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FEECa: Finite Element Exterior Calculus in Haskell

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# FEECa: Finite Element Exterior Calculus in Haskell [![Build Status](https://travis-ci.org/Airini/FEECa.svg?branch=master)](https://travis-ci.org/Airini/FEECa)

[FEECa (\['fi:ka\])](https://en.wikipedia.org/wiki/Fika_(Sweden)) is a library
implementing the mathematical framework that [the theory of finite element
exterior calculus (FEEC), developed by Arnold, Falk and Winther][arnold1] [[1]](#afw-07),
provides for the discretization of partial differential equations (PDEs) that
allows for a universal treatment of a large number of physical problems.

[FEECa][docu] implements the abstract, mathematical concepts of FEEC and
provides a full-fledged basis form generated and framework for computations on
differential forms. It handles polynomial differential forms in arbitrary
dimensions and implements monomial as well as Bernstein bases for polynomials.
The package provides functionality to compute bases of the *P_r L^k* and
*P-_r L^k* spaces of finite element spaces based on the [geometric decomposition
proposed by Arnold, Falk and Winther][arnold2] [[2]](#afw-09).

[arnold1]: http://dx.doi.org/10.1017/S0962492906210018
<a id='afw-07'>[1]</a>
Douglas N. Arnold, Richard S. Falk, and Ragnar Winther: *Finite element exterior
calculus, homological techniques, and applications*. J. Acta Numerica. 2006

[arnold2]: http://dx.doi.org/10.1016/j.cma.2008.12.017
<a id='afw-09'>[2]</a>
Douglas N. Arnold, Richard S. Falk, and Ragnar Winther: *Geometric
decompositions and local bases for spaces of finite element differential forms*.
J. Computer Methods in Applied Mechanics and Engineering. 2009.

[docu]: http://Airini.github.io/FEECa "Online documentation! (in the making)"
The [FEECa online documentation][docu] is under construction.

## Installation

To build and use FEECa, the Haskell compiler [GHC][ghc]
and [Cabal][cabal] should be installed in your system. Or you could
use [Stack][stack], which will install the Haskell tools (including
GHC and Cabal) for you.

Short version (for Ubuntu):
```shell
sudo apt-get install libblas-dev liblapack-dev
sudo apt-get install stack
stack upgrade
git clone https://github.com/Airini/FEECa.git
cd FEECa
stack build
```

Details:

The package and dependencies are tested for GHC 8.0 upwards and will
not build with older versions of the compiler.

If you are new to Haskell or the building environment described, we
recommend you install the [Haskell Platform][hplatform] which provides
GHC, Cabal and stack.

LAPACK and BLAS should also be installed. If not so, and you are on a linux
machine, use `apt-get` (the snippet below will install developer versions of
both):

```
sudo apt-get -qq update
sudo apt-get install -y libblas-dev liblapack-dev
```

For other systems, we recommend you search for the best way of getting these
libraries. On OS X, you may install them via Homebrew or Macports.

*Note:* The "new-style" `cabal` commands may be used in place of the old style
ones in the following snippets.

When these dependencies are ready, FEECa may be built and installed as a Cabal
package using `cabal` (or stack):

```
cabal install --only-dependencies
cabal configure
cabal install
```

The first instruction will install all dependencies (alone); the parameter
`--reorder-goals` might become necessary for some versions of Cabal. If you do
not install them first, `cabal` will display the missing dependencies and
the instructions to install them.

If you wish to run the test-suite:
```
cabal configure --enable-tests
cabal build
cabal test
```

Or:
```
make test-feec
```

[ghc]:  https://www.haskell.org/ghc/

[cabal]: https://www.haskell.org/cabal/

[stack]: https://docs.haskellstack.org/en/stable/README/

[hplatform]: https://www.haskell.org/platform/

## The project

The project (Functional FEEC, initially) has been funded by the Information &
Communication Technology Area of Advance (ICT AoA) of Chalmers University and
is a collaboration between the Computational Mathematics (Department of
Mathematics) and Functional Programming (Department of Computer Science and
Engineering) groups at Chalmers University of Technology, Gothenburg, Sweden.

The resulting implemented package has been developed by (you can find contact
information in the package description file: `feeca.cabal`):
- Simon Pfreundschuh: MSc student in Physics
- Irene Lobo Valbuena: MSc/doctoral student in Computer Science

as joint work with:
- [Anders Logg](http://www.logg.org/anders): professor in Computational
  Mathematics
- [Patrik Jansson](https://www.chalmers.se/en/staff/Pages/patrik-jansson.aspx):
  professor in Computer Science. [github](https://github.com/patrikja)
- [Mary Sheeran](http://www.cse.chalmers.se/~ms): professor in Computer Science

## Presentation

2016-05-18: The project results are presented by
[Simon Pfreundscuh](http://easychair.org/smart-program/FEniCS'16/person11.html)
at the
[FENICS 2016 workshop](http://fenicsproject.org/featured/2016/fenics16_oslo.html).
[Programme](http://easychair.org/smart-program/FEniCS'16/2016-05-18.html#talk:23321).

## Documentation

The FEECa code is written using literate Haskell to combine source code and
documentation. The executable `doc` uses the
[Hakyll](https://jaspervdj.be/hakyll/) framework to compile the code into a
static web page and can be viewed in [your browser](localhost:8000) after
executing:

```
stack build feeca
stack exec doc rebuild
stack exec doc preview
```

or alternatively:

```
cabal run doc rebuild
cabal run doc server
```

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