This tutorial is part of viskex.

Plot subdomains mesh sets of a 3D firedrake mesh

import firedrake

import viskex

import common_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)
cube_hexa = firedrake.UnitCubeMesh(6, 6, 6, hexahedral=True)

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")

error: XDG_RUNTIME_DIR is invalid or not set in the environment.
MESA: error: ZINK: failed to choose pdev
glx: failed to create drisw screen

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

error: XDG_RUNTIME_DIR is invalid or not set in the environment.

MESA: error: ZINK: failed to choose pdev
glx: failed to create drisw screen

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.values_in([2]))

error: XDG_RUNTIME_DIR is invalid or not set in the environment.
MESA: error: ZINK: failed to choose pdev
glx: failed to create drisw screen

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

error: XDG_RUNTIME_DIR is invalid or not set in the environment.
MESA: error: ZINK: failed to choose pdev
glx: failed to create drisw screen

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))  # type: ignore[no-untyped-call]

error: XDG_RUNTIME_DIR is invalid or not set in the environment.
MESA: error: ZINK: failed to choose pdev
glx: failed to create drisw screen

viskex.firedrake.plot_mesh_sets(
    cube_hexa_with_subdomains, 3, "subdomains_2",
    lambda grid: grid.threshold(2))  # type: ignore[no-untyped-call]

error: XDG_RUNTIME_DIR is invalid or not set in the environment.
MESA: error: ZINK: failed to choose pdev
glx: failed to create drisw screen

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")

/home/firedrake/firedrake/lib/python3.12/site-packages/pyvista/plotting/mapper.py:669: RuntimeWarning: All-NaN axis encountered
  clim = [np.nanmin(scalars), np.nanmax(scalars)]
error: XDG_RUNTIME_DIR is invalid or not set in the environment.
MESA: error: ZINK: failed to choose pdev
glx: failed to create drisw screen

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

/home/firedrake/firedrake/lib/python3.12/site-packages/pyvista/plotting/mapper.py:669: RuntimeWarning: All-NaN axis encountered
  clim = [np.nanmin(scalars), np.nanmax(scalars)]
error: XDG_RUNTIME_DIR is invalid or not set in the environment.
MESA: error: ZINK: failed to choose pdev
glx: failed to create drisw screen

What's next?

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