Add maximum marking

[schnellerhase]

Implements a maximum marking criterion for AFEM schemes, i.e. for $\theta \in (0, 1)$ and a marker $\eta \in \mathbb{R}^N$, computes

$$ \mathcal{I} = \left\{ i \ | \ \eta_i > \theta \max_j \eta_j \right\}. $$

In particular this introduces/defines the interface for other marking routines (to follow in the future): based on a process local list of (entity-)indicators the (local) marked index set of it is computed.

Test program to visualise results (parallel ready).

from mpi4py import MPI

import numpy as np

from dolfinx import mesh, plot
import pyvista as pv

mesh_0 = mesh.create_unit_square(comm := MPI.COMM_WORLD, n := 10, n)

cell_im = mesh_0.topology.index_map(tdim := mesh_0.topology.dim)
cell_count = cell_im.size_local + cell_im.num_ghosts

marker = np.random.random(cell_count)
marked_cells = mesh.mark_maximum(marker, theta := 0.5, comm)

mesh_0.topology.create_entities(1)
marked_edges = mesh.compute_incident_entities(mesh_0.topology, marked_cells, tdim, 1)

mesh_1, _, _ = mesh.refine(mesh_0, marked_edges)

grid_0 = pv.UnstructuredGrid(*plot.vtk_mesh(mesh_0))
grid_1 = pv.UnstructuredGrid(*plot.vtk_mesh(mesh_1))

plotter = pv.Plotter(shape=(1, 2))
plotter.subplot(0, 0)
plotter.add_mesh(grid_0, show_edges=True)
plotter.view_xy()
plotter.add_text("mesh_0", position="upper_left")

plotter.subplot(0, 1)
plotter.add_mesh(grid_1, show_edges=True)
plotter.view_xy()
plotter.add_text("mesh_1", position="upper_left")

plotter.link_views()
plotter.show()

Work towards #4141.

outdated

[jhale]

My comments on the floating point comparisons are not resolved.

[chrisrichardson]

@jhale - I think @schnellerhase did address it. Did you mean that it should be a simple > rather than >=?

[jhale]

Yes - the equality is completely redundant in a floating point context and the example given is a contrived one.

[jorgensd]

Should there be something more at the end of this test ?

[schnellerhase]

I just wanted to check that the input works as expected with the refine calls - so the test being "refine works". Not sure what to exactly test for on the refined mesh, up to it being a mesh.