This is the code for obtaining the results of the paper Interface Identification Constrained by Local-to-Nonlocal Coupling by M. Schuster and V. Schulz that can be found on https://arxiv.org/abs/2402.12871.

Build and Install on Ubuntu

In order to clone the project do

git clone https://github.com/schustermatthias/LtNShape.git path/to/local_folder

Since this code contains a customized version of nlfem the following basic requirements of nlfem are needed

gcc, g++, python3-dev, python3-venv, libgmp-dev, libcgal-dev, metis, libmetis-dev, libarmadillo-dev.

On Ubuntu, this can be done via

sudo apt-get install git gcc g++ libarmadillo-dev liblapack-dev libmetis-dev
sudo apt-get install python3-venv python3-dev libgmp-dev libcgal-dev

Moreover, to run nlshape legacy FEniCS(version 2019.1.0) is required. In order to use FEniCS in a virtual environment, it may has to be installed globally and then inherited as a global site package.

A virtual environment can be built and activated via

mkdir venv
python3 -m venv venv/
source venv/bin/activate

Additionally, the packages from the file requirements.txt are neccessary and can be installed by

(venv) python3 -m pip install -r requirements.txt

The creation of the virtual environment and the installation of packages from requirements.txt can probably also be done via your IDE. Finally, nlfem can be installed by

(venv) python3 setup.py build --force install

See https://gitlab.uni-trier.de/pde-opt/nonlocal-models/nlfem for more information.

Further, Gmsh needs to be installed to run the examples where the mesh is remeshed. On Ubuntu Gmsh can be installed via

sudo apt install gmsh

More information on Gmsh can be found on https://gmsh.info.

Running the Examples from the Paper

To run one of the examples of the paper or the PhD thesis, choose in line 8 of main.py the associated configuration file, i.e., "configuration_ex1", "configuration_ex2", "configuration_ex3" or "configuration_ex4".

Raw Data

The data of the experiments in the paper and in the thesis can be found in the folder "LtNShape/results".

License

LtNShape is published under GNU General Public License version 3. Copyright (c) 2025 Matthias Schuster

Parts of the project are taken from nlfem and have been customized.

nlfem is published under GNU General Public License version 3. Copyright (c) 2021 Manuel Klar, Christian Vollmann