This tutorial is part of viskex.

Plot subdomains mesh sets of a 3D firedrake mesh

import firedrake

import viskex

import common_01_firedrake as common  # isort: skip

Generate meshes of the unit cube by dividing each edge of the cube in 6 segments, using either a tetrahedral or hexahedral mesh.

cube_tetra = firedrake.UnitCubeMesh(
    6, 6, 6, hexahedral=False, distribution_parameters={"partitioner_type": "simple"})
cube_hexa = firedrake.UnitCubeMesh(
    6, 6, 6, hexahedral=True, distribution_parameters={"partitioner_type": "simple"})

Mark subdomains according to the $(x, y, z)$ position of the vertices of the mesh:

• if $x \leq \frac{1}{3}$, assign subdomain mesh tag equal to $1$;
• if $x \geq \frac{2}{3}$, assign subdomain mesh tag equal to $2$;
• otherwise, leave the subdomain mesh tag unassigned.

cube_tetra_with_subdomains = common.mark_subdomains(cube_tetra)
cube_hexa_with_subdomains = common.mark_subdomains(cube_hexa)

We plot the resulting subdomains.

viskex.firedrake.plot_mesh_sets(cube_tetra_with_subdomains, 3, "subdomains")

viskex.firedrake.plot_mesh_sets(cube_hexa_with_subdomains, 3, "subdomains")

We can also plot all subdomains that belong to the mesh set $2$, which will be displayed with colors. The rest of the mesh cells are still included in the plot, but are colored in gray.

viskex.firedrake.plot_mesh_sets(
    cube_tetra_with_subdomains, 3, "subdomains_2", viskex.utils.pyvista.values_in([2]))

viskex.firedrake.plot_mesh_sets(
    cube_hexa_with_subdomains, 3, "subdomains_2", viskex.utils.pyvista.values_in([2]))

Alternatively, we can clip the plot so that it only shows the subset of the mesh with subdomain set equal to $2$.

viskex.firedrake.plot_mesh_sets(
    cube_tetra_with_subdomains, 3, "subdomains_2", lambda grid: grid.threshold(2))

viskex.firedrake.plot_mesh_sets(
    cube_hexa_with_subdomains, 3, "subdomains_2", lambda grid: grid.threshold(2))

The mesh sets are stored as part of the firedrake mesh object. If the mesh sets get removed, all cells will be displayed in gray in the plot.

cube_tetra.topology_dm.removeLabel(firedrake.cython.dmcommon.CELL_SETS_LABEL)
cube_hexa.topology_dm.removeLabel(firedrake.cython.dmcommon.CELL_SETS_LABEL)

viskex.firedrake.plot_mesh_sets(cube_tetra, 3, "subdomains")

/usr/local/lib/python3.12/dist-packages/pyvista/plotting/mapper.py:683: RuntimeWarning: All-NaN axis encountered
  clim = [np.nanmin(scalars), np.nanmax(scalars)]

viskex.firedrake.plot_mesh_sets(cube_hexa, 3, "subdomains")

/usr/local/lib/python3.12/dist-packages/pyvista/plotting/mapper.py:683: RuntimeWarning: All-NaN axis encountered
  clim = [np.nanmin(scalars), np.nanmax(scalars)]

What's next?

• next step: plot boundaries
• repeat this step with dolfinx