Investigate convergence of MA QN solver

[joewallwork]

          [The optimisation progress of the quasi-Newton solver with ring radius 0.4] looks like this now:

   0   Volume ratio 12.91   Variation (σ/μ) 1.21e+00   Residual 1.16e+00
   1   Volume ratio  6.77   Variation (σ/μ) 6.15e-01   Residual 4.85e-01
   2   Volume ratio  5.84   Variation (σ/μ) 5.69e-01   Residual 4.26e-01
   3   Volume ratio  6.34   Variation (σ/μ) 5.14e-01   Residual 3.74e-01
   4   Volume ratio  6.38   Variation (σ/μ) 4.88e-01   Residual 3.22e-01
   5   Volume ratio 12.05   Variation (σ/μ) 4.55e-01   Residual 2.57e-01
   6   Volume ratio 11.69   Variation (σ/μ) 4.26e-01   Residual 2.30e-01
   7   Volume ratio 11.98   Variation (σ/μ) 4.23e-01   Residual 1.98e-01
   8   Volume ratio 11.81   Variation (σ/μ) 4.17e-01   Residual 1.95e-01
   9   Volume ratio 12.00   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  10   Volume ratio 12.07   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  11   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  12   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  13   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  14   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  15   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  16   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  17   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  18   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  19   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  20   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  21   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  22   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  23   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  24   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  25   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  26   Volume ratio 12.10   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  27   Volume ratio 12.18   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
  28   Volume ratio 12.38   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
  29   Volume ratio 12.43   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
  30   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
  31   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
  32   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
  33   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
  34   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
  35   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
  36   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
  37   Volume ratio 13.34   Variation (σ/μ) 4.18e-01   Residual 1.94e-01
  38   Volume ratio 15.21   Variation (σ/μ) 4.38e-01   Residual 2.09e-01
  39   Volume ratio 17.20   Variation (σ/μ) 4.76e-01   Residual 2.22e-01
  40   Volume ratio 11.89   Variation (σ/μ) 4.30e-01   Residual 1.45e-01
  41   Volume ratio 12.41   Variation (σ/μ) 4.13e-01   Residual 1.01e-01
  42   Volume ratio  8.76   Variation (σ/μ) 3.79e-01   Residual 7.36e-02
  43   Volume ratio 10.00   Variation (σ/μ) 3.85e-01   Residual 6.36e-02
  44   Volume ratio  8.57   Variation (σ/μ) 3.65e-01   Residual 5.17e-02
  45   Volume ratio  9.48   Variation (σ/μ) 3.72e-01   Residual 4.17e-02
  46   Volume ratio  8.70   Variation (σ/μ) 3.60e-01   Residual 3.51e-02
  47   Volume ratio  9.31   Variation (σ/μ) 3.64e-01   Residual 2.69e-02
  48   Volume ratio  8.82   Variation (σ/μ) 3.57e-01   Residual 2.23e-02
  49   Volume ratio  9.20   Variation (σ/μ) 3.58e-01   Residual 1.44e-02
  50   Volume ratio  8.95   Variation (σ/μ) 3.53e-01   Residual 1.03e-02
  51   Volume ratio  9.08   Variation (σ/μ) 3.52e-01   Residual 4.91e-03
  52   Volume ratio  9.05   Variation (σ/μ) 3.50e-01   Residual 3.98e-03
  53   Volume ratio  9.13   Variation (σ/μ) 3.51e-01   Residual 2.81e-03
  54   Volume ratio  9.11   Variation (σ/μ) 3.50e-01   Residual 2.28e-03
  55   Volume ratio  9.17   Variation (σ/μ) 3.50e-01   Residual 1.51e-03
  56   Volume ratio  9.15   Variation (σ/μ) 3.50e-01   Residual 1.11e-03
  57   Volume ratio  9.19   Variation (σ/μ) 3.50e-01   Residual 5.28e-04
  58   Volume ratio  9.18   Variation (σ/μ) 3.49e-01   Residual 2.89e-04
  59   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.04e-04
  60   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 7.69e-05
  61   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 5.31e-05
  62   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 3.80e-05
  63   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 2.66e-05
  64   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.87e-05
  65   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.36e-05
  66   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 9.55e-06
  67   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 7.22e-06
  68   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 5.04e-06
  69   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 3.88e-06
  70   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 2.50e-06
  71   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.87e-06
  72   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 9.04e-07
  73   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 6.32e-07
  74   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 2.67e-07
  75   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.55e-07
  76   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 8.22e-08
Solver converged in 76 iterations.

