Local refinement scales poorly

[Anders Logg]

Bug reported by Glenn Terje Lines.

Local refinement seems to be n^3 in the number of cells.

Can be reproduced with the following code:

from dolfin import *
import numpy
import time
import random

mesh = UnitCube(10,10,10)

for i in range(10):
    mf = MeshFunction("bool", mesh, 3)
    k = 0
    for cell in mesh.cells():
        mf.values()[k] = (random.random()>0.5)
        k += 1
    t0 = time.time();
    mesh = refine(mesh,mf);
    dt = time.time() - t0;
    print i, dt, k, k/dt

Results:

# results
P = numpy.array([
[0,0.144922018051,6000,41401.5763835],
[1,0.398217916489,11904,29893.1803596],
[2,0.88475394249,22928,25914.5496831],
[3,2.46636891365,47190,19133.3906857],
[4,10.5502009392,94930,8997.93288747],
[5,39.3473289013,184088,4678.53867442],
[6,302.216933966,379850,1256.87861039],
[7,2436.17705512,760484,312.162861234]])
n = P[:,2];

import pylab
pylab.loglog(n,P[:,1],n,4e-5*n,n,1e-9*n**2,n,1e-14*n**3)
pylab.show()

[Anders Logg (logg)]

This bug is "superseded" by https://bugs.launchpad.net/dolfin/+bug/735588 and will (most likely) not be fixed until we reimplement the mesh refinement.