2026-10-11T19:49:28Zhttps://www.radar-service.eu/oai/OAIHandler10.35097/nwa3t4pv0jxwpf5v2026-10-09T10:53:47Zradar4kit
https://dx.doi.org/10.35097/nwa3t4pv0jxwpf5v
Dörner, Julian
Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions
Karlsruhe Institute of Technology
2025
Mathematics
dataset
Software
info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/4.0/legalcode
Dörich, Benjamin
Hochbruck, Marlis
# Error analysis of DGTD for linear Maxwell equations with inhomogeneous interface conditions
This code was used for the numerical experiments in the paper
> ERROR ANALYSIS OF DGTD FOR LINEAR MAXWELL EQUATIONS WITH INHOMOGENEOUS INTERFACE CONDITIONS
>
> By B. Dörich, J. Dörner, M. Hochbruck
This software is published in accordance with the guidelines for safeguarding good research practice and thus serves to reproduce the experiments in the above-mentioned publication.
## Requirements
The code is written in C++17 and uses the software packages
* [deal.II](https://www.dealii.org/), Version 9.5.0
* [CMake](https://cmake.org/), Version 3.22.1
* [TiMaxdG](https://gitlab.kit.edu/kit/ianm/ag-numerik/projects/dg-maxwell/timaxdg), Commit #2002f893
* [fftw](https://www.fftw.org/) Version 3.x.x (with quadmath)
Note that the authors of this paper develope the software package TiMaxdG.
Therefore, the source code is provided within this repository and uses of the main branch with the hash #2002f893.
For plot generation, Python 3 is used with the usual scientific software stack (numpy, scipy, matplotlib ...).
Any reasonable new distribution works.
For convenience, we provide a reproduction environment via [docker](https://www.docker.com/) and [enroot](https://github.com/NVIDIA/enroot).
For that, please consider the installation instructions for the tools and the files:
* .devcontainer/Dockerfile
* .devcontainer/README.md
* .devcontainer/ENROOT.md
## Reproduction
### Figure 2:
The experiment is build with the commands
```bash
mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
cd src
make CavitySolution_Prototype
```
The experiment is executed with the commands
```bash
./CavitySolution_Prototype
```
The experiment produces a tabular file `error.txt` with the results and a folder structure with additional run artifacts.
The plot is generated with
```bash
python3 ../../python/CavityPlots.py error.txt
```
The output file `cavity_error_plot.pdf` is produced.
### Figure 4:
The experiment is build with the commands
```bash
mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
cd src
make ReferenceSolution_Prototype
```
The experiment is executed with the commands
```
mkdir artifacts
cd artifacts
../ReferenceSolution_Prototype ../../../src/config.json
cd ..
../../python/postprocess.py artifacts/
```
The experiment produces a tabular file `error.txt` with the results.
The plots are generated with
```bash
python3 ../../python/ReferenceErrorPlots.py error.txt
```
The output files `full_error_deg_1pdf` and `full_error_deg_2.pdf` are produced.
**Note that this experiment is computationally very costly and the calculations should be distributed on several high performance computers!**
### Figure 5
The experiment is build with the commands
```bash
mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
cd src
make PolynomialSolution_Prototype
```
The experiment is executed with the commands
```bash
./PolynomialSolution_Prototype
```
The experiment produces a tabular file `output/error.txt` with the results and a folder structure `output/` with additional run artifacts.
The plot is generated with
```bash
python3 ../../python/PolynomialErrorPlot.py output/error.txt
```
The output file `polynomial_error_plot.pdf` is produced.
Dörich, Benjamin
Hochbruck, Marlis
https://publikationen.bibliothek.kit.edu/1000185221
application/x-tar