Construct mapping operator (jacobian) to evaluate 3D Nedelec basis functions

[dokken]

@NicoSkibbe

To be sure: Is combining the transformation matrix (Jacobian) with the outcome of the “tabulate” method the correct way to evaluate, e.g., Nedelec basis functions, in dolfinx?

Yes. You would use the correct Piola transform to do this evaluation in “physical” space.

@NicoSkibbe

The “eval” method should require the same functionalities. Are the transformaion matrices build internally just-in-time or are they stored somethere and accessible using the Python interface?

They are built just-in-time and discarded after computation.

@NicoSkibbe

If it is not available: I already found this guide for 2D Advanced finite elements — FEniCS Workshop to manually build the Jacobian. Is there also an example available how to build the Jacobian for 3D Nedelec spaces using the Python interface?

You can use dolfinx.fem.Expression to evaluate your function in any point in physical space.
Expression takes in:

• Your expression: Say the test or trial function (or coefficient) you would like to evaluate
• Points in reference cell

Say:

v = ufl.TestFunction(V)
expr = dolfinx.fem.Expression(v, my_points_in_reference_element, comm=MPI.COMM_SELF)
expr.eval(mesh, np.array([my_cell_index, dtype=np.int32]))

This is for instance how PointSource is implemented in scifem:

src/scifem/point_source.py

which is based on my original post at:

Point Sources (Redux)

Following my post above, with a minor adaptations, a point source can be implemented as follows: # Create a point source for Poisson problem # Author: Jørgen S. Dokken # SPDX-License-Identifier: MIT from mpi4py import MPI from petsc4py import PETSc import dolfinx import dolfinx.fem.petsc import numpy as np import ufl def compute_cell_contributions(V, points): # Determine what process owns a point and what cells it lies within mesh = V.mesh _, _, owning_points, cells = dolfinx.cp…