Build mixed function space with constrained domain (periodic bc)

Question

Hi everybody!

I want to solve a problem using a mixed function space $V \times W$ and I want to equip $V$ with periodic boundary conditions:

from dolfin import *

# define periodic bc
class PeriodicBC(SubDomain):
      def __init__(self, tolerance=DOLFIN_EPS, length = 1.0):
          SubDomain.__init__(self)
          self.tol = tolerance
          self.length = length
      def inside(self, x, on_boundary):
          return bool((near(x[0], 0) or near(x[1], 0) and on_boundary) and \
                      (not ((near(x[0], 0) and near(x[1], self.length)) or \
                      (near(x[0], self.length) and near(x[1], 0)))) and on_boundary)
      def map(self, x, y):
          L = self.length
          if near(x[0], L) and near(x[1], L):
             y[0] = x[0] - L
             y[1] = x[1] - L
          elif near(x[0], L):
             y[0] = x[0] - L
             y[1] = x[1]
          else:  
             y[0] = x[0]
             y[1] = x[1] - L


# create mesh
mesh = RectangleMesh(Point(0.0,0.0),Point(1.0,1.0),4,4,"left/right")

# build function space
PBC = PeriodicBC(length = 1.0)
V  = FunctionSpace(mesh, "CG", 1, constrained_domain=PBC)
W  = FunctionSpace(mesh, "CG", 1)          

MS = MixedFunctionSpace([V,W])

But I get the following error:

*** Error: Unable to create function space.
*** Reason: Nonmatching constrained_domain for mixed function space: [<dolfin.cpp.mesh.SubDomain; proxy of *' at 0x7fec5a8a0210> >, None].
*** Where: This error was encountered inside functionspace.py.
*** Process: 0

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*** DOLFIN version: 1.6.0
*** Git changeset: unknown

What am I doing wrong? I would be very grateful if anyone could help.

Best regards,
Lisa

Answer 1

Hi, consider

# build function space 
PBC = PeriodicBC(length = 1.0)
V  = FunctionSpace(mesh, "CG", 1, constrained_domain=PBC)
W  = FunctionSpace(mesh, "CG", 1, constrained_domain=PBC)          
MS = MixedFunctionSpace([V,W])
print MS.dim()

V = FiniteElement('Lagrange', mesh.ufl_cell(), 1)
W = MixedElement([V, V])
W = FunctionSpace(mesh, W, constrained_domain=PBC)          
print W.dim()

Comments

Hi! Thank you for your quick response.

When I run your code I get the following error:

W = FunctionSpace(mesh, W, constrained_domain=PBC)          

TypeError: init() takes at least 4 arguments (4 given)

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It works for me on dolfin version 2016.1.0.

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Unfortunately, it does not work on FEniCS version 1.6.0.

Can you explain what's wrong or why my code does not work? That would be great.

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Hi, the code shows two approaches which should be equivalent. If it is W = FunctionSpace(mesh, W, constrained_domain=PBC) which does not work use the constructor above. Or is it that both approaches fail?

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I'm sorry. Now I see that I should have explained my original problem a bit more.

So the problem is, that I can not create a mixed function space from one function space with periodic boundary conditions (V) and one function space without periodic boundary conditions (W):

MS = MixedFunctionSpace([V,W])

But the code works, if I want to create a mixed function space from two function spaces, which have both periodic boundary conditions:

MS = MixedFunctionSpace([V,V])

and it works for a mixed space consisting of two spaces without periodic bc.

Do you have an idea what's wrong?

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It is by design that you cannot create such a mixed space. Out of curiosity, what is the application where you need only one variable to be periodic? Also, you could have a look at cbc.block where you can assemble block matrices - mixed spaces are not necessary.