[Dune] [#729] Singularity detection in FieldMatrix' LU decomposition buggy (Attachment added)

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FS#729 - Singularity detection in FieldMatrix' LU decomposition buggy
User who did this - Andreas Lauser (andlaus)

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Sure, I know that it is ill-conditioned and I'm also not surprised. But emerges directly from my physical problem, and I think I should not change the model unnecessarily. What I could do is that I could for example multiply the second row with 10^9, but this would be much more effort than to fix the pivoting (and wouldn't change the conditioning if I'm not mistaken).

To fix the problem properly, I think that the singularity threshold needs to be be dependent on the largest entry that occurs in a column during the decomposition. I just have trouble finding a efficient way to implement this. In the mean time I would like to propose the attached patch to fix the problem, if compiled with -DNDEBUG the singularity detection just breaks down to a comparison with 0, else the singularity thershold is column specific.
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