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# # 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](https://jsdokken.com/FEniCS-workshop/src/deep_dive/expressions.html#evalation-at-a-point),
# 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)
# We can now evaluate the function at the points using the `evaluate_function` function.
u_values = evaluate_function(u, points)
print(u_values)
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