Parallel graph coloring heuristics to color large-scale general jacobian matrices

[Rafael Santos Coelho]

Hello to everyone,

I've been working for some time on this piece of code for estimating
large-scale and general jacobian matrices via finite differences whose
sparsity patterns can be determined a priori. It basically uses a parallel
graph coloring heuristic to find a good vertex coloring for the column
intersection graph relative to the jacobian matrix at hand.

Now, I'd like to integrate that code into PETSc, but the problem is that I
don't know exactly how. So after spending a lot of time sifting through and
trying to grasp "the logic" of PETSc source code, especially, the source
code to the MatFDColoring module, I came up with a "tacky" solution
proposal: firstly, I would call my code in order to obtain the coloring in
parallel, and then I would have a routine (which would have to be embedded
in PETSc code base) that, on each processor, would build the "MatFDColoring"
data structure based on two things, the coloring found and the sparsity
pattern of the jacobian matrix in question.

It seems to me that this might work out, though I'm not entirely sure. What
do you guys think? Is there an easier and/or more "elegant" way to do this?

Thanks in advance,

Rafael
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