Assigning piece-wise constant function to tensor function

Question

Hi!

I want to assign piece-wise constant functions to the components of a tensor. If I wanted to do this for a scalar function I would do the following

• define a mesh and subdomains therein
• define a 'DG' FunctionSpace of order 0 on the mesh
• define a function test
• loop over all cells and depending on the subdomain that the cell is in assign a value x to the function using test.vector()[cell_no] = x[subdomain]

This works fine for scalar functions. However, if I use a tensor function space how do I know which index of vector() corresponds to which cell AND component of my tensor?

Thank you very much for any help!

Answer 1

I use something like that in my script. I start off with a scalar function that labels the areas that I want to have a given constant vector. The mesh is created externally, but basically just labels material 1 with a 1, material 2 with a 2, material 3 with a 3. In the snippet below, I am trying to create the constant vector field for material 3:

D = FunctionSpace(mesh, "DG", 0)
cell_labels = MeshFunction("size_t", mesh, "material_type.xml.gz")
helper    = numpy.asarray(cell_labels.array(), dtype=numpy.int32) - 1
dm        = D.dofmap()
for cell in cells(mesh):
  helper[dm.cell_dofs(cell.index())] = cell_labels[cell] - 1
material_3_location = Function(D)
material_3_location.vector()[:] = numpy.choose(helper, [0., 0., 1.])

You can then make your piecewise constant function by projecting or interpolating.

V = FunctionSpace(mesh, "N1curl", 1)
V3 = project(Constant((0., 1., 0.))*material_3_location, V)