Modelling questions

[И Страшко]

So here are my general modelling question.

Background.   I am working on a heated mass.  This mass, of course, follows the heat equation,

del2(T) = partial(T)/dt + q_e(x)

q_e is some heat flux which comes into the system

This is all coded in something called a function "heat"

Boundary conditions.  For the first (aphysical) model, I've decided that the boundary conditions should simply be that the edges don't change, that is, they are a perfect heat sink.

Question- The "core" of my iterator looks like this.  T is a 4-d matrix in (x,y,z,t)...  Tnow and Tlast are (x,y,z)...

for itime = 2:size(timeaxis)(2)

  disp(itime);

% Tnow is the previous temperature.

  Tlast = Tnow;

% Tnow is now set to the current temperature

  [Tnow, fcn, info] = fsolve(@heat,Tlast); 

% Force Tnow to not lose boundary conditions

  Tnow(1,:,:)=Tzero;

  Tnow(end,:,:)=Tzero;

  Tnow(:,1,:)=Tzero;

  Tnow(:,end,:)=Tzero;

  Tnow(:,:,1)=Tzero;

  Tnow(:,:,end)=Tzero;

% Update the array with the current temperature

  T(:,:,:,itime) = Tnow;

% Continue if we converged.

  if (! (info==1))

    disp("info not one:"),disp(info)

    break

  endif

endfor

Question 2- This concerns the function "heat."  When I rewrite my model to include thin layers of insulators on some walls and not on others, is it possible to compute the laplacian in segments, that is, so that part of the array has big blocks (dx, dy, dz are big) and the insulating walls have smaller blocks (that is, so that this part of the array has dx, dy, dz being small).  I mean, of course I can WRITE this in octave, the question is what the numeric analysis pitfalls will be when attempting this.

Thanks for the help!

-John Staško