Visualizing quadrature functions as point clouds

Author: Henrik N.T. Finsberg

SPDX-License-Identifier: MIT

Quadrature functions are not possible to visualize directly in ParaView, as they are not defined on a mesh. However, we can visualize them as point clouds. In this example we will show how you can use scifem to save your quadrature fuctions as XDMF files, which can be loaded into ParaView for visualization.

Note

This demo requires a backend for writing HDF5 files. Please install scifem with either scifem[adios2] or scifem[h5py].

First, we import the necessary modules.

from mpi4py import MPI
import numpy as np
import basix
import dolfinx
import scifem

Now let’s create a quadrature function on a unit square mesh. We will use the basix.ufl module to create the quadrature element.

mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10, dolfinx.mesh.CellType.triangle, dtype=np.float64)
el = basix.ufl.quadrature_element(
    scheme="default", degree=3, cell=mesh.ufl_cell().cellname(), value_shape=()
)
V = dolfinx.fem.functionspace(mesh, el)
u = dolfinx.fem.Function(V)
u.interpolate(lambda x: np.sin(np.pi * x[0]) * np.sin(np.pi * x[1]))

One option that already exists with the current DOLFINx/Pyvista API is to plot them as points

import pyvista

pyvista.start_xvfb()
plotter = pyvista.Plotter()
plotter.add_points(
    V.tabulate_dof_coordinates(),
    scalars=u.x.array,
    render_points_as_spheres=True,
    point_size=20,
    show_scalar_bar=False,
)
if not pyvista.OFF_SCREEN:
    plotter.show()

Using scifem, we can write the point cloud data to an XDMFFile that can be opened with Paraview.

scifem.xdmf.create_pointcloud("point_cloud.xdmf", [u])

The point cloud can now be loaded into ParaView for visualization, by selecting “Point Gaussian” as the representation.

We can write any dolfinx.fem.FunctionSpace that has support for tabulate_dof_coordinates to a point cloud. For example, we can create a higher order Lagrange space, and write two functions to file.

Q = dolfinx.fem.functionspace(mesh, ("Lagrange", 3, (2, )))
q_1 = dolfinx.fem.Function(Q, name="q_sin")
q_1.interpolate(lambda x: (np.sin(np.pi * x[0]),  np.sin(np.pi * x[1])))
q_2 = dolfinx.fem.Function(Q, name="q_cos")
q_2.interpolate(lambda x: (np.cos(np.pi * x[0]),  np.cos(np.pi * x[1])))

We write these two functions to file as illustrated above

scifem.xdmf.create_pointcloud("point_cloud_lagrange.xdmf", [q_1, q_2])

yielding the following point clouds in ParaView after applying glyphs.