A finite volume PDE solver in Python

## Project description

========
Overview
========

.. only:: latex

:term:`FiPy` is an object oriented, partial differential equation (PDE)
solver, written in :term:`Python`, based on a standard finite volume
(FV) approach. The framework has been developed in the Materials Science
and Engineering Division (MSED_) and Center for Theoretical and
Computational Materials Science (CTCMS_), in the Material Measurement
Laboratory (MML_) at the National Institute of Standards and Technology
(NIST_).

The solution of coupled sets of PDEs is ubiquitous to the numerical
simulation of science problems. Numerous PDE solvers exist, using a
variety of languages and numerical approaches. Many are proprietary,
expensive and difficult to customize. As a result, scientists spend
considerable resources repeatedly developing limited tools for
specific problems. Our approach, combining the FV method and :term:`Python`,
provides a tool that is extensible, powerful and freely available. A
significant advantage to :term:`Python` is the existing suite of tools for
array calculations, sparse matrices and data rendering.

The :term:`FiPy` framework includes terms for transient diffusion,
convection and standard sources, enabling the solution of arbitrary
combinations of coupled elliptic, hyperbolic and parabolic PDEs. Currently
implemented models include phase field :cite:`BoettingerReview:2002`
dendritic, and electrochemical phase transformations, as well as drug
eluting stents :cite:`Saylor:2011p2794`, reactive wetting :cite:`PhysRevE.82.051601`,
photovoltaics :cite:`Hangarter:2011p2795` and a level set treatment of the
electrodeposition process :cite:`NIST:damascene:2001`.

.. only:: latex

The latest information about :term:`FiPy` can be found at
http://www.ctcms.nist.gov/fipy/.

---------------------------------
Even if you don't read manuals...
---------------------------------

as :mod:`examples.diffusion.mesh1D`.

--------------------------------
What's new in version |release|?
--------------------------------

The significant changes since version 3.0 are:

- Level sets are now handled by :ref:`LSMLIBDOC` or :ref:`SCIKITFMM`
solver libraries. These libraries are orders of magnitude faster than the
original, :term:`Python`-only prototype.
- The :term:`Matplotlib` :func:`streamplot()` function can be used to display
vector fields.
- Version control was switched to the Git_ distributed version control
system. This system should make it much easier for :term:`FiPy` users to
participate in development.

Tickets fixed in this release::

62 "Move 'ImplicitDiffusionTerm().solve(var) == 0' ""failure"" from examples.phase.simple to examples.diffusion.mesh1D?"
118 subscriber()._markStale() AttributeError
138 `numerix.dot` doesn't support tensors
143 "Trying to ""solve"" an integer `CellVariable` should raise an error"
195 broken arithmetic face to cell distance calculations
197 ~binOp doesn't work on branches/version-2_0
305 add rhie chow correction term in stokes cavity example
321 Windows interactive plotting mostly broken
324 --pysparse configuration should never attempt MPI imports
341 Fix fipy.terms._BinaryTerm test failure in parallel
365 Rename GridXD
370 Epetra Norm2 failure in parallel
383 move FiPy to distributed version control
385 `diffusionTerm._test()` requires PySparse
391 efficiency_test chokes on liquidVapor2D.py
432 LSMLIB refactor
441 Explicit convetion terms should fail when the equation has no TransientTerm (dt=None)
445 getFaceCenters() should return a FaceVariable
448 Gmsh2D does not respect background mesh
452 Gmsh background mesh doesn't work in parallel
453 faceValue as FaceCenters gives inline failures
454 Assorted errors
456 Web page links seem to be broken
460 Clean up interaction between dependencies and installation process
461 SvnToGit clean up
462 Fix for test failures on loki
465 sign issues for equation with transient, convection and implicit terms
466 "multiplying equation by ""x"" changes the solution"
469 text in source:trunk/examples/convection/source.py is out of date
470 Include mailing list activity frame on front page
473 Gmsh importer can't read mesh elements with no tags
475 getVersion() fails on Py3k
477 Update Ohloh to point at git repo
480 link to mailing list is wrong
481 constrain should return a handle to the constraint for later deletion
484 NIST CSS changed
486 Using `Popen('gmsh ...', shell=True)` rather than `shell=False` security danger
490 Parallel bug in non-uniform grids and conflicting mesh class and factory function names
491 Rename communicator instances
492 unOps can't be pickled
493 Change documentation to promote use of stackoverflow
494 Viewers don't inline well in IPython notebook
496 FIPY_DISPLAY_MATRIX is broken
497 examples/phase/binary.py has problems
513 convection problem with cylindrical grid
539 Bug with numpy 1.7.0
557 NumPy 1.7.0 doesn't have _formatInteger
564 VanLeerConvectionTerm MinMod slope limiter is broken
638 numpy 1.7.1 test failures with physicalField.py
639 Neumann boundary conditions not clearly documented
641 Add support for Matplotlib streamplot
648 Peclet inequalities have the wrong sign
650 CylindricalNonUniformGrid2D doesn't make a FaceVariable for exteriorFaces
652 Documentation change for Ubuntu install
654 Switch to sphinxcontrib-bibtex

