A FEniCS Tutorial - FEniCS Project

UnitSquare to make the mesh object. The result u_box is a BoxField object
that supports ”finite difference” indexing and an underlying grid suitable for
numpy operations on 2D data. Also 1D and 3D meshes (with linear elements)
can be turned into BoxField objects.
The ability to access a finite element field in the way one can access a finite
difference-type of field is handy in many occasions, including visualization and
data analysis. Here is an example of writing out the coordinates and the field
valueatagridpointwithindicesiandj(goingfrom0tonxandny,respectively,
from lower left to upper right corner):
X = 0; Y = 1; Z = 0 # convenient indices
i = nx; j = ny # upper right corner
print ’u(%g,%g)=%g’ % (u_box.grid.coor[X][i],
u_box.grid.coor[Y][j],
u_box.values[i,j])
For instance, the x coordinates are reached by u_box.grid.coor[X]. The grid
attribute is an instance of class UniformBoxGrid.
Many plotting programs can be used to visualize the data in u_box. Matplotlib
is now a very popular plotting program in the Python world and could
be used to make contour plots of u_box. However, other programs like Gnuplot,
VTK, and MATLAB have better support for surface plots at the time of this
writing. OurchoiceinthistutorialistousethePythonpackagescitools.easyviz,
which offers a uniform MATLAB-like syntax as interface to various plotting
packages such as Gnuplot, Matplotlib, VTK, OpenDX, MATLAB, and others.
With scitools.easyviz we write one set of statements, close to what one
would do in MATLAB or Octave, and then it is easy to switch between different
plotting programs, at a later stage, through a command-line option, a line in a
configuration file, or an import statement in the program.
A contour plot is made by the following scitools.easyviz command:
import scitools.easyviz as ev
ev.contour(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values,
5, clabels=’on’)
evtitle(’Contour plot of u’)
ev.savefig(’u_contours.eps’)
# or more compact syntax:
ev.contour(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values,
5, clabels=’on’,
savefig=’u_contours.eps’, title=’Contour plot of u’)
The resulting plot can be viewed in Figure 1.12a. The contour function needs
arrays with the x and y coordinates expanded to 2D arrays (in the same way as
demanded when making vectorized numpy calculations of arithmetic expressions
over all grid points). The correctly expanded arrays are stored in grid.coorv.
The above call to contour creates 5 equally spaced contour lines, and with
clabels=’on’ the contour values can be seen in the plot.
36