Load Balancing and KSPSolve

[Satish Balay]

Can you send the -log_summary for your runs [say p=1, p=8]

Satish

On Tue, 20 Nov 2007, 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.
> 
>