PEMesh

A Graphical Framework to Study the Correlation between Geometric Design and Simulation.

Dependencies

The framework depends on:

• the cinolib library, which is included as a submodule ;
• Triangle library, which is included as a submodule;
• Metis, which is included as a submodule;
• Qt framework, including Qt Charts module, which is assumed to be installed on the local machine (version 6.8.0 or later);
• Boost library, which is assumed to be installed on the local machine.
• Docker App, which is assumed to be installed on the local machine, and open when using PEMesh.

Note that, in the settings of the Docker App, a "Resource Saver" mode is activated by default after some inactivity time. This option should be disabled for the correct functioning of PEMesh.

How to make it work

Please, use --recursive when cloning this repository.

git clone --recursive https://github.com/DanielaCabiddu/PEMesh.2.git

In the following, please consider ${REPO_ROOT} variable as the folder where this README.md lies. PMesh can be built by running either QMake or CMake. In both cases, the PMesh executable will be available in the ${REPO_ROOT}/build folder.

QMake

First, build triangle library

cd ${REPO_ROOT}/external/triangle
mkdir build
cd build
cmake ..
make

Then, build PEMesh by running the following commands:

mkdir -p ${REPO_ROOT}/build
cd build
qmake ../src/PMesh.pro

CMake

Run the following commands:

mkdir -p ${REPO_ROOT}/build
cd build
cmake ../src
make

Triangle library will be automatically built by CMake.

Docker

In both cases, after the installation open Docker App and run the following commands:

cd ${REPO_ROOT}/solver
sudo docker build --no-cache -f Dockerfile --target siggraph_2024_solver . -t siggraph_2024_solver:1.0.0

Developers

• Daniela Cabiddu (CNR IMATI), Tommaso Sorgente (CNR IMATI)

The VEM solver is courtesy of Fabio Vicini (Politecnico di Torino)

Citing us

PEMesh has been published as a Software Paper (https://diglib.eg.org/bitstream/handle/10.2312/stag20221251/011-019.pdf?sequence=1&isAllowed=y).

If you use PEMesh in your academic projects, please consider citing it using the following BibTeX entries:

@inproceedings {pemesh-stag2022,
booktitle = {Smart Tools and Applications in Graphics - Eurographics Italian Chapter Conference},
editor = {Cabiddu, Daniela and Schneider, Teseo and Allegra, Dario and Catalano, Chiara Eva and Cherchi, Gianmarco and Scateni, Riccardo},
title = {{A Graphical Framework to Study the Correlation between Geometric Design and Simulation}},
author = {Cabiddu, Daniela and Patané, Giuseppe and Spagnuolo, Michela},
year = {2022},
publisher = {The Eurographics Association},
ISSN = {2617-4855},
ISBN = {978-3-03868-191-5},
DOI = {10.2312/stag.20221251}
}

If you use the quality indicators, please cite:

@article{benchmark-mcs,
title = {Benchmarking the geometrical robustness of a Virtual Element Poisson solver},
journal = {Mathematics and Computers in Simulation},
volume = {190},
pages = {1392-1414},
year = {2021},
issn = {0378-4754},
doi = {https://doi.org/10.1016/j.matcom.2021.07.018},
url = {https://www.sciencedirect.com/science/article/pii/S0378475421002706},
author = {Marco Attene and Silvia Biasotti and Silvia Bertoluzza and Daniela Cabiddu and Marco Livesu and Giuseppe Patanè and Micol Pennacchio and Daniele Prada and Michela Spagnuolo},
keywords = {Polytopal Element Methods, Virtual Element Methods, Polygonal meshes, Geometric metrics, Geometry-PEM correlation}
}

@inbook{vem-and-the-mesh,
author={ Sorgente, Tommaso and Prada, Daniele and  Cabiddu, Daniela and Biasotti, Silvia and  Patanè, Giuseppe and Pennacchio, Micol  and  Bertoluzza, Silvia and  Manzini, Gianmarco and  Spagnuolo, Michela},
title={VEM and the Mesh},
year={2022},
publisher={Springer Nature Switzerland},
address={Basel},
volume={31},
pages={1--57},
booktitle={The Virtual Element Method and its Applications},
url={https://link.springer.com/book/10.1007/978-3-030-95319-5},
series={SEMA SIMAI Springer Series},
isbn={978-3-030-95318-8},
issn={2199-3041},
doi={10.1007/978-3-030-95319-5},
affiliation={IMATI-CNR, Genova, Pavia, Italy},
language={eng}
}

@inproceedings{sorgente2023survey,
  title={A survey of indicators for mesh quality assessment},
  author={Sorgente, Tommaso and Biasotti, Silvia and Manzini, Gianmarco and Spagnuolo, Michela},
  booktitle={Computer graphics forum},
  volume={42},
  number={2},
  pages={461--483},
  year={2023},
  organization={Wiley Online Library}
}

If you use the VEM quality indicator, please cite:

@article{sorgente2022role,
  title={The role of mesh quality and mesh quality indicators in the virtual element method},
  author={Sorgente, Tommaso and Biasotti, Silvia and Manzini, Gianmarco and Spagnuolo, Michela},
  journal={Advances in Computational Mathematics},
  volume={48},
  number={1},
  pages={3},
  year={2022},
  publisher={Springer}
}

If you use the Mesh Optimization algorithm, please cite:

@article{sorgente2024mesh,
  title={Mesh Optimization for the Virtual Element Method: How Small Can an Agglomerated Mesh Become?},
  author={Sorgente, Tommaso and Vicini, Fabio and Berrone, Stefano and Biasotti, Silvia and Manzini, Gianmarco and Spagnuolo, Michela},
  journal={Journal of Computational Physics},
  pages={113552},
  year={2024},
  publisher={Elsevier}
}
}