Visualizing 2D and 3D vector and tensor data from firedrake in python

[Arijit-Majumdar]

Hi, I am trying to solve linear thermoelasticity problem in firedrake for both 2D and 3D geometries. My function space for displacement and solution function is as follows
V = VectorFunctionSpace(mesh, "CG", 1)
u_soln = Function(V)

Afterwards I am calculating the stress and the strain rate tensor using the following functions
def epsilon(u, Temp):
return 0.5*(grad(u) + grad(u).T) - alpha*Temp*Id

def sigma(u, Temp):
return lambda_*div(u)*Id + 2*mu*epsilon(u, Temp)

I wanted to know what is the syntax for plotting contours of different components of the displacement (u_soln) and stress/strain tensor in python? I tried the following lines for the vertical displacement but it gave me an error

tricontourf(u_soln[1], axes=axes)

Also, for a 3D domain, how do I get the displacement or stress/strain at a given plane (e.g. z = 0.5) and make a contour plot of specific components?

Thanks

[connorjward]

I don't know how to visualise a plane, but to visualise a component of a vector Function you want to use tricontourf(u_soln.sub(1), ...).

For the plane I guess you could build the array you wanted using point evaluation and then plot it with ordinary matplotlib routines.

[Arijit-Majumdar]

Thanks! Does the sub work with tensor as well. For example I am evaluating the strain rate as
epsilon = 0.5*(grad(u) + grad(u).T)
So for 2D problem epsilon will be 2 x 2 tensor at each mesh point. So if I want to plot epsilon[1][1] how should I use sub? The documentation says that sub takes only 1 argument.

[connorjward]

From reading the code it seems like you want to use epsilon.sub(3). I.e. flatten the multiindex to epsilon.sub(1*2 + 1). I agree this isn't at all clear.

[dham]

For serious plotting you should output to VTU and use paraview. This will give you a lot of plotting options beyond those which are in the basic built-in plotting functionality. It will also be vastly faster (especially in 3D).

[Arijit-Majumdar]

Thanks for the suggestion. Actually we are using Firedrake for teaching students in a Finite element course and wanted to keep all the coding and analysis in python for the ease of the students.