[petsc-users] definition of level in PCILU

[Smith, Barry F.]

   There is a hint in a comment in matimpl.h 

  Note: the level of factor(i,j) is set as lvl(i,j) = min{ lvl(i,j), lvl(i,prow)+lvl(prow,j)+1)

   So it uses the "sum" rule.

   Barry



> On Jan 3, 2019, at 9:38 AM, Tim Steinhoff via petsc-users <petsc-users at mcs.anl.gov> wrote:
> 
> 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!