[petsc-users] GAMG scaling

[Zhang, Hong]

Fande:
Hong,
Thanks for your improvements on PtAP that is critical for MG-type algorithms.

On Wed, May 3, 2017 at 10:17 AM Hong <hzhang at mcs.anl.gov<mailto:hzhang at mcs.anl.gov>> wrote:
Mark,
Below is the copy of my email sent to you on Feb 27:

I implemented scalable MatPtAP and did comparisons of three implementations using ex56.c on alcf cetus machine (this machine has small memory, 1GB/core):
- nonscalable PtAP: use an array of length PN to do dense axpy
- scalable PtAP:       do sparse axpy without use of PN array

What PN means here?
Global number of columns of P.

- hypre PtAP.

The results are attached. Summary:
- nonscalable PtAP is 2x faster than scalable, 8x faster than hypre PtAP
- scalable PtAP is 4x faster than hypre PtAP
- hypre uses less memory (see job.ne399.n63.np1000.sh<http://job.ne399.n63.np1000.sh/>)

I was wondering how much more memory PETSc PtAP uses than hypre? I am implementing an AMG algorithm based on PETSc right now, and it is working well. But we find some a bottleneck with PtAP. For the same P and A, PETSc PtAP fails to generate a coarse matrix due to out of memory, while hypre still can generates the coarse matrix.

I do not want to just use the HYPRE one because we had to duplicate matrices if I used HYPRE PtAP.

It would be nice if you guys already have done some compassions on these implementations for the memory usage.
Do you encounter memory issue with  scalable PtAP? Karl had a student in the summer who improved MatPtAP(). Do you use the latest version of petsc?
HYPRE may use less memory than PETSc because it does not save and reuse the matrices.

I do not understand why generating coarse matrix fails due to out of memory. Do you use direct solver at coarse grid?
Hong

Based on above observation, I set the default PtAP algorithm as 'nonscalable'.
When PN > local estimated nonzero of C=PtAP, then switch default to 'scalable'.
User can overwrite default.

For the case of np=8000, ne=599 (see job.ne599.n500.np8000.sh<http://job.ne599.n500.np8000.sh/>), I get
MatPtAP                   3.6224e+01 (nonscalable for small mats, scalable for larger ones)
scalable MatPtAP     4.6129e+01
hypre                        1.9389e+02

This work in on petsc-master. Give it a try. If you encounter any problem, let me know.

Hong

On Wed, May 3, 2017 at 10:01 AM, Mark Adams <mfadams at lbl.gov<mailto:mfadams at lbl.gov>> wrote:
(Hong), what is the current state of optimizing RAP for scaling?

Nate, is driving 3D elasticity problems at scaling with GAMG and we are working out performance problems. They are hitting problems at ~1.5B dof problems on a basic Cray (XC30 I think).

Thanks,
Mark

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