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When I run this code

diskLevels = 
  NDEigenvalues[
                {-Laplacian[u[x, y], {x, y}], 
                DirichletCondition[u[x, y] == 0, True]}, 
                u[x, y], {x, y} \[Element] Disk[], 1000
         ];

Mathematica objects that it can only supply me with 961 eigenvalues:

NDEigenvalues::maxeigen: A maximum number of 961 eigenvalues and functions can be computed for this discretized system.

Is there a way to get more values? I tried messing around with some options but any time I managed to prevent the error message the calculation would not terminate.

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Clear["Global`*"]

(diskLevels = NDEigenvalues[
     {-Laplacian[u[x, y], {x, y}],
      DirichletCondition[u[x, y] == 0, True]},
     u[x, y], {x, y} \[Element] Disk[], 1000,
     Method -> {"SpatialDiscretization" ->
        {"FiniteElement",
         "MeshOptions" ->
          {"MaxCellMeasure" -> 0.0075}}}];) //
 AbsoluteTiming

(* {0.657356, Null} *)

Length@diskLevels

(* 1000 *)
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  • $\begingroup$ Thanks! I thought I would note: the levels returned by this code may not be reliable. If you plot the differences here then they will not be distributed as $P \sim e^{(-s)}.$ But making MaxCellMeasure even smaller recovers the true behavior, although at a much longer time. $\endgroup$
    – Diffycue
    Sep 13 at 17:52

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