[petsc-users] Strong scaling concerns for PCBDDC with Vector FEM
neil liu
liufield at gmail.com
Tue Aug 20 12:35:50 CDT 2024
Hi, Matt,
I think the time listed here represents the maximum total time across
different processors.
Thanks a lot.
2 cpus
4 cpus 8 cpus
Event Count Time (sec) Count
Time (sec) Count Time (sec)
Max Ratio Max Ratio Max Ratio
Max Ratio Max Ratio Max Ratio
VecMDot 530 1.0 7.8320e+01 1.0 530 1.0
4.3285e+01 1.1 530 1.0 3.0476e+01 1.1
VecMAXPY 534 1.0 9.2954e+01 1.0 534 1.0
4.8378e+01 1.1 534 1.0 3.0798e+01 1.1
MatMult 8055 1.0 2.4608e+02 1.0 8103 1.0
1.2663e+02 1.0 8367 1.0 8.2942e+01 1.1
On Tue, Aug 20, 2024 at 1:16 PM Matthew Knepley <knepley at gmail.com> wrote:
> On Tue, Aug 20, 2024 at 1:10 PM neil liu <liufield at gmail.com> wrote:
>
>> Thanks a lot for your explanation, Stefano. Very helpful.
>> Yes. I am using dmplex to read a tetrahdra mesh from gmsh. With parmetis,
>> the scaling performance is improved a lot.
>> I will read your paper about how to change the basis for Nedelec
>> elements.
>>
>> cpu # time for 500 ksp steps (s) parallel efficiency
>> 2 546
>> 4 224 120%
>> 8 170 80%
>> This results are much better than previous attempt. Then I checked the
>> time spent by several Petsc built-in functions for the ksp solver.
>>
>> Functions time(2 cpus) time(4 cpus) time(8 cpus)
>> VecMDot 78.32 43.28 30.47
>> VecMAXPY 92.95 48.37 30.798
>> MatMult 246.08 126.63 82.94
>>
>> It seems from cpu 4 to cpu 8, the scaling is not as good as from cpu 2 to
>> cpu 4.
>> Am I missing something?
>>
>
> Did you normalize by the number of calls?
>
> Thanks,
>
> Matt
>
>
>> Thanks a lot,
>>
>> Xiaodong
>>
>>
>> On Mon, Aug 19, 2024 at 4:15 AM Stefano Zampini <
>> stefano.zampini at gmail.com> wrote:
>>
>>> It seems you are using DMPLEX to handle the mesh, correct?
>>> If so, you should configure using --download-parmetis to have a better
>>> domain decomposition since the default one just splits the cells in chunks
>>> as they are ordered.
>>> This results in a large number of primal dofs on average (191, from the
>>> output of ksp_view)
>>> ...
>>> Primal dofs : 176 204 191
>>> ...
>>> that slows down the solver setup.
>>>
>>> Again, you should not use approximate local solvers with BDDC unless you
>>> know what you are doing.
>>> The theory for approximate solvers for BDDC is small and only for SPD
>>> problems.
>>> Looking at the output of log_view, coarse problem setup (PCBDDCCSet),
>>> and primal functions setup (PCBDDCCorr) costs 35 + 63 seconds, respectively.
>>> Also, the 500 application of the GAMG preconditioner for the Neumann
>>> solver (PCBDDCNeuS) takes 129 seconds out of the 400 seconds of the total
>>> solve time.
>>>
>>> PCBDDCTopo 1 1.0 3.1563e-01 1.0 1.11e+06 3.4 1.6e+03 3.9e+04
>>> 3.8e+01 0 0 1 0 2 0 0 1 0 2 19
>>> PCBDDCLKSP 2 1.0 2.0423e+00 1.7 9.31e+08 1.2 0.0e+00 0.0e+00
>>> 2.0e+00 0 0 0 0 0 0 0 0 0 0 3378
>>> PCBDDCLWor 1 1.0 3.9178e-02 13.4 0.00e+00 0.0 0.0e+00
>>> 0.0e+00 1.0e+00 0 0 0 0 0 0 0 0 0 0 0
>>> PCBDDCCorr 1 1.0 6.3981e+01 2.2 8.16e+10 1.6 0.0e+00 0.0e+00
>>> 0.0e+00 11 11 0 0 0 11 11 0 0 0 8900
>>> PCBDDCCSet 1 1.0 3.5453e+01 4564.9 1.06e+05 1.7 1.2e+03
>>> 5.3e+03 5.0e+01 2 0 1 0 3 2 0 1 0 3 0
>>> PCBDDCCKSP 1 1.0 6.3266e-01 1.3 0.00e+00 0.0 3.3e+02 1.1e+02
>>> 2.2e+01 0 0 0 0 1 0 0 0 0 1 0
>>> PCBDDCScal 1 1.0 6.8274e-03 1.3 1.11e+06 3.4 5.6e+01 3.2e+05
>>> 0.0e+00 0 0 0 0 0 0 0 0 0 0 894
>>> PCBDDCDirS 1000 1.0 6.0420e+00 3.5 6.64e+09 5.4 0.0e+00 0.0e+00
>>> 0.0e+00 1 0 0 0 0 1 0 0 0 0 2995
>>> PCBDDCNeuS 500 1.0 1.2901e+02 2.1 8.28e+10 1.2 0.0e+00 0.0e+00
>>> 0.0e+00 22 12 0 0 0 22 12 0 0 0 4828
>>> PCBDDCCoaS 500 1.0 5.8757e-01 1.8 1.09e+09 1.0 2.8e+04 7.4e+02
>>> 5.0e+02 0 0 17 0 28 0 0 17 0 31 14901
>>>
>>> Finally, if I look at the residual history, I see a sharp decrease and a
>>> very long plateau. This indicates a bad coarse space; as I said before,
>>> there's no hope of finding a suitable coarse space without first changing
>>> the basis of the Nedelec elements, which is done automatically if you
>>> prescribe the discrete gradient operator (see the paper I have linked to in
>>> my previous communication).
