dolfin team mailing list archive

[Marie Rognes <meg@xxxxxxxxxxx>]

Anders Logg wrote:
> On Sun, Aug 10, 2008 at 03:54:25PM +0200, Evan Lezar wrote:
>   
> > Hi there
> >
> > After some time away I have once again been able to try and get do grips with
> > dolfin.  By a bit of a round about way I was able to solve a magnetic-field
> > based eigenvalue problem giving me the cutoff wavenumbers for a square
> > waveguide structure - it is still, however, a work in progress.
> >
> > One question I do have is regarding the visualization of the results I have
> > obtained.  To this end I have two questions - the first is simply the
> > visualization of the basis functions (vector Nedelec) themselves (see the
> > attached image taken from Finite Element Method for Electromagnetics by Volakis
> > et al) - how could this be achieved in dolfin?  Put another way - how can I set
> > the coefficient for a single basis function equal to 1 and zero the rest and
> > display the result?
> >     
>
> Marie Rognes has code for doing just this (plotbases.py in the
> bdm-2007 repository). I don't want to post it myself, but I imagine
> she would be willing to post the code. Marie?
>
>   

Of course!  If it is still interesting, see the attached python script.  
It just extracts the values of the basis functions at a suitable set of 
points on a triangle and gives output for use with matlab plotting.

Try something like

    python plot_bases.py > plot_bases.m
  
and run plot_basis.m in matlab.
  

--
Marie E. Rognes
Ph.D Fellow, 
Centre of Mathematics for Applications, 
University of Oslo
http://folk.uio.no/meg

# Marie Rognes 2007-10-24

# Extract the values of the Nedelec 0 basis functions at certain
# points and output for easy matlab plotting.

from ffc.fem.finiteelement import *
from ffc.fem.vectorelement import *

element = FiniteElement("Nedelec", "triangle", 0)
spacedim = 3

# Number of points for plotting:
n = 8
h = 1.0/n
x = [ 1.0*h*i for i in range(n+1)]
y = [ 1.0*h*i for i in range(n+1)]

points = []
for i in range(n+1):
    for j in range(n+1-i):
        points += [[x[i], y[j]]]
                   
print "figure"
for num in range(spacedim):
    U = []
    V = []
    X = []
    Y = []
    for point in points:
        X += [point[0]]
        Y += [point[1]]
        values = element.tabulate(0, [point])
        numpyvalue = [values[i][0][(0,0)][num] for i in range(len(values))]
        U += [numpyvalue[0][0]]
        V += [numpyvalue[1][0]]
        
    print "X  =", X
    print "Y = ", Y
    print "U = ", U
    print "V = ", V
    print "subplot(1, %d, %d)" % (spacedim, num+1)
    print "quiver(X, Y, U, V)"
    print "axis square"
    print "grid on"
    print