A FEniCS Tutorial - FEniCS Project

dev = numpy.abs(w_e.vector().array() - w.vector().array()).max()
print ’sigma=%g: max deviation=%e’ % (sigma, dev)
# Should be at the end
interactive()
Choosing a small width σ (say 0.01) and a location (x 0 ,y 0 ) toward the
circular boundary (say (0.6Rcosθ,0.6Rsinθ) for any θ ∈ [0,2π]), may produce
an exciting visual comparison of w and f that demonstrates the very smoothed
elastic response to a peak force (or mathematically, the smoothing properties
of the inverse of the Laplace operator). One needs to experiment with the
mesh resolution to get a smooth visual representation of f. You are strongly
encouraged to play around with the plots and different mesh resolutions.
1.8 Quick Visualization with VTK
As we go along with examples it is fun to play around with plot commands
and visualize what is computed. This section explains some useful visualization
features.
The plot(u) command launches a FEniCS component called Viper, which
applies the VTK package to visualize finite element functions. Viper is not a
full-fledged, easy-to-use front-end to VTK (like Mayavi2, ParaView or, VisIt),
but rather a thin layer on top of VTK’s Python interface, allowing us to quickly
visualize a DOLFIN function or mesh, or data in plain Numerical Python arrays,
within a Python program. Viper is ideal for debugging, teaching, and
initial scientific investigations. The visualization can be interactive, or you can
steer and automate it through program statements. More advanced and professional
visualizations are usually better done with advanced tools like Mayavi2,
ParaView, or VisIt.
We have made a program membrane1v.py for the membrane deflection problem
in Section 1.7 and added various demonstrations of Viper capabilities. You
are encouraged to play around with membrane1v.py and modify the code as you
read about various features.
The plot function can take additional arguments, such as a title of the plot,
or a specification of a wireframe plot (elevated mesh) instead of a colored surface
plot:
plot(mesh, title=’Finite element mesh’)
plot(w, wireframe=True, title=’solution’)
The three mouse buttons can be used to rotate, translate, and zoom the
surface. Pressing h in the plot window makes a printout of several key bindings
that are available in such windows. For example, pressing m in the mesh plot
window dumps the plot of the mesh to an Encapsulated PostScript (.eps) file,
while pressing i saves the plot in PNG format. All plotfile names are automatically
generated as simulationX.eps, where X is a counter 0000, 0001, 0002,
etc., being increased every time a new plot file in that format is generated (the
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