Re: Memory low for PDE

*To*: mathgroup at smc.vnet.net*Subject*: [mg123194] Re: Memory low for PDE*From*: Arturo Amador <arturo.amador at ntnu.no>*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 seconds for your code: 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}},<>]}} -- Arturo Amador Cruz Stipendiat Norges Teknisk-Naturvitenskapelige Universitet (NTNU) Institutt for Fysikk Fakultet for Naturvitenskap og Teknologi H=F8gskoleringen 5, Realfagbygget, E5-108 Telefon (735) 93366 NO-7491 TRONDHEIM NORWAY arturo.amador at ntnu.no 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]])/ > Sqrt[DotProduct[(Grad[f, Cartesian[x, y, z]]), (Grad[f, Cartesian[x, > 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 >

**References**:**Memory low for PDE***From:*Sérgio Lira <sergiobodoh@gmail.com>