.. pyOptFEM documentation master file, created by
   sphinx-quickstart on Sun Sep 15 03:44:36 2013.
   You can adapt this file completely to your liking, but it should at least
   contain the root `toctree` directive.

Welcome to pyOptFEM's documentation!
====================================

**pyOptFEM** is a Python module which aims at measuring and comparing 
the performance of three programming techniques for **assembling finite element matrices in 2D and 3D**.
For each of the matrices studied, three assembly versions are available: ``base``, ``OptV1`` and ``OptV2``

Three matrices are currently implemented (more details are given in :ref:`FEM2D-label` and :ref:`FEM3D-label`) :

- **Mass matrix** :

  .. math::
    \mathbb{M}_{i,j}=\int_{\Omega_h} \varphi_j(q)\ \varphi_i(q)dq,\ \ \forall (i,j) \in \{1,...,\nq\}^2.
    
- **Stiffness matrix** : 

  .. math::
    \mathbb{S}_{i,j}=\int_{\Omega_h} \nabla\varphi_j(q).\nabla \varphi_i(q)dq,\ \ \forall (i,j) \in \{1,...,\nq\}^2.
    
- **Elastic stiffness matrix** :

  .. math::
    \mathbb{K}_{m,l}=\int_{\Omega_h} \underline{\pmb{\epsilon}}^t(\psi_l(q)) 
    \underline{\pmb{\sigma}}(\psi_m(q))dq,
    \ \ \forall (m,l) \in \{1,...,d\nq\}^2.
    
  where :math:`d` is the space dimension.
    
 

Contents:

.. toctree::
   :maxdepth: 2

   presentation
   benchmarks2D
   benchmarks3D
   FEM2D
   FEM3D
   valid2D
   valid3D

Quick testing
=============

To test the **pyOptFEM** library, you can run validation tests ``runValids()`` or some benchmarks (see ``runBenchs()``)

Testing and Working
===================
 - Ubuntu 12.04 LTS (x86_64) with

   - python3.3

   - python3.2

 - Works on Windows 7 64 bits (???)


Requirements
=============

**pyOptFEM** works with python3.3.

How to install python3.3.2?

A description of how to compile/install python3.3 under Ubuntu 12.04 LTS (x86_64) is given on `François Cuvelier's website <http://www.math.univ-paris13.fr/~cuvelier/>`_, (section Python in the left menu) and repeated here.

.. note:: 
  How to install python3.3.2 ::

    wget http://www.python.org/ftp/python/3.3.2/Python-3.3.2.tar.bz2
    tar jxvf ./Python-3.3.2.tar.bz2 
    cd Python-3.3.2
    ./configure --prefix=/opt/python3.3.2
    make
    sudo make install

As a result, python is installed in ``/opt/python3.3.2`` directory.


For **pyOptFEM**, you need some python modules. To install them you need easy_install which can be installed like this.

.. note:: 
    How to install setuptools module ::

      wget --check-certificate https://pypi.python.org/packages/source/s/setuptools/setuptools-1.1.4.tar.gz 
      tar zxvf setuptools-1.1.4.tar.gz 
      cd setuptools-1.1.4 
      sudo /opt/python3.3.2/bin/python3 setup.py install


For **pyOptFEM**, you need numpy, scipy, sympy and matplotlib. (For matplotlib, the package libfreetype6-dev may be necessary!)

.. note:: 
    How to install scientific computation modules : numpy, scipy, sympy, matplotlib ::

      sudo /opt/python3.3.2/bin/easy_install numpy 
      sudo /opt/python3.3.2/bin/easy_install scipy 
      sudo /opt/python3.3.2/bin/easy_install sympy 
      sudo /opt/python3.3.2/bin/easy_install matplotlib

Installation
============

.. note::
   To install **pyOptFEM** as root, you should run the following command: ::

     /opt/python3.3.2/bin/python3 setup.py install

.. note::
   To install **pyOptFEM** as a single user, you should run the following command: ::

     /opt/python3.3.2/bin/python3 setup.py install --user



License issues
==============

**pyOptFEM** is published under the terms of the `GNU General Public License <http://www.gnu.org/licenses/>`_.


**pyOptFEM** is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

**pyOptFEM** is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program.  If not, see http://www.gnu.org/licenses/.

Software using source files of this project or significant parts of it, should include the following attribution notice:

``--------------------------------------------------------------------``
 ATTRIBUTION NOTICE:
 This product includes software developed for the **pyOptFEM** project at
 (C) University Paris XIII, Galilee Institute, LAGA, France.

 **pyOptFEM** is a python software package for `P_1`-Lagrange Finite Element Methods in 3D. 
 The project is maintained by
 F. Cuvelier, C. Japhet and  G. Scarella.
 For Online Documentation and Download we refer to 
     http://www.math.univ-paris13.fr/~cuvelier
``--------------------------------------------------------------------``



Indices and tables
==================

* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`