Best practices of define the boundary.

[xfdywy]

Hello, everyone. If the boundary is complex, could anyone tell me what is the best practice of defining the boundary? For example, considering the case I need to distinguish the left, right, top, and bottom boundary. Can I use a python function to define the different boundary just like in fenics:

# Boundaries
def right(x, on_boundary): return x[0] > (1.0 - DOLFIN_EPS)
def left(x, on_boundary): return x[0] < DOLFIN_EPS
def top_bottom(x, on_boundary):
    return x[1] > 1.0 - DOLFIN_EPS or x[1] < DOLFIN_EPS

# No-slip boundary condition for velocity
noslip = Constant((0.0, 0.0, 0.0))
bc0 = DirichletBC(W.sub(0), noslip, top_bottom)

# Inflow boundary condition for velocity
inflow = Expression(("-sin(x[1]*pi)", "0.0", "0.0"), degree=2)
bc1 = DirichletBC(W.sub(0), inflow, right)

Or in this way to modified the facet markers directly like in fenics:

  bndry = MeshFunction("size_t", mesh, mesh.topology().dim()-1)
   for f in facets(mesh):
       mp = f.midpoint()
       if near(mp[0], 0.0):  # inflow
           bndry[f] = 1
       elif near(mp[0], L):  # outflow
           bndry[f] = 2
       elif near(mp[1], 0.0) or near(mp[1], W):  # walls
           bndry[f] = 3
       elif mp.distance(center) <= radius:  # cylinder
           bndry[f] = 5

Or in this way like in fenicsx:

def walls(x):
    return np.logical_or(np.isclose(x[1],0), np.isclose(x[1],1))
wall_dofs = locate_dofs_geometrical(V, walls)
u_noslip = np.array((0,) * mesh.geometry.dim, dtype=PETSc.ScalarType)
bc_noslip = dirichletbc(u_noslip, wall_dofs, V)

Thanks~

[ksagiyam]

RelabeledMesh (https://www.firedrakeproject.org/firedrake.html#firedrake.mesh.RelabeledMesh) lets you make a new mesh with new labels; see https://github.com/firedrakeproject/firedrake/blob/master/tests/regression/test_mark_entities.py for examples.