Quite a few more iterations (up from 52 with np.sqrt(0.15) since it gets stuck a bit as you can see.

Originally posted by @ddundo in #114 (comment)

[ddundo]

Maybe connected to mesh-adaptation/animate#152, do you think it's worth investigating why you got different results than these on your machine?

Edit: I am using our firedrake-parmmg container

[joewallwork]

Maybe connected to mesh-adaptation/animate#152, do you think it's worth investigating why you got different results than these on your machine?

I don't think so right now. Numerical codes will give different results on different machines for all sorts of reasons. If the results were drastically different then it would be worth looking into, but I wouldn't say that's the case here. Running git diff --word-diff gives

diff --git b/demos/monge_ampere_ring.py a/demos/monge_ampere_ring.py
index fd9f944..fb68071 100644
--- b/demos/monge_ampere_ring.py
+++ a/demos/monge_ampere_ring.py
@@ -121,60 +121,58 @@ mover.move()
#      21   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
#      22   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
#      23   Volume ratio 12.09   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
#      24   Volume ratio [-12.09-]{+12.10+}   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
#      25   Volume ratio [-12.09-]{+12.18+}   Variation (σ/μ) 4.16e-01   Residual 1.94e-01
#      26   Volume ratio [-12.10-]{+12.38+}   Variation (σ/μ) 4.16e-01   Residual [-1.94e-01-]{+1.93e-01+}
#      27   Volume ratio [-12.18-]{+12.43+}   Variation (σ/μ) 4.16e-01   Residual [-1.94e-01-]{+1.93e-01+}
#      28   Volume ratio [-12.38-]{+12.44+}   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
#      29   Volume ratio [-12.43-]{+12.44+}   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
#      30   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
#      31   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
#      32   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
#      33   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
#      34   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01
#      35   Volume ratio[-12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01-]
[-#      36   Volume ratio 12.44   Variation (σ/μ) 4.16e-01   Residual 1.93e-01-]
[-#      37   Volume ratio-] 13.34   Variation (σ/μ) 4.18e-01   Residual 1.94e-01
#      [-38-]{+36+}   Volume ratio 15.21   Variation (σ/μ) 4.38e-01   Residual 2.09e-01
#      [-39-]{+37+}   Volume ratio 17.20   Variation (σ/μ) 4.76e-01   Residual 2.22e-01
#      [-40-]{+38+}   Volume ratio 11.89   Variation (σ/μ) 4.30e-01   Residual 1.45e-01
#      [-41-]{+39+}   Volume ratio 12.41   Variation (σ/μ) 4.13e-01   Residual 1.01e-01
#      [-42-]{+40+}   Volume ratio  8.76   Variation (σ/μ) 3.79e-01   Residual 7.36e-02
#      [-43-]{+41+}   Volume ratio 10.00   Variation (σ/μ) 3.85e-01   Residual 6.36e-02
#      [-44-]{+42+}   Volume ratio  8.57   Variation (σ/μ) 3.65e-01   Residual 5.17e-02
#      [-45-]{+43+}   Volume ratio  9.48   Variation (σ/μ) 3.72e-01   Residual 4.17e-02
#      [-46-]{+44+}   Volume ratio  8.70   Variation (σ/μ) 3.60e-01   Residual 3.51e-02
#      [-47-]{+45+}   Volume ratio  9.31   Variation (σ/μ) 3.64e-01   Residual 2.69e-02
#      [-48-]{+46+}   Volume ratio  8.82   Variation (σ/μ) 3.57e-01   Residual 2.23e-02
#      [-49-]{+47+}   Volume ratio  9.20   Variation (σ/μ) 3.58e-01   Residual 1.44e-02
#      [-50-]{+48+}   Volume ratio  8.95   Variation (σ/μ) 3.53e-01   Residual 1.03e-02
#      [-51-]{+49+}   Volume ratio  9.08   Variation (σ/μ) 3.52e-01   Residual 4.91e-03
#      [-52-]{+50+}   Volume ratio  9.05   Variation (σ/μ) 3.50e-01   Residual 3.98e-03
#      [-53-]{+51+}   Volume ratio  9.13   Variation (σ/μ) 3.51e-01   Residual 2.81e-03
#      [-54-]{+52+}   Volume ratio  9.11   Variation (σ/μ) 3.50e-01   Residual 2.28e-03
#      [-55-]{+53+}   Volume ratio  9.17   Variation (σ/μ) 3.50e-01   Residual 1.51e-03
#      [-56-]{+54+}   Volume ratio  9.15   Variation (σ/μ) 3.50e-01   Residual 1.11e-03
...skipping...
