[petsc-users] Scaling with number of cores

[TAY wee-beng]

On 1/11/2015 12:47 AM, Matthew Knepley wrote:
> On Sat, Oct 31, 2015 at 11:34 AM, TAY wee-beng <zonexo at gmail.com 
> <mailto:zonexo at gmail.com>> wrote:
>
>     Hi,
>
>     I understand that as mentioned in the faq, due to the limitations
>     in memory, the scaling is not linear. So, I am trying to write a
>     proposal to use a supercomputer.
>
>     Its specs are:
>
>     Compute nodes: 82,944 nodes (SPARC64 VIIIfx; 16GB of memory per node)
>
>     8 cores / processor
>
>     Interconnect: Tofu (6-dimensional mesh/torus) Interconnect
>
>     Each cabinet contains 96 computing nodes,
>
>     One of the requirement is to give the performance of my current
>     code with my current set of data, and there is a formula to
>     calculate the estimated parallel efficiency when using the new
>     large set of data
>
>     There are 2 ways to give performance:
>     1. Strong scaling, which is defined as how the elapsed time varies
>     with the number of processors for a fixed
>     problem.
>     2. Weak scaling, which is defined as how the elapsed time varies
>     with the number of processors for a
>     fixed problem size per processor.
>
>     I ran my cases with 48 and 96 cores with my current cluster,
>     giving 140 and 90 mins respectively. This is classified as strong
>     scaling.
>
>     Cluster specs:
>
>     CPU: AMD 6234 2.4GHz
>
>     8 cores / processor (CPU)
>
>     6 CPU / node
>
>     So 48 Cores / CPU
>
>     Not sure abt the memory / node
>
>
>     The parallel efficiency ‘En’ for a given degree of parallelism ‘n’
>     indicates how much the program is
>     efficiently accelerated by parallel processing. ‘En’ is given by
>     the following formulae. Although their
>     derivation processes are different depending on strong and weak
>     scaling, derived formulae are the
>     same.
>
>     From the estimated time, my parallel efficiency using  Amdahl's
>     law on the current old cluster was 52.7%.
>
>     So is my results acceptable?
>
>     For the large data set, if using 2205 nodes (2205X8cores), my
>     expected parallel efficiency is only 0.5%. The proposal recommends
>     value of > 50%.
>
> The problem with this analysis is that the estimated serial fraction 
> from Amdahl's Law  changes as a function
> of problem size, so you cannot take the strong scaling from one 
> problem and apply it to another without a
> model of this dependence.
>
> Weak scaling does model changes with problem size, so I would measure 
> weak scaling on your current
> cluster, and extrapolate to the big machine. I realize that this does 
> not make sense for many scientific
> applications, but neither does requiring a certain parallel efficiency.
Ok I check the results for my weak scaling it is even worse for the 
expected parallel efficiency. From the formula used, it's obvious it's 
doing some sort of exponential extrapolation decrease. So unless I can 
achieve a near > 90% speed up when I double the cores and problem size 
for my current 48/96 cores setup, extrapolating from about 96 nodes to 
10,000 nodes will give a much lower expected parallel efficiency for the 
new case.

However, it's mentioned in the FAQ that due to memory requirement, it's 
impossible to get >90% speed when I double the cores and problem size 
(ie linear increase in performance), which means that I can't get >90% 
speed up when I double the cores and problem size for my current 48/96 
cores setup. Is that so?

So is it fair to say that the main problem does not lie in my 
programming skills, but rather the way the linear equations are solved?

Thanks.
>
>   Thanks,
>
>      Matt
>
>     Is it possible for this type of scaling in PETSc (>50%), when
>     using 17640 (2205X8) cores?
>
>     Btw, I do not have access to the system.
>
>
>
>
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>
>
>
>
>
> -- 
> What most experimenters take for granted before they begin their 
> experiments is infinitely more interesting than any results to which 
> their experiments lead.
> -- Norbert Wiener

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