>>>
>>>
>>>
>>> Il giorno dom 18 ago 2024 alle ore 00:37 neil liu <liufield at gmail.com>
>>> ha scritto:
>>>
>>>> Hi, Stefano,
>>>> Please see the attached for the information with 4 and 8 CPUs for the
>>>> complex matrix.
>>>> I am solving Maxwell equations (Attahced) using 2nd-order Nedelec
>>>> elements (two dofs each edge, and two dofs each face).
>>>> The computational domain consists of different mediums, e.g.,
>>>> vacuum and substrate (different permitivity).
>>>> The PML is used to truncate the computational domain, absorbing the
>>>> outgoing wave and introducing complex numbers for the matrix.
>>>>
>>>> Thanks a lot for your suggestions. I will try MUMPS.
>>>> For now, I just want to fiddle with Petsc's built-in features to know
>>>> more about it.
>>>> Yes. 5000 is larger. Smaller value. e.g., 30, converges very slowly.
>>>>
>>>> Thanks a lot.
>>>>
>>>> Have a good weekend.
>>>>
>>>>
>>>> On Sat, Aug 17, 2024 at 9:23 AM Stefano Zampini <
>>>> stefano.zampini at gmail.com> wrote:
>>>>
>>>>> Please include the output of -log_view -ksp_view -ksp_monitor to
>>>>> understand what's happening.
>>>>>
>>>>> Can you please share the equations you are solving so we can provide
>>>>> suggestions on the solver configuration?
>>>>> As I said, solving for Nedelec-type discretizations is challenging,
>>>>> and not for off-the-shelf, black box solvers
>>>>>
>>>>> Below are some comments:
>>>>>
>>>>>
>>>>> - You use a redundant SVD approach for the coarse solve, which can
>>>>> be inefficient if your coarse space grows. You can use a parallel direct
>>>>> solver like MUMPS (reconfigure with --download-mumps and use
>>>>> -pc_bddc_coarse_pc_type lu -pc_bddc_coarse_pc_factor_mat_solver_type mumps)
>>>>> - Why use ILU for the Dirichlet problem and GAMG for the Neumann
>>>>> problem? With 8 processes and 300K total dofs, you will have around 40K
>>>>> dofs per process, which is ok for a direct solver like MUMPS
>>>>> (-pc_bddc_dirichlet_pc_factor_mat_solver_type mumps, same for Neumann).
>>>>> With Nedelec dofs and the sparsity pattern they induce, I believe you can
>>>>> push to 80K dofs per process with good performance.
>>>>> - Why 5000 of restart for GMRES? It is highly inefficient to
>>>>> re-orthogonalize such a large set of vectors.
>>>>>
>>>>>
>>>>> Il giorno ven 16 ago 2024 alle ore 00:04 neil liu <liufield at gmail.com>
>>>>> ha scritto:
>>>>>
>>>>>> Dear Petsc developers,
>>>>>>
>>>>>> Thanks for your previous help. Now, the PCBDDC can converge to 1e-8
>>>>>> with,
>>>>>>
>>>>>> petsc-3.21.1/petsc/arch-linux-c-opt/bin/mpirun -n 8 ./app -pc_type
>>>>>> bddc -pc_bddc_coarse_redundant_pc_type svd -ksp_error_if_not_converged
>>>>>> -mat_type is -ksp_monitor -ksp_rtol 1e-8 -ksp_gmres_restart 5000 -ksp_view
>>>>>> -pc_bddc_use_local_mat_graph 0 -pc_bddc_dirichlet_pc_type ilu
>>>>>> -pc_bddc_neumann_pc_type gamg -pc_bddc_neumann_pc_gamg_esteig_ksp_max_it 10
>>>>>> -ksp_converged_reason -pc_bddc_neumann_approximate -ksp_max_it 500 -log_view
>>>>>>
>>>>>> Then I used 2 cases for strong scaling test. One case only involves
>>>>>> real numbers (tetra #: 49,152; dof #: 324, 224 ) for matrix and rhs. The
>>>>>> 2nd case involves complex numbers (tetra #: 95,336; dof #: 611,432) due
>>>>>> to PML.
>>>>>>
>>>>>> Case 1:
>>>>>> cpu # Time for 500 ksp steps (s) Parallel
>>>>>> efficiency PCsetup time(s)
>>>>>> 2 234.7
>>>>>> 3.12
>>>>>> 4 126.6
>>>>>> 0.92 1.62
>>>>>> 8 84.97
>>>>>> 0.69 1.26
>>>>>> However for Case 2,
>>>>>> cpu # Time for 500 ksp steps (s) Parallel
>>>>>> efficiency PCsetup time(s)
>>>>>> 2 584.5
>>>>>> 8.61
>>>>>> 4 376.8
>>>>>> 0.77 6.56
>>>>>> 8 459.6
>>>>>> 0.31 66.47
>>>>>> For these 2 cases, I checked the time for PCsetup as an example. It
>>>>>> seems 8 cpus for case 2 used too much time on PCsetup.
>>>>>> Do you have any ideas about what is going on here?
>>>>>>
>>>>>> Thanks,
>>>>>> Xiaodong
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>> --
>>>>> Stefano
>>>>>
>>>>
>>>
>>> --
>>> Stefano
>>>
>>
>
> --
> 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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