Entity markers

Author: Jørgen S. Dokken

SPDX-License-Identifier: MIT

DOLFINx gives you full control for marking entities. However, sometimes this can feel a bit repetative. In this example we will show how to use scifem.create_entity_markers().

from mpi4py import MPI
import dolfinx
import numpy as np

We start by creating a simple unit square

mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 60, 60)

Next, we want to mark some of the cells in our domain. We create three marker functions below. Each of them takes in a (3, num_points) array, and returns a boolean array of size num_points.

def left(x):
    return x[0] < 0.2

def right(x):
    return x[0] > 0.9

def inner(x):
    # We use numpy bit operator `&` for "and"
    return (x[0] > 0.3) & (x[0] < 0.7)

We want to mark these entities with with unique integers 1, 3 and 7.

from scifem import create_entity_markers

cell_tag = create_entity_markers(mesh, mesh.topology.dim, [(1, left), (3, right), (7, inner)])

Next we can plot these marked entities

import pyvista

pyvista.start_xvfb()
vtk_grid = dolfinx.plot.vtk_mesh(mesh, cell_tag.dim, cell_tag.indices)
grid = pyvista.UnstructuredGrid(*vtk_grid)
grid.cell_data["Marker"] = cell_tag.values

Create plotter

plotter = pyvista.Plotter()
plotter.add_mesh(grid)
plotter.view_xy()
if not pyvista.OFF_SCREEN:
    plotter.show()

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 mark lower order entities, such as facets

def circle(x):
    return x[0] ** 2 + x[1] ** 2 <= 0.16**2

def top(x):
    return x[1] > 0.9

facet_tags = create_entity_markers(mesh, mesh.topology.dim - 1, [(2, top), (7, circle)])

facet_grid = dolfinx.plot.vtk_mesh(mesh, facet_tags.dim, facet_tags.indices)

fgrid = pyvista.UnstructuredGrid(*facet_grid)
fgrid.cell_data["Marker"] = facet_tags.values

fplotter = pyvista.Plotter()
fplotter.add_mesh(fgrid)
fplotter.view_xy()
if not pyvista.OFF_SCREEN:
    fplotter.show()

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 exclude interior facets by adding on_boundary: True (by default this is set to False).

boundary_facet_tags = create_entity_markers(
    mesh, mesh.topology.dim - 1, [(2, top, True), (7, circle, False)]
)

boundary_grid = dolfinx.plot.vtk_mesh(mesh, boundary_facet_tags.dim, boundary_facet_tags.indices)

bfgrid = pyvista.UnstructuredGrid(*boundary_grid)
bfgrid.cell_data["Marker"] = boundary_facet_tags.values

bfplotter = pyvista.Plotter()
bfplotter.add_mesh(bfgrid)
bfplotter.view_xy()
if not pyvista.OFF_SCREEN:
    bfplotter.show()

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