How to use parfor in explicit method?

When I'm trying to use explicit method to solve a heat transfer problem, I tried to use parfor like

    parfor i=2:n+2
        for j=2:n+2
            Tnew(i,j)=Told(i,j)+k*(Told(i-1,j)+Told(i+1,j)+Told(i,j-1)+Told(i,j+1)-4*To(i,j));
        end
    end

However, this is extremely slow, about 10 times slower than a regular loop. So how to make it run faster? Or is it possible to do this on GPU?

Answer 1

[Walter Roberson]

I am surprised it allowed it. You should have had to write something closer to

    Tnew = zeros(n+2, n+2);
    parfor i=2:n+2
        ToldiPrev = Told(i-1,:);
        Toldi = Told(i,:);
        ToldiNext = Told(i+1,:);
        Tnewi = zeros(1,n+2);
        Toi = To(i,:);
        for j=2:n+2
            Tnewi(j) = Toldi(j) + k * (ToldiPrev(j) + ToldiNext(j) + Toldi(j-1) + Toldi(j+1) - 4 * Toi(j));
        end
        Tnew(i,:) = Tnewi;
    end

Answer 2

[Edric Ellis]

parfor generally doesn't offer much speedup when the body of the loop is a small amount of simple arithmetic like this. In this case, I think you'd be much better off trying to recast the update as a 2D convolution - using conv2. That will almost certainly be much faster (and can even run on the GPU).