Converting this 3-nested for loop for parfor

The context is a finite element assembly routine where I need to loop over a bunch of mesh elements. In principle, each iteration computes a small local matrix (3x3 in this case) and inserts it into the much larger global matrix according to the indices ie and je.

The iterations are completely independent of each other as I'm pretty sure as my code stands now, it could run through the outer loop in any order without any problems. But of course, this version isn't accepted by MATLAB for parfor format. Can anyone help me out here?

    NLoc = 3;

    Klocal = zeros(NLoc);
    blocal = zeros(NLoc,1);

    Aglobal = zeros(NLoc*nElem);
    bglobal = zeros(NLoc*nElem,1);

    for k=1:nElem

        kk = NLoc*(k-1);

        Klocal = function1(nElem,k);

        blocal = function2(nElem,k);

        for i=1:NLoc
            ie = i+kk;

            bglobal(ie) = bglobal(ie) + blocal(i);

            for j=1:NLoc

                je = j+kk;
                Aglobal(ie,je) = Aglobal(ie,je) + Klocal(i,j);

            end

        end

    end

Answer 1

[Matt J]

If I'm interpreting it right, it looks like

    Aglobal = cell(nElem,1);
    bglobal = cell(nElem,1);

    parfor k=1:nElem

     Aglobal{k}=function1(nElem,k);
     bglobal{k}=function2(nElem,k);

    end

    Aglobal=blkdiag(Aglobal{:});
    bglobal=cell2mat(bglobal);

[Justin]

This works for part of my code, so thanks a ton! I might post a follow up as another question that's similar but I think might have to be handled differently.

What happens if we have, say

    Klocal1 = function1(nElem,k);
    Klocal2 = function2(nELem,k);
    Klocal3 = function3(nElem,k);

but these local matrices get inserted into different places in the global matrix? i.e. not just Aglobal{k} = function1(...) + function2(...) + function3(...)

As well, some of the local matrices I've got won't fit a block diagonal structure for blkdiag

[Matt J]

You can create an MxN cell array to hold the blocks and fill them as you wish. Essentially, the same was done above with bglobal, which was not block diagonal.

[Justin]

I've posted another question here: http://www.mathworks.com/matlabcentral/answers/105530-converting-this-nested-for-loop-for-parfor-use

Do you think you could take a look? I'm still not sure I'm understanding how t do it when the matrices need to be inserted in a non-diagonal manner. I understand how to do so for bglobal since essentially each member of the cell array was just inserted right after one another.