I am a new user for fenics, and trying to solve a Poisson-type equation in a 3D box of dimension a. I would like to implement periodic boundary condition in all x,y,z directions. Here is the class for the boundary condition I wrote, together with a simple code.

```
from fenics import *
a = 10
## Create mesh and define function space
mesh = BoxMesh(Point(0.0, 0.0, 0.0), Point(a, a, a), a, a, a)
V = FunctionSpace(mesh, 'Lagrange', 3)
## u_D(x,y) = 1 + x^2 + 2y^2
## Expression object takes mathematical expression in the C++ syntax
u_D = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]', degree=2)
class PeriodicBoundary(SubDomain):
# Left boundary is "target domain" G
def inside(self, x, on_boundary):
# return True if on left or bottom boundary AND NOT on one of the two slave edges
return bool ((near(x[0], 0) or near(x[1], 0) or near(x[2], 0)) and
(not ((near(x[0], a) and near(x[2], a)) or
(near(x[0], a) and near(x[1], a)) or
(near(x[1], a) and near(x[2], a)))) and on_boundary)
# Map right boundary (H) to left boundary (G)
def map(self, x, y):
#### define mapping for a single point in the box, such that 3 mappings are required
if near(x[0], a) and near(x[1], a) and near(x[2],a):
y[0] = x[0] - a
y[1] = x[1] - a
y[2] = x[2] - a
##### define mapping for edges in the box, such that mapping in 2 Cartesian coordinates are required
if near(x[0], a) and near(x[2], a):
y[0] = x[0] - a
y[1] = x[1]
y[2] = x[2] - a
elif near(x[1], a) and near(x[2], a):
y[0] = x[0]
y[1] = x[1] - a
y[2] = x[2] - a
elif near(x[0], a) and near(x[1], a):
y[0] = x[0] - a
y[1] = x[1] - a
y[2] = x[2]
#### right maps to left: left/right is defined as the x-direction
elif near(x[0], a):
y[0] = x[0] - a
y[1] = x[1]
y[2] = x[2]
### back maps to front: front/back is defined as the y-direction
elif near(x[1], a):
y[0] = x[0]
y[1] = x[1] - a
y[2] = x[2]
#### top maps to bottom: top/bottom is defined as the z-direction
elif near(x[2], a):
y[0] = x[0]
y[1] = x[1]
y[2] = x[2] - a
## Define boundary condition
pbc = PeriodicBoundary()
u = TrialFunction(V)
v = TestFunction(V)
a = inner(grad(u), grad(v))*dx
f = Constant(-6.0)
L = f*v*dx
## Compute solution
u = Function (V)
solve(a == L, u, pbc)
```

However, the following error is encountered when trying to run the code

RuntimeError: solve variational problem. Unable to extract boundary condition arguments

I would really appreciate any help.