These are the codes for the numerical demonstrations of the manuscript “Leak localisation with a measure source convection–diffusion model” (arXiv:2605.12095) by Thi Tam Dang and Tuomo Valkonen. It should be relatively easy to to use this package and the algorithms it provides for other PDE-based point source localisation problems. Building Sorry, although the core of program is written in Rust with a modern dependency management and build process, we also have legacy C++ and Python dependencies, i.e., the Fenicsx PDE library. Therefore, the build process is difficult. (We admit it, we made a mistake by going with the crowd and using Fenicsx. In the end it would have been less effort to write low-level PDE code in Rust.) Phase 1: Python and Fenics Option 1.A that avoids Conda hell, but is more work (macOS and Linux) Phase 1.A.1: C++ dependencies of Fenics First install C++ dependencies using Homebrew. Even on Linux, use Homebrew, or install from official sources; distribution packages are usually obsolete and buggy, often non-standard, and will cause problems (see above). brew install openmpi boost pugixml fmt spdlog hdf5-mpi cmake kahip slepc petsc gsl (Fenics recommends ParMETIS instead of Kahip, but only the latter is available from Homebrew at the time of writing this.) There’s no guarantee that this will install compatible versions of these packages. Homebrew, while better than most Linux distributions, is also obsolete in its philosophy: it does not allow easily installing specific versions of packages. Versions known to work are: package version boost 1.90.0 cmake 4.2.1 fmt 12.1.0 hdf5-mpi 1.14.6 kahip 3.22 petsc 3.24.3 pugixml 1.15 slepc 3.24.2 spdlog 1.17.0 gsl 2.8 You can get the list of installed versions with: brew list --versions openmpi boost pugixml fmt spdlog hdf5-mpi cmake kahip slepc petsc gsl Phase 1.A.2: Python dependencies of Fenics In this source directory, create and activate a virtual environment for Python, and install Python packages: python3 -m venv .venv source .venv/bin/activate PETSC_DIR=/opt/homebrew/ SLEPC_DIR=/opt/homebrew/ pip install -r requirements.lock To not have to activate the virtual environment manually every time, and to not mess up your global settings, it is recommended to install direnv and put the following in .envrc in this directory: source .venv/bin/activate export PYTHONPATH=$(echo .venv/lib/python*/site-packages) export PYO3_PYTHON="$(which python)" (The last two lines are required later.) This template is also available in misc/_envrc. For changes .envrc to take effect, you should use direnv allow Phase 1.A.3: Fenicx-basix Install basix from https://github.com/FEniCS/basix/releases/tag/v0.10.0.post0 according to instructions. First do the C++ bit: tar xzf basix-0.10.0.post0.tar.gz cd basix-0.10.0.post0/cpp mkdir build cd build cmake .. make make install Then the Python bit. This has to be done with the venv created above, active. cd ../../python pip install . Phase 1.A.4: Fenicx-dolfinx Install dolfinx from https://github.com/FEniCS/dolfinx/releases/tag/v0.10.0.post5 according to instructions. First do the C++ bit: tar xzf dolfinx-0.10.0.post5.tar.gz cd dolfinx-0.10.0.post5/cpp mkdir build cd build cmake .. make make install Skip the source /usr/local/lib/dolfinx/dolfinx.conf recommended at the end of the compilation. It will likely break things. Then the Python bit. This has to be done with the virtual environment created above, active. cd ../../python python -m scikit_build_core.build requires | python -c "import sys, json; print(' '.join(json.load(sys.stdin)))" | xargs pip install pip install --check-build-dependencies --no-build-isolation . If you didn’t already do these steps with direnv above, you should: export PYTHONPATH=$(echo .venv/lib/python*/site-packages) export PYO3_PYTHON="$(which python)" Option 1.B: Conda You can try to install Fenicsx in Conda according to instructions on the Fenics website. Additionally you need to install scipy: conda create -n fenicsx-env conda activate fenicsx-env conda install -c conda-forge fenics-dolfinx=0.10.0 scipy=1.17.1 mpich This is, however, unlikely to not work, as Conda, despite its sandboxing separation attempts, conflicts with system packages, or Conda packages have weird ideas. You’re likely to run into runtime problems with the FFCX form compiler (bad bad bad idea, running a C compiler runtime) failing due to something, somewhere, in the extremely fragile Conda setup, trying to load system libraries wrongly, etc. Option 1.C: Debian/Ubuntu You may be able to use the system package manager, but beware of obsolete and modified versions. As of 2026–03–23, the packages available in Debian/Ubuntu cause massive memory leaks and eventual system crash. Phase 2: Rust You will only need to install the “nightly” Rust compiler and the GNU Scientific Library manually. At the time of writing this README, alg_tools also needs to be downloaded separately. Install the Rust infrastructure (including Cargo) with rustup. Install a “nightly” release of the Rust compiler. With rustup, installed in the previous step, this can be done with rustup toolchain install nightly Linux / further patching Due to both Fenics and typical Linux system being completely broken, you may need to do further patching to get things to compile: I had to set (in my direnv .envrc) export PKG_CONFIG_PATH=/home/linuxbrew/.linuxbrew/lib/pkgconfig:/usr/local/lib/pkgconfig/:/usr/lib/aarch64-linux-gnu/pkgconfig/ export LD_LIBRARY_PATH=/home/linuxbrew/.linuxbrew/lib Some libraries, in particular libfmt and libspdlog installed in Homebrew, may conflict with system versions, that must be removed. Lack of proper sandboxing in legacy Linux distributions, effectively prohibits multiple versions of the same library. I had to add Libs in /usr/local/lib/pkgconfig/dolfinx.pc the bit -L/home/linuxbrew/.linuxbrew/lib/ -lopenblas. Nothing in the fenics stack seems to explicitly require it. Basix, that depends on openblas, is entirely missing a pkg-config file. Also export export OMP_NUM_THREADS=1 (in .envrc). We don’t do MPI. We cannot do MPI in Fenics' lame “it’s all just parallel solution of PDEs, with no other computation, ever” aka “single-program multiple-data, with no controller at all” way. If you don’t do this, you may have multiple threads wasting CPU just being there. We try to control the thread count in our code, but OpenMPI on Linux doesn’t seem to respect it. Building and running the experiments To compile the program, run cargo build --release When doing this for the first time, several dependencies will be downloaded. Now you can run the experiments in the article with cargo run --release -- \ -o results -a radon_sliding_fb -a radon_fb --max-iter 20000 experiments/laser_and_mirrors_aux.py experiments/laser_and_mirrors_aux2.py The -o results option tells pointsource_pde to write results in the results directory. The other options indicate the algorithms and experiments to run, as well as the maximum number of iterations. The double-dash separates the options for the Cargo build system and pointsource_pde. Visualising the results The results may be plotted with python3 ./plot.py results/laser_and_mirrors_aux/radon_sliding_fb Vary the path to laser_and_mirrors_aux2 and radon_fb for the alternative experiment and basic algorithm. The script misc/copy_results.sh may be generate the images and copy the results in the manuscript to ../gasleak. Documentation Use the --help option to get an extensive listing of command line options to customise algorithm parameters and the experiments performed. Internals If you are interested in the program internals, the integrated source code documentation may be built and opened with cargo doc # build dependency docs misc/cargo-d --open # build and open KaTeX-aware docs for this crate The cargo-d script ensures that KaTeX mathematics is rendered in the generated documentation through an ugly workaround. Unfortunately, rustdoc is stuck in 80’s 7-bit gringo ASCII world, and does not support modern markdown features, such as mathematics.