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Re: NDSolve memory management problem

Ignore my other post in this thread (if it shows up). I forgot that
Daniel from Wolfram once showed a much easier way: simply set  the
range of the time variable inside the NDSolve command to {t,100,100}
instead of {t,0,100}. Since the initial value is given at time zero,
NDSolve still calculates the solution from time 0 to 100, but it only
remembers the values for t in the "interval" from 100 to 100, and so
uses only a small amount of memory.

My first post gave the older method I used before I read about the method
above. A variant of it may still be useful if you want to save as much of the
solution as you have memory for.


On Jul 20, 1:00 pm, David Szekely <dr.szek... at> wrote:
> Hi there!
> I'm currently trying to run a simulation in Mathematica usingNDSolvein se=
veral dimensions. However, it tends to chew up system memory very quickly a=
nd give the standard:
> "No more memory available.
> Mathematica kernel has shut down.
> Try quitting other applications and then retry."
> message.
> Here's some code for the heat equation in 4 dimensions over relatively sm=
all ranges to show what I mean:
> i = 0;
> sol =NDSolve[{D[u[t, x, y, z], t] ==
>     D[u[t, x, y, z], x, x] + D[u[t, x, y, z], y, y] +
>      D[u[t, x, y, z], z, z],
>    u[0, x, y, z] == 0,
>    u[t, 0, y, z] == Sin[t],
>    u[t, 40, y, z] == 0,
>    u[t, x, 0, z] == Sin[t],
>    u[t, x, 40, z] == 0,
>    u[t, x, y, 0] == Sin[t],
>    u[t, x, y, 40] == 0},
>   {u}, {t, 0, 100}, {x, 0, 40}, {y, 0, 40}, {z, 0, 40},
>   MaxSteps -> Infinity, MaxStepSize -> 1,
>   EvaluationMonitor :> If[t > i,
>     Print[{t, MemoryInUse[]/1024^2 // N}];
>     i += 10;]
>   ]
> MemoryInUse[]/1024^2 // N
> The only solutions I need are at t = 0, 5, 10, 15 etc.. Ideally, what i=
'd like to be able to do is add a function in "EvaluationMonitor" which rem=
oves all values of t other than the ones that I need *as it solves the syst=
em*. This would significantly reduce the strain on system memory. I would g=
reatly appreciate help on this problem! Adding more memory is not a good so=
lution since my actual problem kills a system with 12 Gb of memory :(

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