#      [-41-]{+39+}   Volume ratio 12.41   Variation (σ/μ) 4.13e-01   Residual 1.01e-01
#      [-42-]{+40+}   Volume ratio  8.76   Variation (σ/μ) 3.79e-01   Residual 7.36e-02
#      [-43-]{+41+}   Volume ratio 10.00   Variation (σ/μ) 3.85e-01   Residual 6.36e-02
#      [-44-]{+42+}   Volume ratio  8.57   Variation (σ/μ) 3.65e-01   Residual 5.17e-02
#      [-45-]{+43+}   Volume ratio  9.48   Variation (σ/μ) 3.72e-01   Residual 4.17e-02
#      [-46-]{+44+}   Volume ratio  8.70   Variation (σ/μ) 3.60e-01   Residual 3.51e-02
#      [-47-]{+45+}   Volume ratio  9.31   Variation (σ/μ) 3.64e-01   Residual 2.69e-02
#      [-48-]{+46+}   Volume ratio  8.82   Variation (σ/μ) 3.57e-01   Residual 2.23e-02
#      [-49-]{+47+}   Volume ratio  9.20   Variation (σ/μ) 3.58e-01   Residual 1.44e-02
#      [-50-]{+48+}   Volume ratio  8.95   Variation (σ/μ) 3.53e-01   Residual 1.03e-02
#      [-51-]{+49+}   Volume ratio  9.08   Variation (σ/μ) 3.52e-01   Residual 4.91e-03
#      [-52-]{+50+}   Volume ratio  9.05   Variation (σ/μ) 3.50e-01   Residual 3.98e-03
#      [-53-]{+51+}   Volume ratio  9.13   Variation (σ/μ) 3.51e-01   Residual 2.81e-03
#      [-54-]{+52+}   Volume ratio  9.11   Variation (σ/μ) 3.50e-01   Residual 2.28e-03
#      [-55-]{+53+}   Volume ratio  9.17   Variation (σ/μ) 3.50e-01   Residual 1.51e-03
#      [-56-]{+54+}   Volume ratio  9.15   Variation (σ/μ) 3.50e-01   Residual 1.11e-03
#      [-57-]{+55+}   Volume ratio  9.19   Variation (σ/μ) 3.50e-01   Residual 5.28e-04
#      [-58-]{+56+}   Volume ratio  9.18   Variation (σ/μ) 3.49e-01   Residual 2.89e-04
#      [-59-]{+57+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.04e-04
#      [-60-]{+58+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 7.69e-05
#      [-61-]{+59+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 5.31e-05
#      [-62-]{+60+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 3.80e-05
#      [-63-]{+61+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 2.66e-05
#      [-64-]{+62+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.87e-05
#      [-65-]{+63+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.36e-05
#      [-66-]{+64+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 9.55e-06
#      [-67-]{+65+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 7.22e-06
#      [-68-]{+66+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 5.04e-06
#      [-69-]{+67+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 3.88e-06
#      [-70-]{+68+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 2.50e-06
#      [-71-]{+69+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.87e-06
#      [-72-]{+70+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 9.04e-07
#      [-73-]{+71+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 6.32e-07
#      [-74-]{+72+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 2.67e-07
#      [-75-]{+73+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 1.55e-07
#      [-76-]{+74+}   Volume ratio  9.19   Variation (σ/μ) 3.49e-01   Residual 8.22e-08
#    Solver converged in [-76-]{+74+} iterations.
#
# The adapted mesh can be accessed via the `mesh` attribute of the mover. Plotting it,
# we see that the adapted mesh has its resolution focused around a ring, as expected.

which indicates that the differences are rather small. The main difference is that your simulation stalls for two iterations longer than mine.