2026-08-05T07:53:53Zhttps://www.radar-service.eu/oai/OAIHandler

10.35097/12752023-11-15T14:45:26Zradar4kit

10.35097/1275 Freese, Jan Philip Jan Philip Freese Karlsruhe Institute of Technology 2020 2023 Mathematics Maxwell equations Sobolev equation time-integration homogenization heterogeneous multiscale method recursive convolution memory variable Open Access Creative Commons Attribution Non Commercial Share Alike 4.0 International Freese, Jan Philip This code has been used for the numerical experiments in the thesis "Numerical homogenization of time-dependent Maxwell's equations with dispersion effects" by Jan Philip Freese, see https://www.doi.org/10.5445/IR/1000129214. # Readme This code was used for the numerical experiments of the PhD thesis "Numerical homogenization of time-dependent Maxwell's equations with dispersion effects" by P. Freese (cf. Section 7.2, Section 7.3) https://www.doi.org/10.5445/IR/1000129214. The computations are done in C++ using the Finite Element library deal.II. ## Requirements - In order to run the code you need **deal.II** (release 9.1.1), cf. https://www.dealii.org/9.1.1 - For the experiments on the macroscopic level (Section 7.3) you need to compile deal.II using **Trilinos** (version 12.17) and **p4est** (version 2.2), cf. https://www.dealii.org/9.1.1/external-libs/trilinos.html and https://www.dealii.org/9.1.1/external-libs/p4est.html - To get the full functionality of the scripts a **Bash** shell has to be used and at least **cmake** (version 3.13.0) is needed - For the visualization of the data you need **Matlab** (version R2020a Update 2) and **Paraview** (version 5.8.1-RC1) ## Structure The structure is as follows: - The folder **executables** contains Bash scripts for all figures and tables separately. All figures from Section 7.2 may be computed using the `compute_all_micro_figures_and_tables.sh` at ones. Similarly, the figures from Section 7.3 are computed using the `compute_all_macro_figures_and_tables.sh` script. Moreover, the `distclean.sh` script runs the `deal.II` distclean command in all programs. - The folder **matlab_plot_files** contains Matlab scripts for the convergence plots and related tables - The folder **paraview_plot_files** contains Paraview states to generate the solution plots - In **programs** the actual source code is stored within three different programs that are - **hmm_for_Maxwell_conductivity_memory_variable:** Code that applies the Heterogeneous Multiscale Method combined with the memory variable technique as explained in Section 6.2.3 - **hmm_for_Maxwell_conductivity_recursive_convolution:** Code that applies the Heterogeneous Multiscale Method combined with the recursive convolution technique as explained in Section 6.2.2 - **microproblem_conductivity:** Code that solves the microscopic cell problems - In **results** the results of the computations are stored according to the sub structure of the **programs** folder ## Howto In order to run the program, open a terminal session in the folder **executables** and run one of the Bash scripts providing at least the additional argument: - **Number of kernels (-n)**: One should usually use one job for each processor core on the machine Use a command like ```bash bash figure*.sh -n number_of_kernels ``` It may be mandatory to provide the location of your deal.II installation as well. This is done by providing another argument: - **Path to deal (-D)**: Path to the deal.II installation Use a command like ```bash bash figure*.sh -n number_of_kernels -D path_to_deal ``` If you can not execute the Bash scripts, you have to build the program and copy/edit the config/source files yourself. Still, the necessary information is found in the bash scripts, so just use a text editor to open those files and execute the steps by hand. ### Example If you unpack this code within the **examples** folder of **deal.II** you can simply use the following example code to run the Bash script (generating data for Figure 7.2 and Table 7.1 with 4 kernels) ```bash bash figure_7_2_table_7_1.sh -n 4 -D ../../../../ ``` ## Visualization ### Matlab The Matlab scripts are used to generate the plots and tables. The tables are directly prompted to the Matlab output. ### Paraview To load the state files in Paraview, select `File->Load State...`. Select the respective `.pvsm` file of the figure you want to plot. As `Load State Data File Options` choose `Search files under specified directory` and select the `results` folder. Paraview should find the files itself. ## Remarks - The scripts `figure_7_19_table_7_9.sh` and `figure_7_21_table_7_10.sh` save reference solutions that are used to compute the errors between different levels of refinement. These solutions are stored in `programs/hmm_for_Maxwell_conductivity_recursive_convolution/data/`. If you want to run these scripts a second time you either have to delete the solutions (and compute the solutions again) or you have to set the `Output.Reference_Solution` flag in the respective config file in `programs/hmm_for_Maxwell_conductivity_recursive_convolution/config_files/` to false (which makes the computation even faster). - Be aware that, depending on your computer, the computations may take several hours or days. 10.5445/IR/1000129217 application/x-tar