Trial and test functions of mixed Nedelec and Lagrange element

dolfinx
1

I’m trying to port an old Dolfin program based on this paper to DolfinX.
System I’m trying to solve contains \vec{E} vector split into \vec{E}_\perp^\Re, \vec{E}_\perp^\Im, E_z^\Re and E_z^\Im parts. Therefore, to solve the problem I need a pair of vector test functions \vec{w}^\Re and \vec{w}^\Im and a pair of scalar test functions v^\Re and v^\Im.
The old code contained the following definition of test and trial functions for this problem:

Vtr = FiniteElement("Nedelec 1st kind H(curl)", mesh.ufl_cell(), 1)
Vlr = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
Vli = Vlr
Vti = Vtr
V = FunctionSpace(mesh, MixedElement([Vtr, Vti, Vlr, Vli]))
(uvr,uvi,usr,usi) = TrialFunctions(V)
(vvr,vvi,vsr,vsi) = TestFunctions(V)

This snippet is a MWE for DolfinX:

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

mesh = dolfinx.UnitSquareMesh(MPI.COMM_WORLD, 10, 10)

Hcurl = ufl.FiniteElement("Nedelec 1st kind H(curl)", mesh.ufl_cell(), 1)
H1 = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)

V = dolfinx.FunctionSpace(mesh, ufl.MixedElement(Hcurl, Hcurl, H1, H1))
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
print(f"Trial function shape {u.ufl_shape}")
print(f"Test function shape {v.ufl_shape}")

Shape of trial and test functions u and v in this example is (6,). How do I create 2 vector and 2 scalar trial and test functions for this problem?

Could I use the following code?

eperp_re = ufl.as_vector((u[0], u[1]))
eperp_im = ufl.as_vector((u[2], u[3]))
ez_re = u[4]
ez_im = u[5]
wre = ufl.as_vector((v[0], v[1]))
wim = ufl.as_vector((v[2], v[3]))
vre = v[4]
vim = v[5]
2

The code you proposed looks okay, but I think you should also be able to use ufl.TrialFunctions(V) and ufl.TestFunctions(V), as you did with old DOLFIN. (Based on the notation, you might also want to look into DOLFIN-X’s support for complex numbers.)

1 Like
3

Thanks for the reply! Using ufl.TrialFunction(V) and ufl.TestFunction(V) raises too many values to unpack error.

you might also want to look into DOLFIN-X’s support for complex numbers

I will definitely try it after porting the real number version and compare the results.

4

As @kamensky said, you need to use

not

The following code works with the latest dolfinx from docker (docker run -ti -e DISPLAY=$DISPLAY -v /tmp/.X11-unix:/tmp/.X11-unix -v $(pwd):/root/shared -w /root/shared --rm dolfinx/dolfinx)

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

mesh = dolfinx.UnitSquareMesh(MPI.COMM_WORLD, 10, 10)

Hcurl = ufl.FiniteElement("Nedelec 1st kind H(curl)", mesh.ufl_cell(), 1)
H1 = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)

V = dolfinx.FunctionSpace(mesh, ufl.MixedElement(Hcurl, Hcurl, H1, H1))

(uvr,uvi,usr,usi) = ufl.TrialFunctions(V)
(vvr,vvi,vsr,vsi) = ufl.TestFunctions(V)

print(uvr, uvi, usr, usi)
1 Like
5

Yes, after reading the docs it’s obvious:

ufl.TestFunction = TestFunction(function_space, part=None)
UFL value: Create a test function argument to a form.

ufl.TestFunctions = TestFunctions(function_space)
UFL value: Create a TestFunction in a mixed space, and return a
tuple with the function components corresponding to the subelements.

Thanks again!