[petsc-users] no decrease in iteration counts of KSPCG during time stepping

[Jed Brown]

Umut Tabak <u.tabak at tudelft.nl> writes:
> Preconditioner side: my experience was that one should be really lucky 
> to get a good preconditioner which is really really rare, as mentioned, 
> especially for ill-conditioned problems, almost impossible. If my 
> condition number estimate is above, say, 1e4  1e5, I do not expect much 
> from iterative methods, 

Ill-conditioning is a red herring.  For example, FMG can solve
well-behaved problems with 1e12 condition number in one cycle (about 5
"work units").  OTOH, very well-conditioned problems with eigenvalues
encircling the origin converge extremely slowly (these are
nonsymmetric).  Anyway, some SPD industrial problems see poor
performance with AMG, BDDC, and similar otherwise-scalable methods due
to discretization or physical features that elude the heuristics used to
produce good coarse spaces.  Sometimes these problems can be formulated
in more solver-friendly ways.  Other times, custom methods would be
needed.  Or the methods could converge well, but only with high grid
complexity (coarse spaces that do not decay in size fast enough).
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