session, go to the directory of the makefile and call "make". To reproduce the results shown in the paper, run the file "driver" to compute the results. These are then written to the file "res/results.txt" and can be displayed in a simple plot with the Matlab script "res/plot_results.m".
DOI: 10.35097/1512
title: Numerical experiments to "Error analysis of multirate leapfrog-type methods for second-order semilinear odes"

description: This code was used for the numerical experiments in the preprint (CRC Preprint 2021/26; URL: https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-26.pdf) and in the paper "Error analysis of multirate leapfrog-type methods for second-order semilinear odes" by C. Carle and M. Hochbruck.
description: The scripts inside the subfolders are intended to reproduce the figures from the preprint &gt; Error analysis of multirate leapfrog-type methods for second-order semilinear ODEs by Constantin carle and Marlis Hochbruck ### Requirements The codes are tested with Ubuntu 20.04.2 LTS and Python 3.8.5 and the following version of its modules: - numpy - 1.17.4 - scipy - 1.3.3 - dolfin (fenics) - 2019.2.0.dev0 (including mshr) - matplotlib - 3.1.2 - tikzplotlib - 0.9.6 ### Generation of figures In the folder "code_figure_6p1-6p2" open a console and run the commands 1. to obatin Figure 6.1 python3 script_figure_2dimEx.py, 2. to obtain Figure 6.2(a) python3 script_figure_FPUT_error.py 3. to obtain Figure 6.2(b) python3 script_figure_FPUT_hamiltonian.py. In the folder "code_figure_6p3" open a console and run the command python3 script_figure_wave-equation.py to obtain Figure 6.3(a) and (b). Additionally to the plots you can get the tikz-files which were used for generating the plots in the pdf by uncommenting the lines #import tikzplotlib #tikzplotlib.save("*****.tikz") at the end of each of the above scripts.
DOI: 10.35097/1456
title: Numerical experiments to "Error analysis of second-order local time integration methods for discontinuous Galerkin discretizations of linear wave equations"

description: 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.
description: 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
DOI: 10.35097/1301
title: Numerical experiments to "Exponential integrators for quasilinear wave-type equations" (updated version)

description: This code was used for the numerical experiments in the revised preprint (CRC Preprint 2021/12; URL: https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-12.pdf) and in the paper "Exponential integrators for quasilinear wave-type equations" by B. Dörich and M. Hochbruck.
description: This program is intended to reproduce the results from the preprint "Exponential integrators for quasilinear wave-type equations" by Benjamin Dörich and Marlis Hochbruck The codes generates the lines in Figure 1 ##################################################################################### 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 dolfin - 2018.1.0 fenics - 2018.1.0 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 dolfin - 2019.2.0.dev0 fenics - 2019.2.0.dev0 matplotlib - 3.3.2 tikzplotlib - 0.9.4 ##################################################################################### In the folder "DoeH21_quasilinear" open a console and run the following commands after each other. 1) Run "python3 1_generate_initial_matrices.py" 2) Run "python3 2_paper_run_reference_solution.py" 3) Run "python3 3_paper_run_Euler.py" 4) Run "python3 4_paper_run_midpoint.py" ##################################################################################### After running the calculations, the errors can be found in the folder "preprint_DoeH21_quasilinear/extracted_data/". (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.
DOI: 10.35097/1563
title: Numerical experiments to "Exponential integrators for quasilinear wave-type equations"

description: 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 "Exponential integrators for quasilinear wave-type equations" by B. Dörich and M. Hochbruck.
description: This program is intended to reproduce the results from the preprint "Exponential integrators for quasilinear wave-type equations" by Benjamin Dörich and Marlis Hochbruck The codes generates the lines in Figure 1 #### 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 - 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 - dolfin - 2019.2.0.dev0 - fenics - 2019.2.0.dev0 #### Figure 1 In the folder "DoeH21_quasilinear" open a console and run the following commands after each other. 1) Run "python3 1_generate_initial_matrices.py" 2) Run "python3 2_paper_run_reference_solution.py" 3) Run "python3 3_paper_run_Euler.py" 4) Run "python3 4_paper_run_midpoint.py" After running the calculations, the errors can be found in the folder "DoeH21_quasilinear/extracted_data/". (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.
DOI: 10.35097/1503
title: Numerical experiments to "Full discretization error analysis of semilinear wave equations with exponential integrators"

description: This code is used for the numerical experiments in Section 6 of the preprint &gt;"Full discretization error analysis of semilinear wave equations with exponential integrators" by Benjamin Dörich and Jan Leibold. The computations are done in C++ using the Finite Element library deal.II; the plots then are generated with Matlab. To use this code, deal.II (release 9.2.0) has to be installed, cf. https://www.dealii.org/9.2.0 In order to compile the program, open a terminal session in this folder and call cmake -DDEAL_II_DIR=/path/to/deal.II . Next, call make release ; make to compile the files. Finally, run the program with make run This performs the computations and generates files in the "output" folder containing the results of the numerical experiments. After that, the plots can be generated with the Matlab Script plot_figures.m An updated version of this dataset can be found at https://doi.org/10.5445/IR/1000141073
DOI: 10.35097/1539
title: Numerical experiments to "Full discretization error analysis of semilinear wave equations with exponential integrators" (Version 2)

description: This code is used for the numerical experiments in Section 6 of the paper "Full discretization error analysis of semilinear wave equations with exponential integrators" by Benjamin Dörich and Jan Leibold. The computations are done in C++ using the Finite Element library deal.II; the plots then are generated with Matlab. To use this code, deal.II (release 9.2.0) has to be installed, cf. https://www.dealii.org/9.2.0 In order to compile the program, open a terminal session in this folder and call "cmake -DDEAL_II_DIR=/path/to/deal.II .". Next, call "make release" and then "make" to compile the files. Finally, run the program with "make run". This performs the computations and generates files in the "output" folder containing the results of the numerical experiments. Note that the computations take several hours to a few days depending on the computer. After that, the plots can be generated with the Matlab Script 'plot_figures.m'.