readily for this highly nonlinear problem. Initially, I was hardly able to
find solutions for which the energy dropped below 0.005, while the energy
after the final iteration of the program as it is is usually around 0.0003,
-and occasionally down to 3.5e-5.
+and occasionally down to less than 3e-5.
However, this is not enough. In the program, we start the solver on the coarse
mesh many times, with randomly perturbed starting values, and while it
<a name="Results"></a>
<h1>Results</h1>
+
+<p>
+If run, the program generates output like this:
+</p>
+
+<code><pre>
+Realization 0:
+ Energy: 0.00267545
+ Energy: 0.000774987
+ Energy: 0.000369921
+ Energy: 0.000196206
+ Energy: 0.000141912
+ Energy: 0.000128605
+ Energy: 0.000124399
+ Energy: 0.000123254
+ Energy: 0.000122788
+ Energy: 0.00012256
+ Energy: 0.000122465
+ Energy: 0.000122434
+ Energy: 0.000122427
+ Energy: 0.000119443
+ Energy: 0.000119442
+
+Realization 1:
+ Energy: 0.00283288
+ Energy: 0.000830749
+ Energy: 0.000346346
+ Energy: 0.000183367
+ Energy: 0.000139092
+ Energy: 0.000125745
+ Energy: 0.000121538
+ Energy: 0.000120382
+ Energy: 0.000119934
+ Energy: 0.000119677
+ Energy: 0.000119534
+ Energy: 0.000119473
+ Energy: 0.000119462
+ Energy: 0.000119643
+
+....
+
+Realization 9:
+ Energy: 0.0103424
+ Energy: 0.00820572
+ Energy: 0.00771209
+ Energy: 0.00759366
+ Energy: 0.00755131
+ Energy: 0.00753996
+ Energy: 0.00753659
+ Energy: 0.0075344
+ Energy: 0.00753374
+ Energy: 0.00753362
+ Energy: 0.0071671
+ Energy: 0.00716708
+</pre></code>
+
+<p>
+The lowest energy yet seen is in this run (you only get this by increasing the
+number of runs):
+</p>
+<code><pre>
+Realization 18:
+ Energy: 0.00200645
+ Energy: 0.000638519
+ Energy: 0.00022749
+ Energy: 9.18962e-05
+ Energy: 5.42442e-05
+ Energy: 3.94415e-05
+ Energy: 3.42307e-05
+ Energy: 3.30727e-05
+ Energy: 3.19998e-05
+ Energy: 3.18104e-05
+ Energy: 2.97091e-05
+ Energy: 3.5011e-05
+</pre></code>
+
+<p>
+Apparently something went wrong in the last step (the energy increased, which
+it shouldn't - but then this is a strongly nonlinear problem), which is also
+why the program aborted after this iteration.
+</p>
+
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