How to use same vector-valued mathematical expressions with both ufl and numpy?

Hi all,

I’m using this kind of technique to avoid having to write an expression both in ufl (eg for generating the exact right hand side f) and numpy (eg for pointwise evaluations):

import dolfinx
import ufl
from mpi4py import MPI
import numpy as np

mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 5, 5)

def u_exact(m):
    return lambda x: m.sin(m.pi * x[0]) * m.sin(m.pi * x[1])

x = ufl.SpatialCoordinate(mesh)
f = ufl.div(ufl.grad(u_exact(ufl)(x)))
pts = np.array([[0.5, 0.1], [0.1, 0.9]])
u0 = u_exact(np)(pts)

What I cannot get to work is how to do this if u_exact is a vector-valued function. I’m trying to be clever with mixing np.stack and ufl.as_vector but without success. Is there an example somewhere I can look at?


For legacy dolfin there used to be GitHub - MiroK/ulfy: Traslate UFL to SymPy to Expression (ufl ↔ sympy, but then from sympy one could use sympy.lambdify to numpy). I am not aware of similar projects for dolfinx.

The fem.Expression mechanism would be a solution if your points are defined via the same coordinates on the reference element. I am not sure if something is similar with points defined by their global coordinates

Maybe this ?

For point evaluation, you need to specify what cell the point is in, as specified in: Implementation — FEniCSx tutorial

One can of course go through dolfinx.fem.Expression for more advanced code, such as shown in: Evaluation of UFL expression at mesh points - #2 by dokken and subsequent posts.

Other similar resources: