Using locate_cell() mesh method on vertex of cell

[jmm1828]

I am trying to use locate_cell on the nodes of a mesh to see which cells they correspond to. But I ran into the problem that the method only returns one cell number.

Does anyone now a way around this? Any help would be much appreciated.

[wence-]

If you want the topological relationship, you are better off querying the topological mesh, rather than doing geometric searches. What do you want to do with the resulting information? One way to construct this in Python is to take a piecewise linear function space V = FunctionSpace(mesh, "P", 1) and then manually produce the inverse of the V.cell_node_map() whose values you can obtain with V.cell_node_map().values

[jmm1828]

Great, thank you for your help. I will look into tsfc.

[jmm1828]

If we create a mesh, say mesh=UnitSquareMesh(2,2).

Then we create the function space V = FunctionSpace(mesh, "P", 1) and manually produce the inverse of the V.cell_node_map().

Do the values in V.cell_node_map().values correspond with the position of the nodes in the array mesh.coordinates.dat.data?

[wence-]

yes. So if the first row has entries [0, 2, 3] that means the three vertices of the first cell are found at locations 0, 2, and 3 of the coordinate data

[wence-]

I thought this worked. And I think it does. But the relevant UFL geometry object is not correctly exported:

from firedrake import *
from ufl.classes import CellEdgeVectors # this object is not exported by UFL

mesh = UnitSquareMesh(2, 2)
cev = CellEdgeVectors(mesh)

expr = sum(outer(cev[i, :], cev[i, :]) for i in range(3))

cell_matrices = interpolate(expr, TensorFunctionSpace(mesh, "DG", 0, shape=(2, 2)))

Gives you what you want I think.

[jmm1828]

Thank you, it does seem to work. Is there any reason for using discontinuous Lagrange instead of any other space for TensorFunctionSpace?

[wence-]

Well, you want one value per cell, no?

[jmm1828]

Yes, thank you

[dham]

The purpose of locate_cell is to return a cell containing the point in question. This is to enable interpolation to work. Can you please describe more generally what you are trying to achieve. Usually, querying the internals of Firedrake is not the best way to achieve things.