.. warning::

:term:`FiPy` 3 brought unavoidable syntax changes from :term:`FiPy` 2.
Please see :mod:`examples.updating.update2_0to3_0` for guidance on the
changes that you will need to make to your :term:`FiPy` 2.x scripts.

.. _Git: http://git-scm.com/

-------------------------
-------------------------

installation. :term:`FiPy` can be redistributed and/or modified
freely, provided that any derivative works bear some notice that they
are derived from it, and any modified versions bear some notice that
they have been modified.

-------
Support
-------

You can communicate with the :term:`FiPy` developers and with other
users via our `mailing list`_ and we welcome you to use the `issue
tracker`_ for bugs, support requests, feature requests and patch
submissions <https://github.com/usnistgov/fipy/issues>. We also monitor
StackOverflow_ for questions tagged with "fipy". We welcome
collaborative efforts on this project.

:term:`FiPy` is a member of MatForge_, a project of the `Materials
Digital Library Pathway`_. This National Science Foundation funded
service provides a "wiki" space for public contributions of
code snippets, discussions, and tutorials and hosts our testing framework.

.. toctree::

documentation/MAIL

------------------------
Conventions and Notation
------------------------

:term:`FiPy` is driven by :term:`Python` script files than you can view or modify in any
text editor. :term:`FiPy` sessions are invoked from a command-line shell, such
as :command:`tcsh` or :command:`bash`.

Throughout, text to be typed at the keyboard will appear ``like this``.
Commands to be issued from an interactive shell will appear::

\$ like this

where you would enter the text ("``like this``") following the shell prompt,
denoted by "``\$``".

Text blocks of the form::

>>> a = 3 * 4
>>> a
12
>>> if a == 12:
... print "a is twelve"
...
a is twelve

are intended to indicate an interactive session in the :term:`Python` interpreter.
We will refer to these as "interactive sessions" or as "doctest blocks".
The text "``>>>``" at the beginning of a line denotes the *primary prompt*,
calling for input of a :term:`Python` command. The text "``...``" denotes the
*secondary prompt*, which calls for input that continues from the line
above, when required by :term:`Python` syntax. All remaining lines, which begin
at the left margin, denote output from the :term:`Python` interpreter. In all
cases, the prompt is supplied by the :term:`Python` interpreter and should not be
typed by you.

.. warning::

:term:`Python` is sensitive to indentation and care should be taken to enter
text exactly as it appears in the examples.

When references are made to file system paths, it is assumed that the
current working directory is the :term:`FiPy` distribution directory, refered to
as the "base directory", such that::

will correspond to, *e.g.*::

Paths will always be rendered using POSIX conventions (path elements
separated by "``/``"). Any references of the form::

are in the :term:`Python` module notation and correspond to the equivalent POSIX
path given above.

We may at times use a

.. note::

to indicate something that may be of interest

or a

.. warning::

to indicate something that could cause serious problems.

.. _MML: http://www.nist.gov/mml/
.. _CTCMS: http://www.ctcms.nist.gov/
.. _MSED: http://www.nist.gov/mml/msed/
.. _NIST: http://www.nist.gov/
.. _issue tracker: https://github.com/usnistgov/fipy/issues
.. _mailing list: http://www.ctcms.nist.gov/fipy/documentation/MAIL.html
.. _Sourceforge: http://www.sourceforge.net/projects/fipy
.. _Materials Digital Library Pathway: http://matdl.org
.. _MatForge: http://matforge.org/
.. _StackOverflow: http://stackoverflow.com/questions/tagged/fipy