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pyiga |ghbuild| |appveyor| |codecov|

pyiga is a Python research toolbox for Isogeometric Analysis. Its current highlights are:

• Automatic generation of efficient matrix assembling code from a high-level, FEniCS_-like description of the bilinear form. See the section "Assembling custom forms" in the Documentation_ as well as the convection-diffusion and Navier-Stokes examples below.
• Adaptivity via HB- and THB-spline spaces and a local multigrid solver for adaptive IgA (read the paper <http://dx.doi.org/10.1093/imanum/drab041>). See adaptive.ipynb <notebooks/adaptive.ipynb> for an example.
• Fast assembling by a black-box low-rank assembling algorithm described in this paper <http://dx.doi.org/10.1016/j.cma.2018.01.014>_ (or this technical report <http://www.numa.uni-linz.ac.at/publications/List/2017/2017-02.pdf>_).
• Extensive support for fast tensor approximation methods for tensor product IgA.

To find out more, have a look at the Documentation_ and the examples below.

Examples

The notebooks directory contains several examples of how to use pyiga:

• geometry.ipynb <notebooks/geometry.ipynb>_: create and manipulate geometry functions
• solve-poisson.ipynb <notebooks/solve-poisson.ipynb>_: solve a Poisson equation and plot the solution
• multipatch.ipynb <notebooks/multipatch.ipynb>_: solve a Poisson equation in a multipatch domain
• solve-convdiff.ipynb <notebooks/solve-convdiff.ipynb>_: solve a convection-diffusion problem with random inclusions
• solve-stokes.ipynb <notebooks/solve-stokes.ipynb>_: solve stationary Stokes flow and plot the velocity field
• solve-navier-stokes.ipynb <https://nbviewer.jupyter.org/github/c-f-h/pyiga/blob/master/notebooks/solve-navier-stokes.ipynb>_: solve the instationary Navier-Stokes equations with a time-adaptive Rosenbrock integrator and produce an animation of the result
• adaptive.ipynb <https://nbviewer.jupyter.org/github/c-f-h/pyiga/blob/master/notebooks/adaptive.ipynb>_: an adaptive solve-estimate-mark-refine loop using a local multigrid solver.
• mantle-convection.ipynb <https://nbviewer.jupyter.org/gist/c-f-h/060f225465ee990faab4941a6cfd2562>_: Rayleigh-Bénard convection

Installation

pyiga is compatible with Python 3.6 and higher.

Before installing, make sure you have recent versions of Numpy, Scipy and Cython installed and that your environment can compile Python extension modules. Numpy 1.14 or higher is required. If you do not have such an environment set up yet, the easiest way to get it is by installing Anaconda_ (this can be done without administrator privileges).

Clone this repository and execute ::

$ python setup.py install

in the main directory. The installation script should now compile the Cython extensions and then install the package.

If you have Intel MKL installed on your machine, be sure to install the pyMKL package; if pyiga detects this package, it will use the MKL PARDISO sparse direct solver instead of the internal scipy solver (typically SuperLU).

Updating

If you have already installed the package and want to update to the latest
version, assuming that you have cloned it from Github, you can simply move to
the project directory and execute ::

    $ git pull
    $ python setup.py install

Running tests
-------------

`pyiga` comes with a small test suite to test basic functionality. Depending on
your test runner of choice, move to the main directory and execute
``nosetests`` or ``py.test`` to run the tests.

If the test runner fails to find the Cython extensions modules (``pyiga.bspline_cy`` etc.),
you may have to run ``python setup.py build_ext -i`` to build them in-place.

Usage
-----

After successful installation, you should be able to load the package. A simple example:

.. code:: python

    from pyiga import bspline, geometry, assemble

    kv = bspline.make_knots(3, 0.0, 1.0, 50)    # knot vector over (0,1) with degree 3 and 50 knot spans
    geo = geometry.quarter_annulus()            # a NURBS representation of a quarter annulus
    K = assemble.stiffness((kv,kv), geo=geo)    # assemble a stiffness matrix for the 2D tensor product
                                                # B-spline basis over the quarter annulus

There is a relatively complete `Documentation`_. Beyond that, look at the code,
the unit tests, and the `IPython notebooks`_ to learn more.


.. _IPython notebooks: ./notebooks
.. _Documentation: http://pyiga.readthedocs.io/en/latest/
.. _FEniCS: https://fenicsproject.org/
.. _Anaconda: https://www.anaconda.com/distribution/

FAQ
---

During compilation, I get an error message involving ``numpy._build_utils``.
~~~~~

Try installing/upgrading setuptools: ::

    $ pip install --upgrade setuptools