Periodic bc in 1d

Question

I have a 1d periodic space and I just interpolate some function and plot it. But this gives strange answer, please see

https://github.com/cpraveen/fenics/blob/master/1d/cosmic_ray/periodic_test.ipynb

What am I doing wrong ?

Answer 1

It looks like you plot the solution using matplotlib instead of the dolfin built-in visualization tool, see the output in Cell 5. So I guess commenting the '%matplotlib inline' line does solve your problem.
As an alternative approach, you can dump the solution to a .vtk file and check the results using e.g. ParaView.

Comments

dolfin has limited support for matplotlib as the plotting backend via plot(). E.g: plot(u, backend='matplotlib').

Answer 2

Using vtk as the plotting backend, I see no problems.

Furthermore, when I output the data, e.g: XDMFFile("u.xdmf").write(u), the results look fine.

It looks like this may be an issue with the matplotlib plotting backend and constrained domains.

Comments

I cannot get vtk plots to show when I run fenics in docker. I have to save to file and then open with paraview/visit, which is too much work to see a simple 1d plot. Hence I was trying with notebook.

Is there an easier way to plot 1d solutions ? Gnuplot output would have been ideal.

---

I could plot with matplotlib in notebook mode

https://github.com/cpraveen/fenics/blob/master/1d/cosmic_ray/periodic_test.ipynb

Here is the example

%matplotlib inline
%config InlineBackend.figure_format='svg'
import numpy as np
import matplotlib.pyplot as plt
from dolfin import *

# number of points
nc = 100

# Sub domain with periodicity
class PeriodicBoundary(SubDomain):
   def inside(self, x, on_boundary):
      return (near(x[0],0.0) and on_boundary)

   def map(self, x, y):
      y[0] = x[0] - 1.0

u0 = Expression("1.0+0.5*sin(2*pi*x[0])",degree=1)
mesh = UnitIntervalMesh(nc)
V = FunctionSpace(mesh, "CG", 1, constrained_domain=PeriodicBoundary())
u = Function(V)
u.interpolate(u0)
ua=u.vector().array()
x = V.tabulate_dof_coordinates()
i = np.argsort(x)
plt.plot(x[i],ua[i]);