Hello everyone,
I’d like to compute the outward normal vector field on a 2D smooth surface (mesh will triangular cells of topologic dimension 2) embedded in 3D.
I guess I could do it with numpy , the array of the vertices and the local-to-global index mapping (assuming coherent orientation amongst cells)… But I was wandering if there were a more “cleaver”, ''compact", “FEniCS-tics” way of doing such a thing ?
Thanks for your insight !
You can project a FacetNormal into an appropriate space (For instance VectorFunctionSpace(mesh, ("DG", 0)) for linear affine meshes.
See for instance: dolfinx_mpc/mpc_utils.py at main · jorgensd/dolfinx_mpc · GitHub
Thx @dokken for your swift response.
Maybe I did not get it right but the FacetNormal class computes normals on boundaries, right. As I am considering closed surfaces I don’t have boundaries (cf caption).
Are you suggesting to generate a 3D mesh of the whole volume defined by the closed surface and then compute FacetNormal on it ?
If so, I tried such a thing (adding a central point to the spherical mesh and defining tetrahedrons) but it seemed to take ages…
You should then be able to do the same thing replacing FacetNormal with CellNormal. i.e. the rhs will be something like:
import dolfinx
from mpi4py import MPI
import ufl
gdim, shape, degree = 3, "triangle", 1
cell = ufl.Cell(shape, geometric_dimension=gdim)
domain = ufl.Mesh(ufl.VectorElement("Lagrange", cell, degree))
x = [[0., 0., 0.], [0., 1., 0.], [1., 1., 1.]]
cells = [[0, 1, 2]]
msh = dolfinx.mesh.create_mesh(MPI.COMM_WORLD, cells, x, domain)
V = dolfinx.fem.VectorFunctionSpace(msh, ("DG", 0), dim=gdim)
v = ufl.TestFunction(V)
J = dolfinx.fem.form(ufl.inner(ufl.CellNormal(msh), v)*ufl.dx)
print(dolfinx.fem.petsc.assemble_vector(J).array)