How to define mixedfunctionspace when submesh exist

Zhaoyx · May 26, 2024, 3:18pm

Hi,
I am learning to use mixed element.
In general, function spaces are defined in the same mesh as in Mixed formulation for the Poisson equation:

Q_el = element("BDMCF", msh.basix_cell(), k)
P_el = element("DG", msh.basix_cell(), k - 1)
V_el = mixed_element([Q_el, P_el])
V = fem.functionspace(msh, V_el)

I was wondering how to define mixedfunctionspace when one field is solved in the entire mesh and the other field is solved only in the submesh.
Can anyone give me some advice？
Thanks.

dokken · May 27, 2024, 6:27am

You would then use @jpdean co-dim 0 support for assembly in DOLFINx.
See for instance

github.com

FEniCS/dolfinx/blob/42c43485e81ada306f0b3f1dc735d95539174cbc/python/test/unit/fem/test_assemble_submesh.py#L183


      
                  return f * g * measure
              else:
                  assert measure.integral_type() == "interior_facet"
                  return (f("+") + f("-")) * (g("+") + g("-")) * measure
          
          
          @pytest.mark.parametrize("n", [4, 6])
          @pytest.mark.parametrize("k", [1, 3])
          @pytest.mark.parametrize("space", ["Lagrange", "Discontinuous Lagrange"])
          @pytest.mark.parametrize("integral_type", ["dx", "ds", "dS"])
          def test_mixed_dom_codim_0(n, k, space, integral_type):
              """Test assembling forms where the trial and test functions
              are defined over different meshes"""
          
              # Create a mesh
              msh = create_rectangle(
                  MPI.COMM_WORLD, ((0.0, 0.0), (2.0, 1.0)), (2 * n, n), ghost_mode=GhostMode.shared_facet
              )
          
              # Create a submesh of the left half of the mesh
              tdim = msh.topology.dim

Zhaoyx · May 28, 2024, 7:08am

Thank you dokken. That’s very helpful.

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How to define mixedfunctionspace when submesh exist

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