[petsc-dev] DD FAQ

[Jed Brown]

On Mon, 3 May 2010 18:16:09 -0700, Barry Smith <bsmith at mcs.anl.gov> wrote:
>     Ok, we are talking about something different. I was thinking only
> of additive Schwarz but where the "restriction" from the overlapped
> region and the "interpolation" back to the overlapped region was
> scaled by some factors between 0 and 1 instead of being just 0 or 1 as
> is supported in PCASM.

I don't know what benefit that offers, it sounds like going part way
from classical AS to RAS, but I wouldn't expect it to change the
asymptotics.

These optimized methods change the convergence behavior rather
significantly.  In particular, for overlap h, they produce 1-level
preconditioned condition numbers as good as O(h^{-1/5}) instead of the
usual O(h^{-1}) for standard AS, and as good as O(h^{-1/4}) for
nonoverlapping methods with element size h.

Jed