Re: Memory low for PDE

• To: mathgroup at smc.vnet.net
• Subject: [mg123194] Re: Memory low for PDE
• Date: Sat, 26 Nov 2011 05:06:47 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201111250954.EAA11084@smc.vnet.net>

```I Don't think it is of any help, but here is my output after a couple of

During evaluation of In[1]:= General::newpkg: Calculus`VectorAnalysis`
is now available as the Vector Analysis Package. See the Compatibility
Guide for updating information. >>
During evaluation of In[1]:= NDSolve::mxsst: Using maximum number of
grid points 100 allowed by the MaxPoints or MinStepSize options for
independent variable x. >>
During evaluation of In[1]:= NDSolve::mxsst: Using maximum number of
grid points 100 allowed by the MaxPoints or MinStepSize options for
independent variable y. >>
During evaluation of In[1]:= NDSolve::mxsst: Using maximum number of
grid points 100 allowed by the MaxPoints or MinStepSize options for
independent variable x. >>
During evaluation of In[1]:= General::stop: Further output of
NDSolve::mxsst will be suppressed during this calculation. >>
During evaluation of In[1]:= NDSolve::ibcinc: Warning: Boundary and
initial conditions are inconsistent. >>
During evaluation of In[1]:= NDSolve::bcart: Warning: An insufficient
number of boundary conditions have been specified for the direction of
independent variable x. Artificial boundary effects may be present in
the solution. >>
During evaluation of In[1]:= NDSolve::bcart: Warning: An insufficient
number of boundary conditions have been specified for the direction of
independent variable y. Artificial boundary effects may be present in
the solution. >>
During evaluation of In[1]:= Power::infy: Infinite expression 1/0.^0.5
encountered. >>
During evaluation of In[1]:= Power::infy: Infinite expression 1/0.^1.5
encountered. >>
During evaluation of In[1]:= Infinity::indet: Indeterminate expression
0. ComplexInfinity encountered. >>
During evaluation of In[1]:= Power::infy: Infinite expression 1/0.^0.5
encountered. >>
During evaluation of In[1]:= General::stop: Further output of
Power::infy will be suppressed during this calculation. >>
During evaluation of In[1]:= Infinity::indet: Indeterminate expression
0. ComplexInfinity encountered. >>
During evaluation of In[1]:= Infinity::indet: Indeterminate expression
0. ComplexInfinity encountered. >>
During evaluation of In[1]:= General::stop: Further output of
Infinity::indet will be suppressed during this calculation. >>
During evaluation of In[1]:= NDSolve::nlnum: The function value
{0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,<<20352>>} is not a list of numbers with dimensions {20402} at {t,psi[x,y,t],theta[x,y,t]} = {0.0000292503,{<<1>>},{{-0.999971,-0.999971,-0.999971,-0.999971,-0.999971, -0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,<<8>>,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971, -0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,-0.999971,<<51>>},<<49>>,<<51>>}}. >>
During evaluation of In[1]:= NDSolve::eerr: Warning: Scaled local spatial error estimate of 2.0471904396064455`*^23 at t = 0.000020880307835235008` in the direction of independent variable x is much greater than prescribed error tolerance. Grid spacing with 101 points may be too large to achieve the desired accuracy or precision. A singularity may have formed or you may want to specify a smaller grid spacing using the MaxStepSize or MinPoints method options. >>
Out[7]= {{psi->InterpolatingFunction[{{-5.,5.},{-5.,5.},{0.,0.0000208803}},<>],theta->InterpolatingFunction[{{-5.,5.},{-5.,5.},{0.,0.0000208803}},<>]}}

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On Nov 25, 2011, at 10:54 AM, S=E9rgio Lira wrote:

> Hello folks,
>
> I am trying to solve some coupled partial diferential equations using
> NDSolve but after 10 min of calculations the kernel shuts down and
> says: "No more memory available. Mathematica kernel has shut down."
>
> The equations are pretty huge and I have tried to change some
> integration options such as AccuracyGoal, MaxStepFraction,
> PrecisionGoal, MaxSteps, Method, SpatialDiscretization, but still
> couldn't solve the equations.
>
> This is the program:
>
> << Calculus`VectorAnalysis`
>
> Nch[f_, x_, y_, t_] := Nch[f, x,y, t] = (Grad[f, Cartesian[x, y, z]])/
> y, z]])]];
> Sch[f_, x_, y_, t_] :=Sch[f, x, y, t] = CrossProduct[Nch[f, x, y, t],
> {0, 0, 1}];
> K[f_, x_, y_, t_] := K[f, x, y, t] = -Div[Nch[f, x, y, t],
> Cartesian[x, y, z]];
> G[f_, x_, y_, t_] := G[f, x, y, t] = 2*DotProduct[Sch[f, x, y, t],
> (B*Grad[K[f, x, y, t], Cartesian[x, y, z]] - {x, y, 0})];
>
> eps = 0.1; epst = 0.2; B = 0.01;
>
> eqn2 = NDSolve[{
>
> epst*D[psi[x, y, t], t] == Laplacian[psi[x, y, t], Cartesian[x, y,
> z]]
> + 1/(eps*Sqrt[8])*G[theta[x, y, t], x, y, t]*(1 - (theta[x, y,
> t])^2),
>
> eps^2*D[theta[x, y,t], t] == Laplacian[theta[x, y, t], Cartesian[x, y,
> z]] + eps^2*DotProduct[{0, 0, 1}, CrossProduct[Grad[psi[x,y, t],
> Cartesian[x, y, z]], Grad[theta[x, y, t], Cartesian[x, y, z]]]],
>
> psi[x, y, 0] == 0, psi[-5, y, t] == 0, psi[5, y, t] == 0, psi[x, -5,
> t] == 0, psi[x, 5, t] == 0,
>
> theta[x, y, 0] == Tanh[(1 - Sqrt[x^2 + y^2])/(0.1*Sqrt[2])],
> theta[x, -5, t] == 0, theta[x, 5, t] == 0, theta[-5, y, t] ==0,
> theta[5, y, t] == 0},
> {psi, theta}, {x, -5, 5}, {y, -5, 5}, {t, 0, 5}]
>
>
> Should I try to decrease the integration step and grid? Is there any
> method that could help?
>
> Cheers,
> Sergio
>

```

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