[petsc-users] definition of level in PCILU

[Tim Steinhoff]

Dear PETSc Team

I checked the references that are stated on

https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCILU.html

to get an idea of the definition of <level> that is used in PETSc's
ILU(k) implementation. I haven't found anything of substance in the
first reference (T. Dupont, R. Kendall, and H. Rachford) and only a
rather vague description in the third one (Sec. 3.1 in the book). The
second one isn't yet available to me.

Additionally, I checked

https://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf

which gives a thorough explanation in Subsec. 10.3.3. Also, I took a look at

https://www.cs.odu.edu/~pothen/Papers/ilu-levels.pdf

which gives _two_ different definitions of level (p. 3 'sum' and
'max'). The sum-version equals the one in Saad. The statement on
Wikipedia defines level according to the nonzero pattern of powers of
A.

So the question is: Which definition of <level> was utilized for the
implementation in PETSc? Any of the above? Or something else?

Thanks and kind regards
tim

P.S.: Happy New Year!