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# Nuerical implementation of “Leak localisation with a measure source convection–diffusion model”

These are the codes for the numerical demonstrations of the manuscript
_“Leak localisation with a measure source convection--diffusion model”_
([arXiv:2605.12095](https://arxiv.org/abs/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](https://brew.sh).
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](https://direnv.net) 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.

1.  Install the [Rust] infrastructure (including Cargo) with [rustup].
2.  Install a “nightly” release of the Rust compiler. With rustup, installed in
    the previous step, this can be done with
    
        rustup toolchain install nightly

3. Download [alg_tools], [pointsource_algs], and [measures] and unpack them under
   the same directory as this package.

  [rustup]: https://rustup.rs
  [alg_tools]: https://tuomov.iki.fi/software/alg_tools/
  [pointsource_algs]: https://tuomov.iki.fi/software/pointsource_algs/
  [measures]: https://tuomov.iki.fi/repos/measures/
  [Rust]: https://www.rust-lang.org/
  [GNU Scientific Library]: https://www.gnu.org/software/gsl/
  [rust-GSL]: https://docs.rs/GSL/6.0.0/rgsl/
  [Homebrew]: https://brew.sh
  [arXiv:2212.02991]: https://arxiv.org/abs/2212.02991
  [arXiv:2502.12417]: https://arxiv.org/abs/2502.12417
  [doi:10.46298/jnsao-2023-10433]: http://doi.org/10.46298/jnsao-2023-10433

### 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:

  1. I had to set (in my [direnv](https://direnv.net) `.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
    
  2. 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.
  2. 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.
  3. 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.