SubMesh mapped to parent mesh and mirror mapping

mesh
1

Hello,

I have a mesh symmetric about, say, y = x,
image

and would like to build a mapping: cellmap= [[2,1], [3,4]]

I
The dolfin version is : 2019.1.0

import time
import numpy as np
from dolfin import *

Nx = Ny = 21
mesh = RectangleMesh(Point(0.0, 0.0), Point(1, 1), Nx, Ny, "crossed")

class Southeast(SubDomain):
    def inside(self, x, on_boundary):
        return x[0] >= x[1]


southeast = Southeast()
submesh = SubMesh(mesh, southeast)

gdim = mesh.geometry().dim()

cellmap = np.zeros([submesh.num_cells(), 3], dtype=int)

subindex = 0
# to optimize
tic = time.perf_counter()
for subcell in cells(submesh):
    cellmap[subindex, 0] = subcell.index()
    for cell in cells(mesh):
        if cell.contains(subcell.midpoint()):
            cellmap[subindex, 1] = cell.index()
            break
    for cell in cells(mesh):
        if cell.contains(Point(subcell.midpoint().y(), subcell.midpoint().x())):
            cellmap[subindex, 2] = cell.index()
            break
    subindex += 1
print(cellmap.T)
toc = time.perf_counter()
print(f"Map cells in {toc - tic:0.4f} seconds")

It is working.

For small Nx, it is OK.
For large Nx, for example, Nx = 101, it takes centuries.

Could you help me to optimize this script?

Many thanks.