Thank you for your reply. I understand that DD methods are not quite
that popular now. But I wanted to explore the avenue keeping in mind the
issue of scalability as well. For scalability, as you mention
communication is probably the bottleneck.
No, communication is not the issue. It's not a computational problem but
a mathematical one: in each DD iteration, you only transport information
from one subdomain to the next subdomain. If you split the domain into
too many subdomains, you will need a lot of iterations to transport
information across the entire domain. In other words, the reason why DD
methods are not good for large processor counts is because the number of
outer iterations grows with the number of processors you have -- it just
doesn't scale.
A different perspective is that DD methods lack some kind of coarse grid
correction in which you exchange information globally. You could
presumably use a non-overlapping mortar method and get good parallel
scalability if you had a good preconditioner for the Schur complement
posed on the skeleton (i.e., the DoFs that are located on the interfaces
between subdomains). Of course, constructing such preconditioners has
also proven to be difficult.
It would be very helpful if you could provide me with some pointers for
where and how to change the p4est functions in deal.II.
All of the code that interfaces with p4est is in
source/distributed/tria.cc. We build the ghost layer in line 2532 where
we call p4est_ghost_new (through its dimension independent alias). That
function is defined here:
http://p4est.github.io/api/p4est__ghost_8h.html#a34a0bfb7169437f6fc2382a67c47e89d
You'll probably have to call p4est_ghost_expand() one or more times:
http://p4est.github.io/api/p4est__ghost_8h.html#ab9750fa62cbc17285a0eb5cfe13a1e28
I would just stick a call to this function right after the one to
ghost_new as a trial and see what happens in a small test program that
on each processor just outputs information about what cells are locally
owned and which are ghosts.
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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