how do I set boundaries for domain composition

Question

Domain decompositon: how to set up the boundaries

Decompose a domain into 9 hexagons labeled 0 to 8.

Each of the hexagons has a boundary labeled 'a', 'b', 'c' … 'f', Now assume for the moment that the external edges for example 2b, 2c, 2d etc. are set to some Dirichlet boundary. Further assume that each hexagon is covered with the same symmetric mesh so that the points of the mesh of neighboring domains are exactly matching.

mesh = Mesh('hexagon.xml')
V = FunctionSpace(mesh, "CG", 2)
u0 = TrialFunction(V)
u1 = TrialFunction(V)
…
u8 = TrialFunction(V)

So the precise question is: How do I set up the boundary between 2f and 4c such that the Dirichlet boundary for u2(x, y) in domain 2 is u2(x, y) == u4(x, y) on 2f-4c.

Comments

For example cover a square with equilateral triangles

Square can't be triangulated using equilaterals.

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Cover means that for each point in the square one can find a triangle to which belongs to with the exception of the border which can belong to several triangles. It does not mean that that each triangle has to fit. If you have anything to say about the actual problem I would be delighted to hear.

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here is a related question:
how to specify an internal boundary with boundary condition?
imagine an isolated hot water pipe.
the geometry is two concentrical cylinders.
NS flow with heat transfer in the inner pipe and a pure heat equation throughout the isolating mantle. Apparently one cannot have two meshes, as then the boundary would become ambiguous. Consequently a subdomain for the inner pipe is called for. But how to define the internal boundary that is the boundary between the pipe and the isolation? For the flow problem a non-slip condition is needed.
Any suggestions?

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Both of you did not ask a question with a sufficient level of specificity. You should go through demos (not tutorials, these are outdated) and FEniCS book. Then you can start playing arounf with FEniCS, developing your code and ask well-posed question in troubles.

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Comment removed. See the more detailed question above.

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If you want to solve a coupled problem on domain composed of hexagons 0-8 then rather mesh the whole domain.

I don't think it is a much domain decomposition method when you want to enforce these conditions and solve still fully-coupled problem.

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For the definition of domain decomposition have a look at the freefem++ manual page starting page 257. And yes I want to solve the coupled system but decomposed in cells so if you wish I want to know how to set up an internal boundary and that was exactly the same question as Achim was asking. I have been able to set up (and solve) my problem in freefem++. I was just looking in to fenics because it has a more "rational" interface.

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Sorry, I'm not gonna study for you. Still your question is too vague.