Reduce computational time for ODE solver

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Hi all
i have this code
for iDom_hot = 1:numel(Dall_hot)
xRange_hot = Dall_hot{iDom_hot};
for iInitial_hot = 1:numel(Y0_Lhot)
Mach_hot=Mach_cell_hot{iInitial_hot};
Tw_hot=Tnew_cell_hot{iDom_hot};
Ch_hot=ChL_cell_hot{iDom_hot,iInitial_hot};
Fc_hot=fL_cell_hot{iDom_hot,iInitial_hot};
Hrrj_hot=hrrj_cell_hot{iDom_hot};
Aeff_hot=Aeff_cell_hot{iDom_hot,iInitial_hot};
Perim_hot=Perim_cell_hot{iDom_hot,iInitial_hot};
L_Ength_hot=L_cell_hot{iDom_hot};
Pend_chamb_hot=Pressure_ED_chamber_cell_hot{iDom_hot};
if Ch_hot>0&&Fc_hot>0&&Hrrj_hot>0&&Tw_hot>0 &&Mach_hot>0&&Perim_hot>0&&Aeff_hot>0&&L_Ength_hot>0&&Pend_chamb_hot>0
[xSol_hot{iDom_hot,iInitial_hot},YSol_L_hot{iDom_hot,iInitial_hot}]=ode23(@(x,Y)...
chambesinglebobbTWVARIABILEHOT(x,Y,Ch_hot,Aeff_hot,Perim_hot,Fc_hot,Tw_hot),xRange_hot,Y0_Lhot{iInitial_hot});
if(any(YSol_L_hot{iDom_hot,iInitial_hot}(:,3)>0.8))
disp([ ' condizione verificata'])
disp (iDom_hot)
disp(iInitial_hot)
break
end
end
end
end
that solve iteratively an ODE system:
function dYdx=tubosinglebobb(x,Y,Ch_hot,Aeff_hot,Perim_hot,Fc_hot,Tw_hot)
gamma=1.667;
Dexttantalum=0.001500000000000;
Tt=Y(1);
Pt=Y(2);
M=Y(3);
dTtdx=Ch_hot*(Tw_hot-Tt)*(Perim_hot/Aeff_hot);
dPtdx=Pt*((-gamma*((M^2)/2)*Fc_hot*(Perim_hot/Aeff_hot))-...
(gamma*((M^2)/2)*dTtdx*(1/Tt)));
dMdx=M*(((1+((gamma-1)/2)*M^2)/(1-M^2))*((gamma*(M^2)*Fc_hot*...
Perim_hot)/(2*Aeff_hot))+...
((0.5*((gamma*M^2)+1))*(1+((gamma-1)/2)*M^2)/(1-M^2))*...
(Ch_hot*(Tw_hot-Tt)*Perim_hot)/(Aeff_hot*Tt));
dYdx=[dTtdx;dPtdx;dMdx];
end
the computational time for solving the ODE system is very very large (days) due to ( i think) one problem. In particular:
numel(Dall_ho) is more or less equal to 700, while numel(Y0_Lhot) is equal to 30, those domains dimensions should not be problematic, the real problem is on the oscillation of the solution YSol_L_hot when its third column reach value around 1. I have prepared a break for this eventuality but doesn't seem to reduce computational time!! I don't really know which is the problem, could it be a syntax error?
Thank you all for the help
Regards

Accepted Answer

Bjorn Gustavsson
Bjorn Gustavsson on 19 Sep 2020
Have you tried the other ODE-integrating functions? From your problem description it sounds like your ODEs are stiff - for that ode23 is not the optimal function, perhaps you get much better success with ode15s or oed23s that both are designed for stiff ODEs. One further note is that to me it seems like the temperature-derivative does not depend on the other 2 parameters, perhaps you can refactor the problem to first integrate that ODE and then use that solution when integrating the other 2.
  8 Comments
Bjorn Gustavsson
Bjorn Gustavsson on 20 Sep 2020
Since you're modelling some physical system, where you have some assumptions and some physical constraints on what makes a valid solution. You have to make some analysis of what happens with your solutions (M < 0) and also make some checks on what happens around those periods. For handling things like this you can use the options to force (some components of) the solution to be positive: ode-options, and to handle shocks and transitions you can use the even-handling: event-location.

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