.. image:: https://app.codacy.com/project/badge/Grade/bd772b3ca7134651a9225d8051db8c41 :target: https://www.codacy.com/gh/spectralDNS/shenfun/dashboard?utm_source=github.com&utm_medium=referral&utm_content=spectralDNS/shenfun&utm_campaign=Badge_Grade .. image:: https://dev.azure.com/spectralDNS/shenfun/_apis/build/status/spectralDNS.shenfun?branchName=master :target: https://dev.azure.com/spectralDNS/shenfun .. image:: https://github.com/spectralDNS/shenfun/workflows/github-CI/badge.svg?branch=master :target: https://github.com/spectralDNS/shenfun .. image:: https://codecov.io/gh/spectralDNS/shenfun/branch/master/graph/badge.svg :target: https://codecov.io/gh/spectralDNS/shenfun .. image:: https://anaconda.org/conda-forge/shenfun/badges/platforms.svg :target: https://anaconda.org/conda-forge/shenfun .. |binder| image:: https://mybinder.org/badge_logo.svg :target: https://mybinder.org/v2/gh/spectralDNS/shenfun/master?filepath=binder
Try it in a jupyter hub using Binder
Shenfun is a high performance computing platform for solving partial differential equations (PDEs) by the spectral Galerkin method. The user interface to shenfun is very similar to
FEniCS <https://fenicsproject.org>, but applications are limited to multidimensional tensor product grids, using either Cartesian or curvilinear grids (e.g., but not limited to, polar, cylindrical, spherical or parabolic). The code is parallelized with MPI through the
mpi4py-fft <https://bitbucket.org/mpi4py/mpi4py-fft> package.
Shenfun enables fast development of efficient and accurate PDE solvers (spectral order and accuracy), in the comfortable high-level Python language. The spectral accuracy is ensured by using high-order global orthogonal basis functions (Fourier, Legendre, Chebyshev first and second kind, Ultraspherical, Jacobi, Laguerre and Hermite), as opposed to finite element codes that are using low-order local basis functions. Efficiency is ensured through vectorization (
Numpy <https://www.numpy.org/>), parallelization (
mpi4py <https://bitbucket.org/mpi4py/mpi4py>) and by moving critical routines to
Cython <https://cython.org/> or
Numba <https://numba.pydata.org>. Shenfun has been used to run turbulence simulations (Direct Numerical Simulations) on thousands of processors on high-performance supercomputers, see the
spectralDNS <https://github.com/spectralDNS/spectralDNS>_ repository.
The demo folder contains several examples for the Poisson, Helmholtz and Biharmonic equations. For extended documentation and installation instructions see
ReadTheDocs <http://shenfun.readthedocs.org>. For interactive demos, see the
jupyter book <https://mikaem.github.io/shenfun-demos>. Note that shenfun currently comes with the possibility to use two non-periodic directions (see
biharmonic demo <https://github.com/spectralDNS/shenfun/blob/master/demo/biharmonic2D_2nonperiodic.py>), and equations may be solved coupled and implicit (see
Note that shenfun works with curvilinear coordinates. For example, it is possible to solve equations on a
sphere <https://github.com/spectralDNS/shenfun/blob/master/demo/sphere_helmholtz.py> (using spherical coordinates), on the surface of a
torus <https://github.com/spectralDNS/shenfun/blob/master/binder/Torus.ipynb>, on a
Möbius strip <https://mikaem.github.io/shenfun-demos/content/moebius.html> or along any
curved line in 2D/3D <https://github.com/spectralDNS/shenfun/blob/master/demo/curvilinear_poisson1D.py>. Actually, any new coordinates may be defined by the user as long as the coordinates lead to a system of equations with separable coefficients. After defining new coordinates, operators like div, grad and curl work automatically with the new curvilinear coordinates. See also
this notebook on the sphere <https://github.com/spectralDNS/shenfun/blob/master/binder/sphere-helmholtz.ipynb> or an illustration of the
vector Laplacian <https://github.com/spectralDNS/shenfun/blob/master/binder/vector-laplacian.ipynb>.
.. image:: https://cdn.jsdelivr.net/gh/spectralDNS/spectralutilities@master/figures/moebius8_trans.png :target: https://mikaem.github.io/shenfun-demos/content/moebius.html :alt: The eigenvector of the 8'th smallest eigvalue on a Möbius strip .. image:: https://cdn.jsdelivr.net/gh/spectralDNS/spectralutilities@master/figures/smallcoil2.png :alt: Solution of Poisson's equation on a Coil .. image:: https://cdn.jsdelivr.net/gh/spectralDNS/spectralutilities@master/figures/spherewhite4.png :target: https://mikaem.github.io/shenfun-demos/content/sphericalhelmholtz.html :alt: Solution of Poisson's equation on a spherical shell .. image:: https://cdn.jsdelivr.net/gh/spectralDNS/spectralutilities@master/figures/torus2.png :target: https://github.com/spectralDNS/shenfun/blob/master/binder/Torus.ipynb :alt: Solution of Poisson's equation on the surface of a torus
For a more psychedelic experience, have a look at the
simulation <https://github.com/spectralDNS/shenfun/blob/master/demo/Ginzburg_Landau_sphere_IRK3.py>_ of the Ginzburg-Landau equation on the sphere (click for Youtube-video):
.. image:: https://cdn.jsdelivr.net/gh/spectralDNS/spectralutilities@master/figures/GLimage.png :target: https://youtu.be/odsIoHVcqek :alt: Ginzburg-Landau spherical coordinates
Shenfun can also be used to approximate analytical functions with global spectral basis
functions <https://mikaem.github.io/shenfun-demos/content/functions.html>, and to integrate over highly complex domains, like the seashell below, see
this demo <https://mikaem.github.io/shenfun-demos/content/surfaceintegration.html>.
.. image:: https://cdn.jsdelivr.net/gh/spectralDNS/spectralutilities@master/figures/seashell3.png :alt: The surface of a seashell
Shenfun can be installed using either
pip <https://pypi.org/project/pip/> or
conda <https://conda.io/docs/>, see
installation chapter on readthedocs <https://shenfun.readthedocs.io/en/latest/installation.html>_.
* `Python <https://www.python.org/>`_ 3.3 or above. Test suits are run with Python 3.7, 3.8 and 3.9. * A functional MPI 2.x/3.x implementation like `MPICH <https://www.mpich.org>`_ or `Open MPI <https://www.open-mpi.org>`_ built with shared/dynamic libraries. * `FFTW <http://www.fftw.org/>`_ version 3, also built with shared/dynamic libraries. * Python modules: * `Numpy <https://www.numpy.org/>`_ * `Scipy <https://www.scipy.org/>`_ * `Sympy <https://www.sympy.org>`_ * `Cython <https://cython.org/>`_ * `mpi4py <https://bitbucket.org/mpi4py/mpi4py>`_ * `mpi4py-fft <https://bitbucket.org/mpi4py/mpi4py-fft>`_
For comments, issues, bug-reports and requests, please use the issue tracker of the current repository, or see
How to contribute? <https://shenfun.readthedocs.io/en/latest/howtocontribute.html>_ at readthedocs. Otherwise the principal author can be reached at::
Mikael Mortensen mikaem at math.uio.no https://mikaem.github.io/ Department of Mathematics University of Oslo Norway