[petsc-dev] New implementation of PtAP based on all-at-once algorithm

[Zhang, Hong]

I would suggest Fande add this new implementation into petsc. What is the algorithm?
I'll try to see if I can further reduce memory consumption of the current symbolic PtAP when I get time.
Hong

On Fri, Apr 12, 2019 at 8:27 AM Mark Adams via petsc-dev <petsc-dev at mcs.anl.gov<mailto:petsc-dev at mcs.anl.gov>> wrote:


On Thu, Apr 11, 2019 at 11:42 PM Smith, Barry F. <bsmith at mcs.anl.gov<mailto:bsmith at mcs.anl.gov>> wrote:


> On Apr 11, 2019, at 9:07 PM, Mark Adams via petsc-dev <petsc-dev at mcs.anl.gov<mailto:petsc-dev at mcs.anl.gov>> wrote:
>
> Interesting, nice work.
>
> It would be interesting to get the flop counters working.
>
> This looks like GMG, I assume 3D.
>
> The degree of parallelism is not very realistic. You should probably run a 10x smaller problem, at least, or use 10x more processes.

   Why do you say that? He's got his machine with a certain amount of physical memory per node, are you saying he should ignore/not use 90% of that physical memory for his simulation?

In my experience 1.5M equations/process about 50x more than applications run, but this is just anecdotal. Some apps are dominated by the linear solver in terms of memory but some apps use a lot of memory in the physics parts of the code.

The one app that I can think of where the memory usage is dominated by the solver does like 10 (pseudo) time steps with pretty hard nonlinear solves, so in the end they are not bound by turnaround time. But they are kind of a odd (academic) application and not very representative of what I see in the broader comp sci community. And these guys do have a scalable code so instead of waiting a week on the queue to run a 10 hour job that uses 10% of the machine, they wait a day to run a 2 hour job that takes 50% of the machine because centers scheduling policies work that way.

He should buy a machine 10x bigger just because it means having less degrees of freedom per node (whose footing the bill for this purchase?). At INL they run simulations for a purpose, not just for scalability studies and there are no dang GPUs or barely used over-sized monstrocities sitting around to brag about twice a year at SC.

I guess the are the nuke guys. I've never worked with them or seen this kind of complexity analysis in their talks, but OK if they fill up memory with the solver then this is representative of a significant (DOE)app.


   Barry



> I guess it does not matter. This basically like a one node run because the subdomains are so large.
>
> And are you sure the numerics are the same with and without hypre? Hypre is 15x slower. Any ideas what is going on?
>
> It might be interesting to scale this test down to a node to see if this is from communication.
>
> Again, nice work,
> Mark
>
>
> On Thu, Apr 11, 2019 at 7:08 PM Fande Kong <fdkong.jd at gmail.com<mailto:fdkong.jd at gmail.com>> wrote:
> Hi Developers,
>
> I just want to share a good news.  It is known PETSc-ptap-scalable is taking too much memory for some applications because it needs to build intermediate data structures.  According to Mark's suggestions, I implemented the  all-at-once algorithm that does not cache any intermediate data.
>
> I did some comparison,  the new implementation is actually scalable in terms of the memory usage and the compute time even though it is still  slower than "ptap-scalable".   There are some memory profiling results (see the attachments). The new all-at-once implementation use the similar amount of memory as hypre, but it way faster than hypre.
>
> For example, for a problem with 14,893,346,880 unknowns using 10,000 processor cores,  There are timing results:
>
> Hypre algorithm:
>
> MatPtAP               50 1.0 3.5353e+03 1.0 0.00e+00 0.0 1.9e+07 3.3e+04 6.0e+02 33  0  1  0 17  33  0  1  0 17     0
> MatPtAPSymbolic       50 1.0 2.3969e-0213.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00  0  0  0  0  0   0  0  0  0  0     0
> MatPtAPNumeric        50 1.0 3.5353e+03 1.0 0.00e+00 0.0 1.9e+07 3.3e+04 6.0e+02 33  0  1  0 17  33  0  1  0 17     0
>
> PETSc scalable PtAP:
>
> MatPtAP               50 1.0 1.1453e+02 1.0 2.07e+09 3.8 6.6e+07 2.0e+05 7.5e+02  2  1  4  6 20   2  1  4  6 20 129418
> MatPtAPSymbolic       50 1.0 5.1562e+01 1.0 0.00e+00 0.0 4.1e+07 1.4e+05 3.5e+02  1  0  3  3  9   1  0  3  3  9     0
> MatPtAPNumeric        50 1.0 6.3072e+01 1.0 2.07e+09 3.8 2.4e+07 3.1e+05 4.0e+02  1  1  2  4 11   1  1  2  4 11 235011
>
> New implementation of the all-at-once algorithm:
>
> MatPtAP               50 1.0 2.2153e+02 1.0 0.00e+00 0.0 1.0e+08 1.4e+05 6.0e+02  4  0  7  7 17   4  0  7  7 17     0
> MatPtAPSymbolic       50 1.0 1.1055e+02 1.0 0.00e+00 0.0 7.9e+07 1.2e+05 2.0e+02  2  0  5  4  6   2  0  5  4  6     0
> MatPtAPNumeric        50 1.0 1.1102e+02 1.0 0.00e+00 0.0 2.6e+07 2.0e+05 4.0e+02  2  0  2  3 11   2  0  2  3 11     0
>
>
> You can see here the all-at-once is a bit slower than ptap-scalable, but it uses only much less memory.
>
>
> Fande
>

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