Vertex on Mesh Boundary

Question

I need to know the vertices on mesh physical boundary.

I know I could define a function to check the coordinators of each vertex. But my mesh boundary is not fixed, and I need to rewrite the function each time.

I am wondering whether there is a simply way to check whether a vertex is on the mesh physical boundary.

I also find "DirichletBC" object has a "markers()" function, which returns the boundary markers. But the return value is a swig object and I can not see the value in python.

Answer 1

First find facets that are on the boundary (i.e., facets that are connected to only one cell), then iterate over the vertices of facets that are on the boundary.

Answer 2

You can find the vertices on the boundary like this:

from dolfin import *
mesh = UnitSquareMesh(4, 4)

# Mark a CG1 Function with ones on the boundary
V = FunctionSpace(mesh, 'CG', 1)
bc = DirichletBC(V, 1, DomainBoundary())
u = Function(V)
bc.apply(u.vector())

# Get vertices sitting on boundary
d2v = dof_to_vertex_map(V)
vertices_on_boundary = d2v[u.vector() == 1.0]

# Mark VertexFunction to check
vf = VertexFunction('size_t', mesh, 0)
vf.array()[vertices_on_boundary] = 1.

plot(vf)
interactive()

The DirichletBC.markers() returns a vector (numpy array in python) of the facets on that boundary, at least for development version.

Comments

My FEniCS doesn't have this function "dof_to_vertex_map". I need a more recent version of FEniCS?

---

You probably need dolfin-1.3.0. Older versions have the function as part of the dofmap, try:

d = V.dofmap()
d2v = d.dof_to_vertex_map(mesh)