[Trilinos-Users] AztecOO Convergence

Randall Bramley bramley at cs.indiana.edu
Mon Nov 21 09:01:39 MST 2005

> In AztecOO, why does convergence deteriorate as the number
> of processors is increased?

At last, a question I can answer. :-)

The preprocessing is usually block diagonal, and as the number of
processors increases, the blocks become smaller - in the limit, the
preconditioner becomes diagonal scaling.  Fewer processors leads to
the block becoming larger, in the limit becoming an incomplete
factorization on the whole matrix.  This is generally a more
accurate preconditioner since it brings in more off-diagonal elements
and hence accounts for longer-range interactions in the linear system.

So it's normal to have the quality of preconditioning lower (and hence
number of iterations higher) when the number of processors increases.

> Is there any options one can use to eliminate this problem?
> Are there any particular solvers which will yield same
> convergence regardless of the number of processors?

Yes, but they are not good ones to choose: use no preconditioning or
just diagonal scaling.  But you're likely to find the wall clock
time increases over letting the number of iterations increase.

-Randall Bramley

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