Tim,
This is an unrelated comment, but may help you with scaling to
many processes.
Since the matrix is so SMALL it will be hard to get good scaling on
the linear solves
for a large number of processes, but since you need MANY right hand
sides you
might consider having different groups of processes (MPI_Comms) handle
collections
of right hand sides. For example if you have 64 processes you might
use 4 MPI_Comm's
each of size 16, or even 8 MPI_Comm's each of size 8. Coding this is easy
simply use MPI to generate the appropriate communicator (for the
subsets of processes)
and then create the Mat, the KSP etc on that communicator instead of
MPI_COMM_WORLD
Barry
On Nov 20, 2007, at 11:45 AM, Tim Stitt wrote:
Hi all (again),
I finally got some data back from the KSP PETSc code that I put
together to solve this sparse inverse matrix problem I was looking
into. Ideally I am aiming for a O(N) (time complexity) approach to
getting the first 'k' columns of the inverse of a sparse matrix.
To recap the method: I have my solver which uses KSPSolve in a loop
that iterates over the first k columns of an identity matrix B and
computes the corresponding x vector.
I am just a bit curious about some of the timings I am
obtaining...which I hope someone can explain. Here are the timings I
obtained for a global sparse matrix (4704 x 4704) and solving for the
first 1176 columns in the identity using P processes (processors) on
our cluster.
(Timings are given in seconds for each process performing work in the
loop and were obtained by encapsulating the loop with the cpu_time()
Fortran intrinsic. The MUMPS package was requested for
factorisation/solving, although similar timings were obtained for
both the native solver and SUPERLU)
P=1 [30.92]
P=2 [15.47, 15.54]
P=4 [4.68, 5.49, 4.67, 5.07]
P=8 [2.36, 4,23, 2.81, 2.54, 3.42, 2.22, 1.41, 3.15]
P=16 [1.04, 0.45, 1.08, 0.27, 0.87, 0.93, 1.1, 1.06, 0.29, 0.34,
0.73, 0.25, 0.43, 1.09, 1.08, 1.1]
Firstly, I notice very good scalability up to 16 processes...is this
expected (by those people who use these solvers regularly)?
Also I notice that the timings per process vary as we scale up. Is
this a load-balancing problem related to more non-zero values being
on a given processor than others? Once again is this expected?
Please excuse my ignorance of matters relating to these solvers and
their operation...as it really isn't my field of expertise.
Regards,
Tim.
--Dr. Timothy Stitt <timothy_dot_stitt_at_ichec.ie>
HPC Application Consultant - ICHEC (www.ichec.ie)
Dublin Institute for Advanced Studies
5 Merrion Square - Dublin 2 - Ireland
+353-1-6621333 (tel) / +353-1-6621477 (fax)