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added 431 characters in body
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Feyre
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Monitor[NDSolve[{eq, bc1, bc2, ic}, 
  z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
  StepMonitor :> (time = t)], 
 ProgressIndicator[time/100]]

enter image description here

This doesn't appear to slow down the evaluation in any significant way:

RepeatedTiming[
  NDSolve[{eq, bc1, bc2, ic}, 
   z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol], 60]

RepeatedTiming[
 Monitor[NDSolve[{eq, bc1, bc2, ic}, 
   z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
   StepMonitor :> (time = t)], ProgressIndicator[time/100]], 60]

RepeatedTiming[
 Monitor[NDSolve[{eq, bc1, bc2, ic}, 
   z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
   EvaluationMonitor :> (time = t)], ProgressIndicator[time/100]], 60]

11.46

12.

11.9

Monitor[NDSolve[{eq, bc1, bc2, ic}, 
  z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
  StepMonitor :> (time = t)], 
 ProgressIndicator[time/100]]

enter image description here

Monitor[NDSolve[{eq, bc1, bc2, ic}, 
  z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
  StepMonitor :> (time = t)], 
 ProgressIndicator[time/100]]

enter image description here

This doesn't appear to slow down the evaluation in any significant way:

RepeatedTiming[
  NDSolve[{eq, bc1, bc2, ic}, 
   z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol], 60]

RepeatedTiming[
 Monitor[NDSolve[{eq, bc1, bc2, ic}, 
   z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
   StepMonitor :> (time = t)], ProgressIndicator[time/100]], 60]

RepeatedTiming[
 Monitor[NDSolve[{eq, bc1, bc2, ic}, 
   z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
   EvaluationMonitor :> (time = t)], ProgressIndicator[time/100]], 60]

11.46

12.

11.9

edited body
Source Link
Feyre
  • 8.7k
  • 2
  • 29
  • 48
Monitor[NDSolve[{eq, bc1, bc2, ic}, 
  z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
  StepMonitor :> (time = t)], 
 ProgressIndicator[time/100]]

enter image description hereenter image description here

Monitor[NDSolve[{eq, bc1, bc2, ic}, 
  z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
  StepMonitor :> (time = t)], 
 ProgressIndicator[time/100]]

enter image description here

Monitor[NDSolve[{eq, bc1, bc2, ic}, 
  z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
  StepMonitor :> (time = t)], 
 ProgressIndicator[time/100]]

enter image description here

Source Link
Feyre
  • 8.7k
  • 2
  • 29
  • 48

Monitor[NDSolve[{eq, bc1, bc2, ic}, 
  z, {t, 0, 100}, {x, -Lx, Lx}, {y, -Ly, Ly}, Method -> mol, 
  StepMonitor :> (time = t)], 
 ProgressIndicator[time/100]]

enter image description here