[Trilinos-Users] AztecOO Convergence

[Mike Heroux]

Ammar,

Just to round out the discussion of increasing iterations as processor count
increases, here are two more observations:

1) Allowing overlap in the subdomains for domain decomposition
preconditioners (redundantly computing some rows of the local
preconditioner, something that both AztecOO and Ifpack support) reduces the
rate of iteration increases, but with extra cost per iteration.  Typically
one or two levels of overlap can have a net positive effect.

2) Multi-level preconditioners, such as those in the Trilinos package ML,
suffer somewhat from the same problem, since they often use the same type of
local domain solvers as smoothers.  However, there is a relatively new
approach (using a very old method) of using Chebyshev polynomials as
smoothers.  The advantage of this approach is that polynomial
preconditioners can be applied globally regardless of the number of
processors, so they don't suffer from the iteration increases.

Mike