1
$\begingroup$

This is my codes to calculate a wave equation by NDSolveValue:

Block[{nSteps = 0, Timer = 0, L = 100, T = 100, a = 0.1, b = 10},
  Monitor[
   sol = NDSolveValue[
     {
      D[u[t, x], t, t] - D[u[t, x], x, x] + a Exp[-(x)^2/b] u[t, x] ==
        0,
      u[0, x] == Exp[-1 (x - 1)^2], Derivative[1, 0][u][0, x] == 0,
      DirichletCondition[u[t, x] == 0, True]
      }, u, {t, 0, T}, {x, -L, L},
     Method -> {"PDEDiscretization" -> {"MethodOfLines", 
         "SpatialDiscretization" -> {"FiniteElement", 
           "MeshOptions" -> {"MaxCellMeasure" -> 0.1}}}}, 
     StepMonitor :> (Timer = t; ++nSteps)],
   {nSteps, Timer}]
  ] // AbsoluteTiming

To get a precise solution, I use "MaxCellMeasure" -> 0.1, but the volume of output InterpolatingFunction reaches 1050.8 MB, which makes it run slowly when I try to use the output function sol. So is there a way to get a small output with "MaxCellMeasure" -> 0.1 fixed here?

Improve this question
$\endgroup$
4
  • $\begingroup$ 1. "…is there a way to get a small output with "MaxCellMeasure" -> 0.1 fixed here" Do you mean you don't want to change the spatial grid size in InterpolatingFunction, or you just don't want to change it in solving process? 2. "it run slowly when I try to use the output function sol", how will you use sol? $\endgroup$ Commented Jul 4 at 4:53
  • $\begingroup$ @xzczd 1. To get a precise solution, I don't want to change it in solving process, but I want to change the spatial grid size in the output InterpolatingFunction. 2. For example, Plot[sol[t,50],{t,0,100}] runs slowly, although I found that sol[Range[0,100,0.1],50]//ListPlot is acceptable. $\endgroup$ Commented Jul 4 at 5:08
  • 1
    $\begingroup$ This sounds strange. In v14.2.1, Linux (Wolfram cloud) Plot[sol[t,50],{t,0,100}] is just a bit slower than sol[Range[0,100,0.1],50]//ListPlot: wolframcloud.com/obj/xzczd/Published/SE%20test.nb (I have to enlarge MaxCellMeasure a bit on cloud, but this should not be a problem. ) Which version are you in? $\endgroup$ Commented Jul 4 at 5:53
  • $\begingroup$ The size of an interpolating function should not have much if any effect on the performance of evaluation of these functions. Can you show an example where the size has an effect? $\endgroup$ Commented Jul 7 at 5:15

0

Reset to default

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.