# Volumential

Volumential (VOLUME poteNTIAL) provides toolset to solve volume potential integral equations
efficiently via Fast Multipole Method.

[Name `volumential` courtesy of Andreas Klöckner.](https://gitlab.tiker.net/xywei/volumential/issues/2)

This repository uses `git-lfs`.

**NOTE**: If you would like to skip downloading large resource files (IPython
notebooks etc.), use
```
GIT_LFS_SKIP_SMUDGE=1 git clone SERVER-REPOSITORY
```
This does not affect using the library.

Volumential is under the MIT license.

## Singular Integral Methods

- `Transform`: Apply coordinate transforms to remove the singularity (or, hide the singularity into the Jacobian of the transform).

- `DrosteSum`: Subdivide the box iteratively into layers of "bricks" towards the singular point. The name comes from **Droste effect** ([Wikipedia](https://en.wikipedia.org/wiki/Droste_effect)).

## Notes on meshgen_dealii

A simple way to compile `meshgen_dealii`:

- Install everything in `conda-forge`
- Download `deal-ii` and compile it with all things disabled (~15min)
- Build `meshgen11_dealii` under `contrib` in the conda env (`python 3.6` must be used)

## License

Volumential is developed and released under the terms of the MIT license,
though it also makes use of third-party packages under their own licensing
terms. See the [LICENSE](./LICENSE.md) file for details.

## Acknowledgements

We would like to thank people and organizations that contributed to or supported the
Volumential project, without whom the project would not have been possible.

The research that started the Volumential project was supported by the
[National Science Foundation][nsf] under grant DMS-1654756,
and by the [Department of Computer Science][uiuc-cs] at the
[University of Illinois at Urbana-Champaign][uiuc].
Part of the work was performed while the authors were participating in
the [HKUST][hkust]-[ICERM][icerm] workshop "Integral Equation Methods, Fast
Algorithms and Their Applications to Fluid Dynamics and Materials
Science" held in 2017.

Thanks very much to the [Department of Mathematics][hkust-math] at
[Hong Kong University of Science and Technology][hkust]
for funding Xiaoyu Wei to work on the project
as a PhD student under the Postgraduate Studentship and
the Overseas Research Award.

[nsf]: https://www.nsf.gov/
[hkust-math]: https://www.math.ust.hk/
[hkust]: https://www.ust.hk/home
[icerm]: https://icerm.brown.edu/
[uiuc-cs]: https://cs.illinois.edu/
[uiuc]: https://illinois.edu/