Python Bindings for the DUNE-FEM module

dune-fempy aims to provide Python bindings for the dune-fem discretization module. Here an example for solving Poisson's equation:

import math
from ufl import *
import dune.ufl
import dune.create as create

grid = create.grid("ALUConform", dune.grid.cartesianDomain([0, 0], [1, 1], [8, 8]), dimgrid=2)

# set up a diffusion reaction model using UFL
uflSpace = dune.ufl.Space((grid.dimGrid, grid.dimWorld), 1, field="double")
u = TrialFunction(uflSpace)
v = TestFunction(uflSpace)
x = SpatialCoordinate(uflSpace.cell())
a = (inner(grad(u), grad(v)) + inner(u,v)) * dx
# provide an exact solution that will be used to add suitable forcing and dirichlet b.c.
exact = as_vector( [cos(2.*pi*x[0])*cos(2.*pi*x[1])] )
model = create.model("elliptic", grid, a==0, exact=exact, dirichlet={ 1:exact } )

# set up a space and a conforming finite element scheme and solve the PDE
space  = dune.create.space("Lagrange", grid, dimrange=1, order=1)
scheme = create.scheme("h1", space, model, "cg")
uh,info = scheme.solve()

# make 'exact' into a grid function for output and uh into an UFL coefficient for error computation
exact_gf = create.function("ufl", grid, "exact", 5, exact)
uh_coeff = dune.ufl.GridCoefficient(uh)
# now define a grid function representing the pointwise error
l2error_gf = create.function("ufl", grid, "error", 5, as_vector([(exact[0]-uh_coeff[0])**2]) )

error = math.sqrt( l2error_gf.integrate() )
print("size:",grid.size(0),"L2-error:",error)
grid.writeVTK("laplace", pointdata=[ uh, l2error_gf, exact_gf ])

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Dependencies

dune-fempy depends on the following DUNE modules:

• dune-common 2.7+
• dune-geometry 2.7+
• dune-grid 2.7+
• dune-corepy 2.7+
• dune-fem 2.7+

In addition to the dependencies of these DUNE modules, the following software packages are required:

• a C++14 compatible C++ compiler (e.g., GCC 4.9+, clang 3.5+)
• Python 2.7+

We strongly recommend installing the following Pyhton packages to make full use of dune-fempy:

• numpy
• mpi4py
• ufl (2016.1.0+)

Quick Dive-In Using Docker

Users who simply want to use the functionality of dune-fempy as-is, e.g., for experimenting, can do so using Docker and a web browser.

To run the docker container with the latest release just type

docker run --rm -v dune:/dune -p 127.0.0.1:8888:8888 registry.dune-project.org/dune-fem/dune-fempy

at the command prompt and connect to localhost:8888 using your favorite web browser. Log into Jupyter using the password dune and have fun. The development version can be accessed using the unstable tag, i.e.,

docker run --rm -v dune:/dune -p 127.0.0.1:8888:8888 registry.dune-project.org/dune-fem/dune-fempy:unstable

For your convenience, the demo notebooks are provided in the folder dune-fempy.

With the above command, your notebooks will be kept persistent in a Docker volume called dune. To remove this volume, simply type

docker volume rm dune

at the command prompt.

To share python scripts and other files located in the current directory and also share the output with the docker container use

docker run -it -v $PWD:/home/dune/work registry.dune-project.org/dune-fem/dune-fempy bash

The content of the current directory is then available in the work directory in the docker volume.

Note for MAC users: docker on MAC allocates 2GB to docker by default which does not suffice for compiling the Dune shared libraries. Please increase the value to at least 3GB.

Installation

To download/install dune-fempy on your system follow the instructions in dune-python. After building dune-fempy add the python folder in the build directory to your PYTHON_PATH or (having set the cmake PYTHON_INSTALL_LOCATION flag) use the setup-dunepy.py script or call make python_install1 in the build directory of dune-fempy to install the dune-fem part of the Dune python package.