Workaround of tabulate_dof_coordinates() in parallel?

mesh
1

I have a time dependant phase separation problem, where I would like to track the radius of a half circle a the upper boundary of a square mesh over time. This MWE works in serial

import dolfin as dlf 
import numpy as np 

class InitialConditions(dlf.UserExpression):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)
    def eval_cell(self, values, x, ufc_cell):
        values[0]   = 1.0/dlf.pi * ( dlf.pi/2.0 + dlf.atan((dlf.sqrt( ( x[0]- .5 )**2 \
                                + ( x[1] - 1.0  )**2 )-0.1)/1.0e-3))    
        values[1]   = 0.0
    def value_shape(self):
        return (2,)

def get_data(u):
    m           = dlf.assemble(u.split()[0]*dlf.dx)
    DG_elem     = dlf.FiniteElement("DG", u.function_space().mesh().ufl_cell(), 0)
    V_DG        = dlf.FunctionSpace(u.function_space().mesh(), DG_elem*DG_elem)
    u_dg        = dlf.project(u, V_DG)
    c_dg        = u_dg.vector().get_local()[0::2]
    cell_midpt  = V_DG.tabulate_dof_coordinates()[0::2]
    indexes     = np.where(c_dg <= 0.50)[0]
    if len(indexes) != 0:
        mid_y   = cell_midpt[indexes][:,1]
        r       = ( 1.0 - np.amin(mid_y) )
    else:
        r       = 0.0
    return m, r

n       = 100
nx, ny  = n, n
mesh    = dlf.UnitSquareMesh(nx, ny, "left/right")
da      = dlf.Measure("dx", domain=mesh)
x       = dlf.SpatialCoordinate(mesh)
CG_elem = dlf.FiniteElement("CG", mesh.ufl_cell(), 1)
V_CG    = dlf.FunctionSpace(mesh, CG_elem*CG_elem)

u_cg    = dlf.Function(V_CG)
c, mu   = dlf.split(u_cg)
u_cg    = dlf.interpolate(InitialConditions(degree=1), V_CG)

m, r    = get_data(u_cg)
print("m = %.3e, r = %3e" % (m, r))

But since the dofs get scatter when running in parallel, tabulate_dof_coordinates() does not do the trick anymore. Does anybody know a workaround to this?

Greetings