How to match the nodes at the boundaries of two different domains

Question

Hi
I need to mesh two different domains separately and match the nodes at the boundaries of two domains.

I wrote a simple code:

from dolfin import *
import mshr

# Domain
domain1 = mshr.Rectangle(Point(2,4.5), Point(8,5.5))

domain2 = mshr.Rectangle(Point(0,0), Point(10,10))\
          - mshr.Rectangle(Point(2,4.5), Point(8,5.5))

# Mesh
mesh1 = mshr.generate_mesh(domain1, 20)
mesh2 = mshr.generate_mesh(domain2, 20)

# Build multimesh
multimesh = MultiMesh()
multimesh.add(mesh1)
multimesh.add(mesh2)
multimesh.build()

plot(mesh1)
plot(mesh2)

interactive()

Now I can plot the meshes for different domains :
Domain.1:

Domain.2:

But:
1- How can I match (make coincident) the nodes of the domain.1 and domain.2 at the boundaries of the domain.1 and domain.2?
2- How can I plot the mesh for the domain.1 and domain.2 in one figure?

After all I expect to get something like this:

Does anybody know how I can do it in FEniCS?
Thanks

Comments

Maybe you can add markers to the subdomains, but it really depends on what you want to do, so maybe you can give more information on your problem. Docs for a reference: https://fenicsproject.org/olddocs/dolfin/1.4.0/python/demo/documented/subdomains/python/documentation.html

---

Hi
Thanks for your response. I used the same idea and resolved this issue:

from dolfin import *

mesh = RectangleMesh(Point(0.0, 0.0), Point(0.1, 0.1), 50, 50)

subdomain = CompiledSubDomain("x[1] > 0.04 && x[1] < 0.06 && x[0] > 0.025 && x[0] < 0.075")
mf = MeshFunction("size_t", mesh, 2)
mf.set_all(0)
subdomain.mark(mf, 1)
plot(mf, interactive = True)

Here is the results that is what I expected to get:

---

Great, then please close the question. Best regs.