Determination of the linked dofs created by periodic boundary condition

General
1

Hello everyone,

The code below defines a periodic boundary condition class, which maps (links) the nodes in x and z directions.

I would like to get the linked dof numbers in pairs.

If you have any suggestions, I would appreciate.

Fenics version: 2019.2.0.dev0

from fenics import *
from ufl import j
import numpy as np

xmin, xmax, ymin, ymax, zmin, zmax = 0, 1, 0, 1, 0, 1

TOL = 1E-10

class PeriodicBoundary(SubDomain):
    def inside(self, x, on_boundary):
    	return bool( on_boundary and
    	( 
    	    ( near(x[0], xmin, TOL) and not ( near(x[2], zmax, TOL) and near(x[0], xmin, TOL) ) )
        or  ( near(x[2], zmin, TOL) and not ( near(x[2], zmin, TOL) and near(x[0], xmax, TOL) ) )
        )
        )
    	
    def map(self, x, y):
    	if near(x[2], zmax, TOL) and near(x[0], xmax, TOL):
    		y[0] = x[0] - (xmax-xmin)
    		y[1] = x[1]
    		y[2] = x[2] - (zmax-zmin)
    	elif near(x[0], xmax, TOL):
    		y[0] = x[0] - (xmax-xmin)
    		y[1] = x[1]
    		y[2] = x[2]
    	else:
    		y[0] = x[0]
    		y[1] = x[1]
    		y[2] = x[2] - (zmax-zmin)


mesh = BoxMesh(Point(0,0,0), Point(1, 1, 1), 2, 2, 2)

Ve = VectorElement("CG", mesh.ufl_cell(), 1)
Space = FunctionSpace(mesh, Ve, constrained_domain=PeriodicBoundary())
delta_u = TestFunction(Space)
u = TrialFunction(Space)

M = PETScMatrix()
assemble(delta_u[j]*u[j]*dx , tensor = M)