Evaluating a function at a point

Author: Henrik N.T. Finsberg

SPDX-License-Identifier: MIT

In this example we will show a how to to scifem for evaluating a function at a point. Note that the implementation is based on the approach outlined here, and users are encouraged to read this for more details.

Let us start by creating a rectangle mesh and a function space.

from mpi4py import MPI
import numpy as np
import dolfinx

from scifem import evaluate_function

comm = MPI.COMM_WORLD
Lx = Ly = 2.0
nx = ny = 10

mesh = dolfinx.mesh.create_rectangle(
    comm=comm,
    points=[np.array([0.0, 0.0]), np.array([Lx, Ly])],
    n=[nx, ny],
    cell_type=dolfinx.mesh.CellType.triangle
)

V = dolfinx.fem.functionspace(mesh, ("P", 1))
u = dolfinx.fem.Function(V)

Now let us interpolate a function \(f(x, y) = x + 2y\) into the function space. and use this as an example for evaluating the function at a set of points.

f = lambda x: x[0] + 2 * x[1]
u.interpolate(f)

Let us pick a few points to evaluate the function at.

points = np.array([[0.0, 0.0], [0.2, 0.2], [0.5, 0.5], [0.7, 0.2]])

The expected values of the function at the points are

exact = np.array(f(points.T)).T
print(exact)

[0.  0.6 1.5 1.1]

We can now evaluate the function at the points using the evaluate_function function.

u_values = evaluate_function(u, points)
print(u_values)

[[2.58507369e-17]
 [6.00000000e-01]
 [1.50000000e+00]
 [1.10000000e+00]]